Bibliography

What the program answers to

Two lists. First the observables: every external measurement, bound and forecast the program will be judged against, grouped by the quantity that has to come out right. Then the literature WHD builds on, argues with, and has to survive. Each entry says where it stands to the program, and why.

Observables

Every way the program can fail, and the measurements each one will be judged against. None of these has been evaluated on a complete run of the model yet: every run so far has been a diagnostic run of a reduced configuration. Each source carries the same stance labels as the literature; a measurement that neither confirms nor refutes the model's number yet is context.

  • prediction a number the model fixes, with no free parameter left
  • derived a result on paper with no free parameter, still to be confirmed by a complete run
  • input a measurement used to set the model’s units — not a prediction
  • constraint something the model must satisfy
  • candidate only a prediction of the string completion, not of the core theory
  • not yet a claim a computation the program has not yet accepted as a claim

The dark-energy density prediction

  • The claim. Once two measured constants — the Hubble constant and Newton’s constant — are used to set the model’s units, the dark-energy density is fixed. Nothing is left to adjust.
  • Ruled out if. The predicted density does not match the measured one.
  • Waiting on. A complete run of the model. Every run so far has been a diagnostic run of a reduced configuration, so the number has not been evaluated yet.
A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s⁻¹ Mpc⁻¹ Uncertainty from the Hubble Space Telescope and the SH0ES Team (2022) measurement context strong

Riess, Adam G. and others · 2022

Result. H₀ = 73.04 ± 1.04 km/s/Mpc from the Cepheid–supernova distance ladder with the Hubble Space Telescope — a 5σ difference from the value Planck + ΛCDM predicts (67.4 ± 0.5).

The local measurement of the Hubble constant: H₀ = 73.04 ± 1.04 km/s/Mpc from the Cepheid-calibrated supernova distance ladder, with the uncertainty brought to one km/s/Mpc. It differs from the Planck + ΛCDM value by 5σ — the “Hubble tension”.

Connection to WHD. The program uses the Hubble constant as an input, not a prediction: it decides which moment of the simulation is today. Both candidate values are carried — 67.4 from Planck and 73.0 from this measurement — and the prediction for the dark-energy density inherits whichever is used. WHD does not claim to explain the tension. The spread between the two is an uncertainty on the input, and the honest statement is that the model’s dark-energy density must come out right for the Hubble constant it is handed; it has one shot per choice and no parameter to absorb the difference. Filed as context for that reason.

Source ↗
@article{riess2022sh0es,
  author  = {Riess, Adam G. and others},
  title   = {A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s$^{-1}$ Mpc$^{-1}$ Uncertainty from the Hubble Space Telescope and the SH0ES Team},
  journal = {The Astrophysical Journal Letters},
  volume  = {934},
  number  = {1},
  pages   = {L7},
  year    = {2022},
  eprint  = {2112.04510},
  archivePrefix = {arXiv},
  doi     = {10.3847/2041-8213/ac5c5b}
}
Planck 2018 results. VI. Cosmological parameters (2020) measurement context strong

Planck Collaboration and Aghanim, N. and others · 2020

Result. Planck 2018 base-ΛCDM parameters: H₀ = 67.4 ± 0.5 km/s/Mpc; Ω_m = 0.315 ± 0.007; dark-matter density Ω_c h² = 0.120 ± 0.001 and baryon density Ω_b h² = 0.0224 ± 0.0001 (a dark-to-ordinary ratio of about 5.4); N_eff = 2.99 ± 0.17 with BAO; Σm_ν < 0.12 eV (95% CL).

The current best measurement of the effective number of relativistic species in the early universe, N_eff = 2.99 ± 0.17 — consistent with the Standard Model’s three neutrino species and no additional light relic, but with enough remaining uncertainty (ΔN_eff ≲ 0.3 at current precision) to leave room for a small extra contribution.

Connection to WHD. This is the external dataset the UV completion candidate’s one sharp, near-term prediction has to answer to: a small, positive excess ΔN_eff from vents leaking preferentially into the program’s forced hidden sector. Filed as context rather than supports or threatens because the current measurement neither confirms nor rules out WHD’s predicted small excess yet — it only excludes the large, “democratic” leak a symmetric mechanism would predict, which WHD already doesn’t predict. This entry should be revisited (and likely reclassified) once the one owed number — the vent’s hidden-vs-visible branching ratio — is computed, and again once CMB-S4-class data (roughly ten times more precise) is available.

Three more of the program’s tests run through this paper. Its Hubble constant, 67.4 ± 0.5 km/s/Mpc, is one of the two values used to set the model’s clock (the other is the local measurement, riess2022sh0es); with Newton’s constant it fixes the units for the prediction of the dark-energy density, which then has no freedom left. Its densities Ω_c h² = 0.120 and Ω_b h² = 0.0224 give the observed ratio of dark to ordinary matter, about 5.4, which a valid census of vents must reproduce with no adjustable parameter. None of these has been evaluated on a complete run of the model yet; this entry is the measurement they will be judged against.

Source ↗
@article{planck2020params,
  author  = {{Planck Collaboration} and Aghanim, N. and others},
  title   = {Planck 2018 results. VI. Cosmological parameters},
  journal = {Astronomy \& Astrophysics},
  volume  = {641},
  pages   = {A6},
  year    = {2020},
  eprint  = {1807.06209},
  archivePrefix = {arXiv},
  doi     = {10.1051/0004-6361/201833910}
}

How dark energy changes with time — and the same drift read as a changing Newton’s constant derived

  • The claim. On the brane, Newton’s constant is set by the wall’s effective tension. As the loaded wall sheds its stored energy back into the bulk, that tension drifts, and the drift shows up twice: as a slow change in the dark-energy equation of state w(z), and as a slow change in Newton’s constant, Ġ/G. The rate of shedding is derived — its exponent is 3/2 — and it decides how much dark energy is left over.
  • Ruled out if. The w(z) shape from galaxy surveys and the Ġ/G bound from lunar ranging disagree, or the shedding exponent measured in a complete run leaves its band around 3/2.
  • Waiting on. A complete run. Diagnostic runs so far give 1.46 ± 0.17 for the exponent — consistent with 3/2, but not yet on a run that counts. The surveys below are the comparison.
The Pantheon+ Analysis: Cosmological Constraints (2022) measurement context strong

Brout, Dillon and others · 2022

Result. 1701 light curves of 1550 Type Ia supernovae over z = 0.001–2.26. Ω_M = 0.334 ± 0.018 from supernovae alone (flat ΛCDM); w = −0.90 ± 0.14 from Pantheon+ alone and w = −0.978 (+0.024 / −0.031) with the CMB and BAO — consistent with a cosmological constant.

The Pantheon+ compilation: 1701 light curves of 1550 spectroscopically confirmed Type Ia supernovae from z = 0.001 to 2.26, the supernova leg of most current dark-energy fits. On their own the supernovae give Ω_M = 0.334 ± 0.018 in a flat ΛCDM universe and a constant equation of state w = −0.90 ± 0.14; with the CMB and BAO the equation of state tightens to w = −0.978 (+0.024 / −0.031). Both are consistent with a cosmological constant.

Connection to WHD. Supernovae fix the low-redshift end of the range in which WHD’s w(z) drift is read, and they are the dataset DESI’s evolving-dark-energy significance depends on — 2.5σ with this sample, higher with Union3 and DES-SN5YR (desi2024bao). The program’s own number is not on the table yet, so this is filed as context: the measurement WHD’s drift has to pass through at redshifts below about one, not a verdict. When the run exists the comparison is made against the combined BAO, supernova and CMB fit, not against supernovae alone.

Source ↗
@article{brout2022pantheonplus,
  author  = {Brout, Dillon and others},
  title   = {The Pantheon+ Analysis: Cosmological Constraints},
  journal = {The Astrophysical Journal},
  volume  = {938},
  number  = {2},
  pages   = {110},
  year    = {2022},
  eprint  = {2202.04077},
  archivePrefix = {arXiv},
  doi     = {10.3847/1538-4357/ac8e04}
}
Accelerating universes with scaling dark matter (2001) method context moderate

Chevallier, Michel and Polarski, David · 2001

Result. Introduces the equation of state linear in the scale factor, later written w(a) = w₀ + wₐ(1 − a): the two-parameter form in which surveys report an evolving dark energy.

The paper that introduced the equation of state linear in the scale factor, now written w(a) = w₀ + wₐ(1 − a) and known — with Linder’s 2003 paper — as the CPL parametrization. It is the two-number language every dark-energy survey reports in: w₀ is the equation of state today, wₐ its slope back in time, and (−1, 0) is a cosmological constant.

Connection to WHD. The program does not predict two numbers; it predicts a function — the drift of w(z) set by the wall’s shedding exponent. To compare it with survey results the function has to be projected onto (w₀, wₐ). WHD’s pipeline does that by least squares with uniform weight in the scale factor over redshifts from 0.05 to 2, and carries a caveat of its own: a real survey fit weights redshifts by their information content, so the uniform projection is a stated convention until a data-weighted one replaces it. The residual between WHD’s w(z) and its best two-parameter fit is itself a future test — a drift that is not of this form would show up as exactly that.

Source ↗
@article{chevallierpolarski2001,
  author  = {Chevallier, Michel and Polarski, David},
  title   = {Accelerating universes with scaling dark matter},
  journal = {International Journal of Modern Physics D},
  volume  = {10},
  pages   = {213--224},
  year    = {2001},
  eprint  = {gr-qc/0009008},
  archivePrefix = {arXiv},
  doi     = {10.1142/S0218271801000822}
}
DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations (2025) measurement context strong

DESI Collaboration and Adame, A. G. and others · 2025

Result. First-year DESI BAO in seven redshift bins from more than 6 million objects over 0.1 < z < 4.2. Ω_m = 0.295 ± 0.015 from BAO alone; H₀ = 68.52 ± 0.62 km/s/Mpc with a BBN prior and the CMB acoustic scale. The w₀wₐ model is preferred over ΛCDM at 2.6σ (DESI + CMB) and at 2.5σ / 3.5σ / 3.9σ with the Pantheon+ / Union3 / DES-SN5YR supernova samples, favouring w₀ > −1 and wₐ < 0.

The first cosmological results from DESI’s first year of data: baryon acoustic oscillations measured in seven redshift bins from more than 6 million galaxies, quasars and Lyman-α forest spectra over 0.1 < z < 4.2. On their own the BAO give Ω_m = 0.295 ± 0.015; with a nucleosynthesis prior and the CMB acoustic scale they give H₀ = 68.52 ± 0.62 km/s/Mpc. Combined with the CMB and supernovae the data prefer a dark-energy equation of state that evolves — w₀ > −1 today, wₐ < 0 — over a cosmological constant, at 2.5σ to 3.9σ depending on which supernova sample is used.

Connection to WHD. The first of the two DESI results the program’s dark-energy prediction will be read against, over the redshifts between about 0.3 and 2 where the drift is expected to show. The direction the data favours — w₀ > −1, wₐ < 0 — is the shape a complete run of the model must either reproduce or contradict; it is recorded here without a verdict, because no such run has produced WHD’s own w(z) yet. Superseded in precision by the second data release (desi2025dr2bao); kept because the sample-by-sample breakdown shows how much the conclusion leans on the supernova anchor at low redshift.

Source ↗
@article{desi2024bao,
  author  = {{DESI Collaboration} and Adame, A. G. and others},
  title   = {DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations},
  journal = {Journal of Cosmology and Astroparticle Physics},
  volume  = {02},
  pages   = {021},
  year    = {2025},
  eprint  = {2404.03002},
  archivePrefix = {arXiv},
  doi     = {10.1088/1475-7516/2025/02/021}
}
DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints (2025) measurement context strong

DESI Collaboration and Abdul Karim, M. and others · 2025

Result. Baryon acoustic oscillations from more than 14 million galaxies and quasars (DESI DR2). ΛCDM sits in a mild 2.3σ tension with the CMB; an evolving dark-energy equation of state (the w₀wₐ form) is preferred over a cosmological constant at 3.1σ with DESI BAO + CMB, and at 2.8–4.2σ once supernovae are added, depending on the supernova sample.

The second data release of the Dark Energy Spectroscopic Instrument: baryon acoustic oscillation distances from more than 14 million galaxies and quasars, the largest such measurement made. The BAO scale agrees with the acoustic angular scale Planck measures, but the ΛCDM parameters it prefers sit in a mild 2.3σ tension with the CMB, and a dark-energy density allowed to change with time — the w₀wₐ parametrization — is preferred over a constant one at 3.1σ with the CMB alone and at 2.8–4.2σ with supernovae. It is the sharpest indication so far that dark energy may not be a constant.

Connection to WHD. The drift of w(z) is the program’s external test of how fast the loaded wall sheds its stored energy back into the bulk. The shedding exponent is derived to be 3/2, and the same drift appears as a slow change in Newton’s constant. A complete run of the model produces a w(z) shape with nothing left to adjust, and this is the dataset it is compared with. Filed as context rather than supports because WHD’s own w(z) has not yet been computed on a run that counts; a hint of evolving dark energy is not evidence for or against the program until it has. A run whose drift disagrees with DESI-class w(z), or whose exponent leaves its band around 3/2, rules the mechanism out.

Source ↗
@article{desi2025dr2bao,
  author  = {{DESI Collaboration} and Abdul Karim, M. and others},
  title   = {DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints},
  journal = {Physical Review D},
  volume  = {112},
  number  = {8},
  pages   = {083515},
  year    = {2025},
  eprint  = {2503.14738},
  archivePrefix = {arXiv},
  doi     = {10.1103/tr6y-kpc6}
}
Euclid. I. Overview of the Euclid mission (2025) forecast context moderate

Euclid Collaboration and Mellier, Y. and others · 2025

Result. ESA's Euclid mission: a wide survey of about 14 000 deg² of extragalactic sky in visible and near-infrared imaging and spectroscopy, designed to measure the expansion history and the growth of structure — the w(z) dataset after DESI.

The overview paper of ESA’s Euclid mission: a space telescope surveying about 14 000 square degrees of extragalactic sky with visible imaging and near-infrared imaging and spectroscopy, built to measure the geometry of the universe and the growth of its structure through weak lensing and galaxy clustering, and so to constrain the dark-energy equation of state and its evolution.

Connection to WHD. The survey after DESI. The program’s w(z) drift is a single derived function with a fixed exponent behind it, and a survey that maps the expansion history over a wider redshift range with independent systematics is where an agreement with DESI would be confirmed or a tension resolved. Filed as context and as a forecast: no WHD number exists yet to compare, and Euclid’s cosmology results are still to come.

Source ↗
@article{euclid2025overview,
  author  = {{Euclid Collaboration} and Mellier, Y. and others},
  title   = {Euclid. I. Overview of the Euclid mission},
  journal = {Astronomy \& Astrophysics},
  volume  = {697},
  pages   = {A1},
  year    = {2025},
  eprint  = {2405.13491},
  archivePrefix = {arXiv},
  doi     = {10.1051/0004-6361/202450810}
}
Relativistic tests with lunar laser ranging (2018) bound context strong

Hofmann, F. and Müller, J. · 2018

Result. Lunar laser ranging 1970–January 2015: Ġ/G = (7.1 ± 7.6) × 10⁻¹⁴ yr⁻¹; Nordtvedt parameter η = (−0.2 ± 1.1) × 10⁻⁴; β − 1 = (−4.5 ± 5.6) × 10⁻⁵, γ − 1 = (−1.2 ± 1.2) × 10⁻⁴; geodetic precession confirmed within 0.09%. No deviation from general relativity.

The tightest lunar-laser-ranging analysis: forty-five years of data (1970 to January 2015) give a drift of Newton’s constant of Ġ/G = (7.1 ± 7.6) × 10⁻¹⁴ per year — an order of magnitude below the 2004 bound — with the equivalence principle, the post-Newtonian parameters β and γ, and the geodetic precession all within their general-relativistic values.

Connection to WHD. The current ceiling on the Ġ/G side of the twin measurement. A complete run of the model reports the drift of the wall’s tension, and it has to fit under this bound — about one part in 10¹³ per year — while the same drift, read as w(z), matches the survey data. Filed as context until the run exists.

Source ↗
@article{hofmannmuller2018llr,
  author  = {Hofmann, F. and M{\"u}ller, J.},
  title   = {Relativistic tests with lunar laser ranging},
  journal = {Classical and Quantum Gravity},
  volume  = {35},
  number  = {3},
  pages   = {035015},
  year    = {2018},
  doi     = {10.1088/1361-6382/aa8f7a}
}
Exploring the expansion history of the universe (2003) method context moderate

Linder, Eric V. · 2003

Result. Shows that w(a) = w₀ + wₐ(1 − a) tracks the expansion history of scalar-field dark-energy models to high accuracy, and argues for the slope of the equation of state as the observable — the second parent of the CPL convention.

The second parent of the CPL convention. Linder shows that the two-parameter form w(a) = w₀ + wₐ(1 − a) reproduces the expansion history of a wide class of scalar-field dark-energy models to high accuracy over the redshifts surveys can reach, and argues that the slope of the equation of state — how w changes with the logarithm of the scale factor — is the quantity that separates a cosmological constant from a dynamical field.

Connection to WHD. The wall’s stored energy drains at a rate the derivation fixes, and an observer on the brane reads that drain as a changing w. Linder’s argument is why the slope, not the value, is where the program’s signature sits: a constant w = −1 is the one thing the mechanism cannot produce while the wall is still shedding energy. The two-parameter form is used here as an interpreter between WHD’s function and the surveys’ two numbers, not as a model of the physics.

Source ↗
@article{linder2003,
  author  = {Linder, Eric V.},
  title   = {Exploring the expansion history of the universe},
  journal = {Physical Review Letters},
  volume  = {90},
  pages   = {091301},
  year    = {2003},
  eprint  = {astro-ph/0208512},
  archivePrefix = {arXiv},
  doi     = {10.1103/PhysRevLett.90.091301}
}
Progress in lunar laser ranging tests of relativistic gravity (2004) bound context strong

Williams, James G. and Turyshev, Slava G. and Boggs, Dale H. · 2004

Result. Lunar laser ranging: Ġ/G = (4 ± 9) × 10⁻¹³ yr⁻¹; equivalence-principle test Δ(M_G/M_I) = (−1.0 ± 1.4) × 10⁻¹³; geodetic precession within 0.6% of general relativity.

Thirty-five years of laser ranging to the retroreflectors on the Moon, turned into tests of gravity: no drift of Newton’s constant, Ġ/G = (4 ± 9) × 10⁻¹³ per year; the equivalence principle holding to Δ(M_G/M_I) = (−1.0 ± 1.4) × 10⁻¹³; the geodetic precession of the lunar orbit within 0.6% of general relativity.

Connection to WHD. On the brane, Newton’s constant is set by the wall’s effective tension, so any drift in that tension appears directly as a drift in G. It is the same drift the program reads elsewhere as the change of w(z) with time — one physical quantity with two readouts. A complete run of the model therefore has to satisfy both at once: its Ġ/G inside the lunar-ranging band, its w(z) matching the surveys. If the two readouts disagree the mechanism is wrong, whatever each fit says on its own. This is the classic bound; the tighter one is hofmannmuller2018llr.

Source ↗
@article{williams2004llr,
  author  = {Williams, James G. and Turyshev, Slava G. and Boggs, Dale H.},
  title   = {Progress in lunar laser ranging tests of relativistic gravity},
  journal = {Physical Review Letters},
  volume  = {93},
  pages   = {261101},
  year    = {2004},
  eprint  = {gr-qc/0411113},
  archivePrefix = {arXiv},
  doi     = {10.1103/PhysRevLett.93.261101}
}

The ratio of dark to ordinary matter derived

  • The claim. Vents are small black holes that evaporate into the bulk rather than into our three dimensions, so a vent lives for a time proportional to the square of its mass. Given the population of vents a birth run produces, the split between what survives as remnants and what evaporates fixes the ratio of dark to ordinary matter, with no adjustable parameter.
  • Ruled out if. A valid census of vents cannot reproduce the observed ratio of about 5.4.
  • Waiting on. A valid census of vents. None exists yet: the vents seen in earlier low-resolution runs were an artefact of the resolution and were withdrawn.
Planck 2018 results. VI. Cosmological parameters (2020) measurement context strong

Planck Collaboration and Aghanim, N. and others · 2020

Result. Planck 2018 base-ΛCDM parameters: H₀ = 67.4 ± 0.5 km/s/Mpc; Ω_m = 0.315 ± 0.007; dark-matter density Ω_c h² = 0.120 ± 0.001 and baryon density Ω_b h² = 0.0224 ± 0.0001 (a dark-to-ordinary ratio of about 5.4); N_eff = 2.99 ± 0.17 with BAO; Σm_ν < 0.12 eV (95% CL).

The current best measurement of the effective number of relativistic species in the early universe, N_eff = 2.99 ± 0.17 — consistent with the Standard Model’s three neutrino species and no additional light relic, but with enough remaining uncertainty (ΔN_eff ≲ 0.3 at current precision) to leave room for a small extra contribution.

Connection to WHD. This is the external dataset the UV completion candidate’s one sharp, near-term prediction has to answer to: a small, positive excess ΔN_eff from vents leaking preferentially into the program’s forced hidden sector. Filed as context rather than supports or threatens because the current measurement neither confirms nor rules out WHD’s predicted small excess yet — it only excludes the large, “democratic” leak a symmetric mechanism would predict, which WHD already doesn’t predict. This entry should be revisited (and likely reclassified) once the one owed number — the vent’s hidden-vs-visible branching ratio — is computed, and again once CMB-S4-class data (roughly ten times more precise) is available.

Three more of the program’s tests run through this paper. Its Hubble constant, 67.4 ± 0.5 km/s/Mpc, is one of the two values used to set the model’s clock (the other is the local measurement, riess2022sh0es); with Newton’s constant it fixes the units for the prediction of the dark-energy density, which then has no freedom left. Its densities Ω_c h² = 0.120 and Ω_b h² = 0.0224 give the observed ratio of dark to ordinary matter, about 5.4, which a valid census of vents must reproduce with no adjustable parameter. None of these has been evaluated on a complete run of the model yet; this entry is the measurement they will be judged against.

Source ↗
@article{planck2020params,
  author  = {{Planck Collaboration} and Aghanim, N. and others},
  title   = {Planck 2018 results. VI. Cosmological parameters},
  journal = {Astronomy \& Astrophysics},
  volume  = {641},
  pages   = {A6},
  year    = {2020},
  eprint  = {1807.06209},
  archivePrefix = {arXiv},
  doi     = {10.1051/0004-6361/201833910}
}

Dark radiation — a small excess in the number of light species candidate only

  • The claim. The string completion of the program forces a second, hidden sector to exist off our wall. Because vents deposit their energy toward the brane, any leak into that hidden sector heats it less than it heats us. The prediction is a small, positive excess in the effective number of relativistic species, N_eff — never the excess of about one that a symmetric leak would give, which is already excluded.
  • Ruled out if. A measured excess near one, or a computed excess that the next generation of microwave-background surveys then excludes.
  • Waiting on. One number: the fraction of a vent’s output that goes into the hidden sector. Until it is computed the prediction is a sign and a ceiling, not a size.
The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models (2025) measurement context strong

Atacama Cosmology Telescope Collaboration and Calabrese, Erminia and others · 2025

Result. ACT DR6 extended-model constraints: N_eff = 2.86 ± 0.13 from ACT DR6, and 2.89 ± 0.11 combined with big-bang nucleosynthesis; Σm_ν < 0.082 eV (95% CL); self-interacting dark radiation N_idr < 0.134; running dn_s/d ln k = 0.0062 ± 0.0052; no statistically significant departure from ΛCDM.

The Atacama Cosmology Telescope’s sixth data release, tested against models beyond ΛCDM: the effective number of relativistic species comes out at N_eff = 2.86 ± 0.13 (2.89 ± 0.11 with nucleosynthesis data), the sum of neutrino masses below 0.082 eV, self-interacting dark radiation limited to N_idr < 0.134, no neutrino self-interactions, and no statistically significant preference for any departure from the baseline model.

Connection to WHD. The most recent measurement of the number the string completion’s one sharp prediction lives in. With the Standard Model at N_eff = 3.044 and ACT’s central value slightly below it, the room left for a positive excess is now roughly 0.2 to 0.3 at two standard deviations — far below the excess of about one that is already excluded, and a tighter box than Planck’s for the still-to-be-computed size to land in. The limit on self-interacting dark radiation is a separate bound the hidden sector must respect, since its only connection to us is gravitational. Filed as context: the prediction is a sign and a ceiling until the size is computed.

Source ↗
@article{act2025dr6extended,
  author  = {{Atacama Cosmology Telescope Collaboration} and Calabrese, Erminia and others},
  title   = {The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models},
  journal = {Journal of Cosmology and Astroparticle Physics},
  volume  = {11},
  pages   = {063},
  year    = {2025},
  eprint  = {2503.14454},
  archivePrefix = {arXiv},
  doi     = {10.1088/1475-7516/2025/11/063}
}
CMB-S4 Science Case, Reference Design, and Project Plan (2019) forecast context moderate

CMB-S4 Collaboration and Abazajian, Kevork and others · 2019

Result. The CMB-S4 reference design and project plan: the conceptual design reaches σ(N_eff) < 0.03 over the seven-year survey — several times tighter than Planck's ±0.17 — alongside the primordial-B-mode and neutrino-mass targets.

The reference design and project plan for CMB-S4: the survey strategy, instrument configuration and schedule that turn the 2016 science case into numbers. For light relics the conceptual design reaches σ(N_eff) < 0.03 over the seven-year survey, against Planck’s ±0.17 today — precise enough that any light particle that was ever in thermal equilibrium with the Standard Model leaves a detectable trace in N_eff.

Connection to WHD. This is the precision that makes the dark-radiation prediction decidable. Today the prediction is a sign and a ceiling: a small positive excess, bounded by Planck’s N_eff = 2.99 ± 0.17 (room for about 0.3 or less), with its size still to be computed from the fraction of a vent’s output that goes into the hidden sector. At σ(N_eff) < 0.03 that computed size becomes a target the survey either finds or excludes; a computed excess that CMB-S4 then excludes rules the string completion out. Filed as context because it is a forecast, not a measurement; it will move once the fraction is computed and again once CMB-S4 reports.

Source ↗
@misc{cmbs4referencedesign2019,
  author  = {{CMB-S4 Collaboration} and Abazajian, Kevork and others},
  title   = {CMB-S4 Science Case, Reference Design, and Project Plan},
  year    = {2019},
  eprint  = {1907.04473},
  archivePrefix = {arXiv},
  primaryClass = {astro-ph.IM},
  note    = {FERMILAB-PUB-19-431-AE-SCD}
}
CMB-S4 Science Book, First Edition (2016) forecast context moderate

CMB-S4 Collaboration and Abazajian, Kevork N. and others · 2016

Result. The science case for the Stage-4 ground-based CMB program: primordial B-mode polarization, the number and masses of the neutrinos, new light relics beyond the Standard Model (N_eff), dark energy, and tests of general relativity on cosmological scales.

The first edition of the science case for CMB-S4, the Stage-4 ground-based cosmic microwave background experiment: a search for the B-mode signature of primordial gravitational waves, a determination of the number and masses of the neutrinos, a search for light relics beyond the Standard Model through the effective number of relativistic species, and constraints on dark energy and on gravity at cosmological scales.

Connection to WHD. The effective number of light species is the one sharp observational handle on the hidden sector the string completion forces into existence. Vents deposit their energy toward the brane, so a leak into that sector heats it less than it heats us, and the prediction is a small, positive excess — never the excess of about one a symmetric leak would give, which Planck already excludes. This is where N_eff enters the next generation’s design as a primary target; the precision the program relies on, σ(N_eff) < 0.03, is in the 2019 reference design (cmbs4referencedesign2019). Filed as context: a forecast the prediction will be judged by, once the one missing number — the fraction of a vent’s output that goes into the hidden sector — turns the sign into a size.

Source ↗
@book{cmbs4sciencebook2016,
  author  = {{CMB-S4 Collaboration} and Abazajian, Kevork N. and others},
  title   = {CMB-S4 Science Book, First Edition},
  year    = {2016},
  eprint  = {1610.02743},
  archivePrefix = {arXiv},
  primaryClass = {astro-ph.CO},
  doi     = {10.2172/1352047}
}
Big-Bang Nucleosynthesis after Planck (2020) measurement context strong

Fields, Brian D. and Olive, Keith A. and Yeh, Tsung-Han and Young, Charles · 2020

Result. Big-bang nucleosynthesis with Planck's baryon density as input: the deuterium abundance is now measured more precisely than it is predicted, the lithium problem persists, and the effective number of neutrino species at the epoch of nucleosynthesis is N_ν = 2.86 ± 0.15.

Standard big-bang nucleosynthesis re-evaluated with the Planck baryon density: the predicted light-element abundances against the observed ones (deuterium is now measured more precisely than theory predicts it; the lithium discrepancy remains), and an independent early-time determination of the number of relativistic species, N_ν = 2.86 ± 0.15 at the epoch of nucleosynthesis — a few minutes into the hot phase, long before the CMB.

Connection to WHD. Two constraints in one. The light-element abundances must come out as observed: reheating vent by vent has to deliver an ordinary hot big bang whose nuclear history matches, and the census of vents will decide whether it does. And the number of light species at nucleosynthesis is a second, earlier bound on dark radiation, complementary to the microwave background: the small positive excess the string completion predicts has to be present already at this epoch and consistent with both readings. Filed as context until the census and the size of the excess exist.

Source ↗
@article{fields2020bbn,
  author  = {Fields, Brian D. and Olive, Keith A. and Yeh, Tsung-Han and Young, Charles},
  title   = {Big-Bang Nucleosynthesis after Planck},
  journal = {Journal of Cosmology and Astroparticle Physics},
  volume  = {03},
  pages   = {010},
  year    = {2020},
  eprint  = {1912.01132},
  archivePrefix = {arXiv},
  doi     = {10.1088/1475-7516/2020/03/010},
  note    = {Erratum: JCAP 11, E02 (2020)}
}
Planck 2018 results. VI. Cosmological parameters (2020) measurement context strong

Planck Collaboration and Aghanim, N. and others · 2020

Result. Planck 2018 base-ΛCDM parameters: H₀ = 67.4 ± 0.5 km/s/Mpc; Ω_m = 0.315 ± 0.007; dark-matter density Ω_c h² = 0.120 ± 0.001 and baryon density Ω_b h² = 0.0224 ± 0.0001 (a dark-to-ordinary ratio of about 5.4); N_eff = 2.99 ± 0.17 with BAO; Σm_ν < 0.12 eV (95% CL).

The current best measurement of the effective number of relativistic species in the early universe, N_eff = 2.99 ± 0.17 — consistent with the Standard Model’s three neutrino species and no additional light relic, but with enough remaining uncertainty (ΔN_eff ≲ 0.3 at current precision) to leave room for a small extra contribution.

Connection to WHD. This is the external dataset the UV completion candidate’s one sharp, near-term prediction has to answer to: a small, positive excess ΔN_eff from vents leaking preferentially into the program’s forced hidden sector. Filed as context rather than supports or threatens because the current measurement neither confirms nor rules out WHD’s predicted small excess yet — it only excludes the large, “democratic” leak a symmetric mechanism would predict, which WHD already doesn’t predict. This entry should be revisited (and likely reclassified) once the one owed number — the vent’s hidden-vs-visible branching ratio — is computed, and again once CMB-S4-class data (roughly ten times more precise) is available.

Three more of the program’s tests run through this paper. Its Hubble constant, 67.4 ± 0.5 km/s/Mpc, is one of the two values used to set the model’s clock (the other is the local measurement, riess2022sh0es); with Newton’s constant it fixes the units for the prediction of the dark-energy density, which then has no freedom left. Its densities Ω_c h² = 0.120 and Ω_b h² = 0.0224 give the observed ratio of dark to ordinary matter, about 5.4, which a valid census of vents must reproduce with no adjustable parameter. None of these has been evaluated on a complete run of the model yet; this entry is the measurement they will be judged against.

Source ↗
@article{planck2020params,
  author  = {{Planck Collaboration} and Aghanim, N. and others},
  title   = {Planck 2018 results. VI. Cosmological parameters},
  journal = {Astronomy \& Astrophysics},
  volume  = {641},
  pages   = {A6},
  year    = {2020},
  eprint  = {1807.06209},
  archivePrefix = {arXiv},
  doi     = {10.1051/0004-6361/201833910}
}

The speed of gravitational waves and the mass of the graviton derived

  • The claim. The graviton bound to the wall is not exactly massless: its mass is √2 times today’s Hubble rate — about 2 × 10⁻³³ eV — and it tracks the Hubble rate as the universe expands. Gravitational waves travel at exactly the speed of light.
  • Ruled out if. A confirmed graviton mass different from √2 times the Hubble rate, or gravitational waves that do not travel at the speed of light.
  • Waiting on. Nothing on the program’s side. The derived mass sits ten orders of magnitude below current bounds, so only cosmological tests can reach it.
Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A (2017) measurement supports weak

LIGO Scientific Collaboration and Virgo Collaboration and Fermi-GBM and INTEGRAL and Abbott, B. P. and others · 2017

Result. GRB 170817A arrived (+1.74 ± 0.05) s after the gravitational-wave signal GW170817 from the same binary neutron star merger; the difference between the speed of gravity and the speed of light is constrained to between −3 × 10⁻¹⁵ and +7 × 10⁻¹⁶ times c.

The neutron-star merger seen in both gravitational waves and gamma rays: GRB 170817A followed GW170817 by 1.74 ± 0.05 seconds after a journey of about 130 million years, which pins the speed of gravity to the speed of light to between −3 × 10⁻¹⁵ and +7 × 10⁻¹⁶ of c. Any theory in which gravitational waves travel at a different speed from light over cosmological distances was ruled out that day.

Connection to WHD. The graviton bound to the wall in the brane picture is not quite massless, but it travels at the speed of light to every precision tested — the model has no room for a difference. This is a constraint the program passes by construction rather than a test that singles it out, since general relativity passes it too, which is why it is filed as supports at weak strength: consistent, not decisive. The decisive statement in this group is the graviton mass, √2 times the Hubble rate, and what would rule it out is a confirmed mass different from that (ligo2025gwtc3tgr).

Source ↗
@article{abbott2017gw170817grb,
  author  = {{LIGO Scientific Collaboration and Virgo Collaboration and Fermi-GBM and INTEGRAL} and Abbott, B. P. and others},
  title   = {Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A},
  journal = {The Astrophysical Journal Letters},
  volume  = {848},
  number  = {2},
  pages   = {L13},
  year    = {2017},
  eprint  = {1710.05834},
  archivePrefix = {arXiv},
  doi     = {10.3847/2041-8213/aa920c}
}
Graviton Mass Bounds (2017) bound context moderate

de Rham, Claudia and Deskins, J. Tate and Tolley, Andrew J. and Zhou, Shuang-Yong · 2017

Result. Review of the observational and theoretical bounds on a graviton mass — solar-system and binary-pulsar dynamics, gravitational waves, cosmology and structure formation — and of the consistency conditions massive-gravity theories must meet.

The standard map of how heavy a graviton is allowed to be: the review collects the bounds from planetary orbits and binary pulsars, from gravitational-wave dispersion, from the growth of cosmic structure and the expansion history, and lays out the theoretical constraints — ghosts, strong coupling, the Vainshtein screening — that any consistent theory of a massive graviton has to satisfy.

Connection to WHD. The program’s graviton mass is set by the Hubble rate itself, which puts it in the one corner of this map where the observational bounds are weakest and the theoretical questions are sharpest: a mass of order H₀ is invisible to laboratory and solar-system tests and can only be reached through cosmology. This review is the reference for what a graviton of that mass is and is not allowed to do, and for the consistency conditions the brane’s gravitational sector will be held to when its perturbation theory is written out. Filed as context: it bounds the space the derived value lives in without yet testing the value.

Source ↗
@article{derham2017gravitonmass,
  author  = {de Rham, Claudia and Deskins, J. Tate and Tolley, Andrew J. and Zhou, Shuang-Yong},
  title   = {Graviton Mass Bounds},
  journal = {Reviews of Modern Physics},
  volume  = {89},
  number  = {2},
  pages   = {025004},
  year    = {2017},
  eprint  = {1606.08462},
  archivePrefix = {arXiv},
  doi     = {10.1103/RevModPhys.89.025004}
}
Tests of General Relativity with GWTC-3 (2025) bound context strong

LIGO Scientific Collaboration and Virgo Collaboration and KAGRA Collaboration and Abbott, R. and others · 2025

Result. Tests of general relativity across the GWTC-3 catalog: from gravitational-wave dispersion, a graviton mass m_g ≤ 2.42 × 10⁻²³ eV/c² at 90% credibility; post-Newtonian coefficients, spin-induced quadrupole moments, polarization content, post-merger echoes and ringdown frequencies all consistent with GR.

The LIGO–Virgo–KAGRA battery of general-relativity tests on the third gravitational-wave catalog: waveform residuals consistent with noise, post-Newtonian deformation coefficients at their GR values, Kerr spin-induced quadrupoles, no extra polarizations, no echoes, ringdown frequencies and damping times as predicted, and — from the absence of dispersion in the propagating waves — a graviton mass bound of m_g ≤ 2.42 × 10⁻²³ eV/c² at 90% credibility.

Connection to WHD. The program’s graviton is the wall-bound mode with a mass of √2 times the Hubble rate, tracking the expansion so that it keeps that value in every epoch. Today that is about 2 × 10⁻³³ eV — ten orders of magnitude below this bound, so the bound is a ceiling the derived value clears easily, not a test it is close to failing. What would rule the derivation out is sharper than any bound: a confirmed graviton mass that differs from √2 times the Hubble rate. Filed as context because current data cannot resolve a mass this small in either direction.

Source ↗
@article{ligo2025gwtc3tgr,
  author  = {{LIGO Scientific Collaboration and Virgo Collaboration and KAGRA Collaboration} and Abbott, R. and others},
  title   = {Tests of General Relativity with GWTC-3},
  journal = {Physical Review D},
  volume  = {112},
  number  = {8},
  pages   = {084080},
  year    = {2025},
  eprint  = {2112.06861},
  archivePrefix = {arXiv},
  doi     = {10.1103/PhysRevD.112.084080}
}

The spectrum of evaporating vents derived

  • The claim. Because a vent’s lifetime scales with the square of its mass rather than the cube, the light end of the mass distribution of delivered remnants rises linearly with mass — a four-dimensional population would rise quadratically — and a dying vent brightens as (t_f − t)^(−1/2) while its temperature rises as (t_f − t)^(−1/4).
  • Ruled out if. A measured remnant spectrum or terminal flare with the four-dimensional exponents.
  • Waiting on. The vent census and the absolute scale of the model. The exponents themselves have no adjustable parameter.
Constraints on primordial black holes (2021) bound context moderate

Carr, Bernard and Kohri, Kazunori and Sendouda, Yuuiti and Yokoyama, Jun'ichi · 2021

Result. Review of the observational constraints on the abundance of primordial black holes across the whole mass range — evaporation (γ-rays, nucleosynthesis, CMB), lensing, dynamical, accretion and gravitational-wave limits — and of the mass windows that remain open.

The reference compilation of what the universe allows primordial black holes to be: limits from their Hawking evaporation (γ-ray backgrounds, light-element abundances, CMB anisotropies), from micro- and millilensing, from the dynamics of stars and galaxies, from accretion, and from gravitational waves, assembled across some twenty decades in mass, with the windows in which primordial black holes could still be a significant part of the dark matter.

Connection to WHD. The program’s vents are black holes that evaporate into the bulk, not into four dimensions, and that changes the exponents this whole map is built on: a vent’s lifetime scales with the square of its mass rather than the cube, so the light end of the delivered mass distribution rises linearly in mass where a four-dimensional population would rise quadratically, and the terminal flare brightens as (t_f − t)^(−1/2) while its temperature rises as (t_f − t)^(−1/4). Those exponents have no adjustable parameter; the absolute spectrum waits on a valid census of vents and on the model’s overall scale. This review is the four-dimensional constraint map the five-dimensional spectrum has to be re-derived against once that census exists — every evaporation bound here assumes the four-dimensional law and has to be recomputed, not copied. Filed as context.

Source ↗
@article{carr2021pbhconstraints,
  author  = {Carr, Bernard and Kohri, Kazunori and Sendouda, Yuuiti and Yokoyama, Jun'ichi},
  title   = {Constraints on primordial black holes},
  journal = {Reports on Progress in Physics},
  volume  = {84},
  number  = {11},
  pages   = {116902},
  year    = {2021},
  eprint  = {2002.12778},
  archivePrefix = {arXiv},
  doi     = {10.1088/1361-6633/ac1e31}
}

The Hubble constant and Newton’s constant input

  • The claim. These two measurements are inputs, not predictions. The Hubble constant sets which moment of the simulation is today; Newton’s constant sets the length unit. Everything else has to come out of the model.
  • Ruled out if. Nothing — but the dark-energy density above has to come out right for the values the model is given.
  • Waiting on. The choice between the two Hubble-constant measurements, which disagree with each other; the model is tested against each.
A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s⁻¹ Mpc⁻¹ Uncertainty from the Hubble Space Telescope and the SH0ES Team (2022) measurement context strong

Riess, Adam G. and others · 2022

Result. H₀ = 73.04 ± 1.04 km/s/Mpc from the Cepheid–supernova distance ladder with the Hubble Space Telescope — a 5σ difference from the value Planck + ΛCDM predicts (67.4 ± 0.5).

The local measurement of the Hubble constant: H₀ = 73.04 ± 1.04 km/s/Mpc from the Cepheid-calibrated supernova distance ladder, with the uncertainty brought to one km/s/Mpc. It differs from the Planck + ΛCDM value by 5σ — the “Hubble tension”.

Connection to WHD. The program uses the Hubble constant as an input, not a prediction: it decides which moment of the simulation is today. Both candidate values are carried — 67.4 from Planck and 73.0 from this measurement — and the prediction for the dark-energy density inherits whichever is used. WHD does not claim to explain the tension. The spread between the two is an uncertainty on the input, and the honest statement is that the model’s dark-energy density must come out right for the Hubble constant it is handed; it has one shot per choice and no parameter to absorb the difference. Filed as context for that reason.

Source ↗
@article{riess2022sh0es,
  author  = {Riess, Adam G. and others},
  title   = {A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s$^{-1}$ Mpc$^{-1}$ Uncertainty from the Hubble Space Telescope and the SH0ES Team},
  journal = {The Astrophysical Journal Letters},
  volume  = {934},
  number  = {1},
  pages   = {L7},
  year    = {2022},
  eprint  = {2112.04510},
  archivePrefix = {arXiv},
  doi     = {10.3847/2041-8213/ac5c5b}
}
CODATA recommended values of the fundamental physical constants: 2018 (2021) measurement context

Tiesinga, Eite and Mohr, Peter J. and Newell, David B. and Taylor, Barry N. · 2021

Result. The CODATA 2018 adjustment: Newton's constant G = 6.674 30(15) × 10⁻¹¹ m³ kg⁻¹ s⁻², relative standard uncertainty 2.2 × 10⁻⁵ — the least precisely known of the fundamental constants, and unchanged in the 2022 adjustment.

The CODATA least-squares adjustment of the fundamental constants for 2018 — the first after the SI was redefined in terms of fixed constants. Newton’s constant is the odd one out: G = 6.674 30(15) × 10⁻¹¹ m³ kg⁻¹ s⁻², known to only 22 parts per million and the least precise of the fundamental constants, a value the 2022 adjustment left unchanged.

Connection to WHD. In the solver’s units every quantity is a power of one unknown length scale. On the brane, Newton’s constant is set by the wall’s tension, and the measured value of G fixes that scale — the ruler, as the Hubble constant is the clock. An input, not a prediction: once G and H₀ are spent, the dark-energy density has no freedom left, which is what makes its prediction a real test. The 22-parts-per-million uncertainty on G is far below anything that test can resolve today; the entry is here so the input’s provenance is on the page.

Source ↗
@article{tiesinga2021codata,
  author  = {Tiesinga, Eite and Mohr, Peter J. and Newell, David B. and Taylor, Barry N.},
  title   = {CODATA recommended values of the fundamental physical constants: 2018},
  journal = {Reviews of Modern Physics},
  volume  = {93},
  number  = {2},
  pages   = {025010},
  year    = {2021},
  doi     = {10.1103/RevModPhys.93.025010}
}
Planck 2018 results. VI. Cosmological parameters (2020) measurement context strong

Planck Collaboration and Aghanim, N. and others · 2020

Result. Planck 2018 base-ΛCDM parameters: H₀ = 67.4 ± 0.5 km/s/Mpc; Ω_m = 0.315 ± 0.007; dark-matter density Ω_c h² = 0.120 ± 0.001 and baryon density Ω_b h² = 0.0224 ± 0.0001 (a dark-to-ordinary ratio of about 5.4); N_eff = 2.99 ± 0.17 with BAO; Σm_ν < 0.12 eV (95% CL).

The current best measurement of the effective number of relativistic species in the early universe, N_eff = 2.99 ± 0.17 — consistent with the Standard Model’s three neutrino species and no additional light relic, but with enough remaining uncertainty (ΔN_eff ≲ 0.3 at current precision) to leave room for a small extra contribution.

Connection to WHD. This is the external dataset the UV completion candidate’s one sharp, near-term prediction has to answer to: a small, positive excess ΔN_eff from vents leaking preferentially into the program’s forced hidden sector. Filed as context rather than supports or threatens because the current measurement neither confirms nor rules out WHD’s predicted small excess yet — it only excludes the large, “democratic” leak a symmetric mechanism would predict, which WHD already doesn’t predict. This entry should be revisited (and likely reclassified) once the one owed number — the vent’s hidden-vs-visible branching ratio — is computed, and again once CMB-S4-class data (roughly ten times more precise) is available.

Three more of the program’s tests run through this paper. Its Hubble constant, 67.4 ± 0.5 km/s/Mpc, is one of the two values used to set the model’s clock (the other is the local measurement, riess2022sh0es); with Newton’s constant it fixes the units for the prediction of the dark-energy density, which then has no freedom left. Its densities Ω_c h² = 0.120 and Ω_b h² = 0.0224 give the observed ratio of dark to ordinary matter, about 5.4, which a valid census of vents must reproduce with no adjustable parameter. None of these has been evaluated on a complete run of the model yet; this entry is the measurement they will be judged against.

Source ↗
@article{planck2020params,
  author  = {{Planck Collaboration} and Aghanim, N. and others},
  title   = {Planck 2018 results. VI. Cosmological parameters},
  journal = {Astronomy \& Astrophysics},
  volume  = {641},
  pages   = {A6},
  year    = {2020},
  eprint  = {1807.06209},
  archivePrefix = {arXiv},
  doi     = {10.1051/0004-6361/201833910}
}

The smoothness of the microwave background, the light elements, and the first spectrum constraint

  • The claim. Reheating happens vent by vent — many small hot big bangs rather than one. For the sky to look as uniform as it does, the vents must have been numerous and close-packed, and the abundances of the light elements made in the first minutes must come out as observed. The model also produces a first spectrum of fluctuations — red, and lopsided at birth — but that computation has not been accepted as a claim of the program yet.
  • Ruled out if. A vent population too sparse to blend into the observed uniformity, or light-element abundances that do not match.
  • Waiting on. The vent census. The first-spectrum computation awaits a decision on how the birth is to be read, and stands outside the program’s claims until then.
Big-Bang Nucleosynthesis after Planck (2020) measurement context strong

Fields, Brian D. and Olive, Keith A. and Yeh, Tsung-Han and Young, Charles · 2020

Result. Big-bang nucleosynthesis with Planck's baryon density as input: the deuterium abundance is now measured more precisely than it is predicted, the lithium problem persists, and the effective number of neutrino species at the epoch of nucleosynthesis is N_ν = 2.86 ± 0.15.

Standard big-bang nucleosynthesis re-evaluated with the Planck baryon density: the predicted light-element abundances against the observed ones (deuterium is now measured more precisely than theory predicts it; the lithium discrepancy remains), and an independent early-time determination of the number of relativistic species, N_ν = 2.86 ± 0.15 at the epoch of nucleosynthesis — a few minutes into the hot phase, long before the CMB.

Connection to WHD. Two constraints in one. The light-element abundances must come out as observed: reheating vent by vent has to deliver an ordinary hot big bang whose nuclear history matches, and the census of vents will decide whether it does. And the number of light species at nucleosynthesis is a second, earlier bound on dark radiation, complementary to the microwave background: the small positive excess the string completion predicts has to be present already at this epoch and consistent with both readings. Filed as context until the census and the size of the excess exist.

Source ↗
@article{fields2020bbn,
  author  = {Fields, Brian D. and Olive, Keith A. and Yeh, Tsung-Han and Young, Charles},
  title   = {Big-Bang Nucleosynthesis after Planck},
  journal = {Journal of Cosmology and Astroparticle Physics},
  volume  = {03},
  pages   = {010},
  year    = {2020},
  eprint  = {1912.01132},
  archivePrefix = {arXiv},
  doi     = {10.1088/1475-7516/2020/03/010},
  note    = {Erratum: JCAP 11, E02 (2020)}
}
Planck 2018 results. X. Constraints on inflation (2020) measurement context strong

Planck Collaboration and Akrami, Y. and others · 2020

Result. Scalar spectral index n_s = 0.9649 ± 0.0042 (68% CL) with no evidence for running; tensor-to-scalar ratio r₀.₀₀₂ < 0.10 from Planck alone and < 0.056 with BICEP2/Keck Array; the polarization data give a stringent test of adiabatic initial conditions; no evidence for parameterized features in the power spectrum.

Planck’s constraints on the primordial perturbations: a nearly scale-invariant, red spectrum with n_s = 0.9649 ± 0.0042 and no measurable running; primordial gravitational waves limited to r₀.₀₀₂ < 0.10 (< 0.056 with BICEP2/Keck); polarization data that test the adiabaticity of the initial conditions stringently; and no evidence for oscillatory or other parameterized features in the spectrum.

Connection to WHD. Two of the program’s tests meet this paper. The first is a constraint that must hold: reheating in WHD happens vent by vent — many small hot big bangs — and the observed smoothness and adiabaticity of the microwave background bound how numerous and how close-packed the vents must have been to blend. The second is not yet a claim: the model’s computation of the birth produces a red first spectrum and a universe lopsided at birth, but the program has not accepted that computation, pending a decision on how the birth is to be read. This entry records the measurement both will face; it does not score either.

Source ↗
@article{planck2020inflation,
  author  = {{Planck Collaboration} and Akrami, Y. and others},
  title   = {Planck 2018 results. X. Constraints on inflation},
  journal = {Astronomy \& Astrophysics},
  volume  = {641},
  pages   = {A10},
  year    = {2020},
  eprint  = {1807.06211},
  archivePrefix = {arXiv},
  doi     = {10.1051/0004-6361/201833887}
}

What does not test this program — underground dark-matter detectors candidate only

  • The claim. The hidden sector the string completion forces into existence is not a weakly interacting massive particle. Its only connection to us is gravity and exchanges suppressed at the string scale, so detectors built to catch a particle scattering off a nucleus do not test it; any signal would sit far below the neutrino background those experiments already face.
  • Ruled out if. Nothing here can rule it out or confirm it. These results are listed so they are not misread as either.
  • Waiting on. Nothing. The test of the hidden sector is the dark-radiation excess above.
Dark Matter Search Results from 4.2 Tonne-Years of Exposure of the LUX-ZEPLIN (LZ) Experiment (2025) bound context

LZ Collaboration and Aalbers, J. and others · 2025

Result. 4.2 ± 0.1 tonne-years of exposure (280 live days): no dark-matter signal; the spin-independent WIMP–nucleon cross section is excluded above 2.2 × 10⁻⁴⁸ cm² at a WIMP mass of 40 GeV/c² (90% CL), the leading limit for masses above 9 GeV/c².

The LUX-ZEPLIN experiment’s 4.2 tonne-year search: no evidence of weakly interacting massive particles scattering off xenon nuclei, and the strongest exclusion to date on the spin-independent WIMP–nucleon cross section, 2.2 × 10⁻⁴⁸ cm² at 40 GeV/c², with world-leading limits for every mass above 9 GeV/c².

Connection to WHD. Listed so that a null result is not misread. The hidden sector the string completion forces into existence is not a weakly interacting massive particle: its only connection to our sector is gravity and exchanges suppressed at the string scale, so a detector built to catch a particle scattering off a xenon nucleus does not test it, and any signal would sit far below the neutrino background these experiments already face. Neither this exclusion nor a future detection at these cross sections bears on the program. The observational handle on the hidden sector is the dark-radiation excess (act2025dr6extended, cmbs4referencedesign2019).

Source ↗
@article{lz2025results,
  author  = {{LZ Collaboration} and Aalbers, J. and others},
  title   = {Dark Matter Search Results from 4.2 Tonne-Years of Exposure of the LUX-ZEPLIN (LZ) Experiment},
  journal = {Physical Review Letters},
  volume  = {135},
  number  = {1},
  pages   = {011802},
  year    = {2025},
  eprint  = {2410.17036},
  archivePrefix = {arXiv},
  doi     = {10.1103/4dyc-z8zf}
}
First Dark Matter Search with Nuclear Recoils from the XENONnT Experiment (2023) bound context

XENON Collaboration and Aprile, E. and others · 2023

Result. XENONnT's first nuclear-recoil search: no significant excess between 3.3 and 60.5 keV; the spin-independent WIMP–nucleon cross section is excluded above 2.58 × 10⁻⁴⁷ cm² at a WIMP mass of 28 GeV/c² (90% CL).

The first WIMP search of the XENONnT detector: nuclear-recoil events between 3.3 and 60.5 keV, no excess above the expected background, and an upper limit on the spin-independent WIMP–nucleon cross section of 2.58 × 10⁻⁴⁷ cm² at 28 GeV/c² — an improvement on XENON1T at equal exposure.

Connection to WHD. As with lz2025results, this experiment is listed because a reader will expect a dark-matter claim to answer to it, and the answer is that it does not apply. The hidden sector couples to us through gravity and string-scale exchange only; a direct-detection null result is neither evidence against it nor room for it. Its test is elsewhere: the sign and size of the dark-radiation excess, and the existence of the decoupled sector itself.

Source ↗
@article{xenonnt2023,
  author  = {{XENON Collaboration} and Aprile, E. and others},
  title   = {First Dark Matter Search with Nuclear Recoils from the XENONnT Experiment},
  journal = {Physical Review Letters},
  volume  = {131},
  number  = {4},
  pages   = {041003},
  year    = {2023},
  eprint  = {2303.14729},
  archivePrefix = {arXiv},
  doi     = {10.1103/PhysRevLett.131.041003}
}

Literature

The work WHD builds on, argues with, and has to survive.

Gravitational effects on and of vacuum decay (1980) threatens strong settled

Coleman, Sidney and De Luccia, Frank · 1980

The standard mechanism for how a metastable vacuum decays including gravity’s back-reaction: a bubble of true vacuum nucleates quantum- mechanically inside the false vacuum and expands, with gravity setting the bubble’s critical size and the geometry on both sides of the wall matched by an Israel-type junction condition. For decades, this has been the default toolkit for “how does a new region of spacetime come into being from an unstable state.”

Connection to WHD. This is the competing mechanism WHD’s birth story most needs to distinguish itself from, since both start from “an unstable field configuration” and both end with “a new region of spacetime.” WHD does not use Coleman–De Luccia bounce nucleation: the birth slice is a homogeneous, closed hilltop configuration (the Hawking–Moss regime applies instead — the instability is shallow enough, relative to the expansion rate, that there’s no localized bubble at all), and the seed spectrum is derived from a de Sitter-throat mode decomposition rather than a bounce solution’s profile. This distinction was examined and ruled on directly within the program (no bubble nucleation; a homogeneous, derived-spectrum seed) — hence status: settled from WHD’s side, even though the comparison itself remains permanently worth stating for anyone encountering the birth-run claim for the first time.

Source ↗
@article{colemandeluccia1980,
  author  = {Coleman, Sidney and De Luccia, Frank},
  title   = {Gravitational effects on and of vacuum decay},
  journal = {Physical Review D},
  volume  = {21},
  number  = {12},
  pages   = {3305--3315},
  year    = {1980},
  doi     = {10.1103/PhysRevD.21.3305}
}
Death of White Holes in the Early Universe (1974) threatens strong

Eardley, Douglas M. · 1974

The classical result every “white hole” proposal has to answer for: a white hole immersed in even a thin bath of infalling radiation is classically unstable and converts to an ordinary black hole almost immediately — any infalling matter at all is enough to collapse the outgoing horizon. If this argument applies unmodified to WHD’s engine, the engine’s claimed longevity is dead on arrival.

Connection to WHD. This is the single strongest classical objection the birth-run paper (birth-run) has to survive, which is why it’s marked threatens at strong rather than filed as background. WHD’s answer is not to deny the mechanism but to note the setup differs from Eardley’s assumptions in a load-bearing way: the engine here is not sitting in an ambient bath of pre-existing infalling matter — it is the source of the outward flux in a closed, symmetric configuration, with the brane’s own mirror boundary reflecting radiation back rather than letting it free-fall inward past the horizon indefinitely. Whether that distinction is sufficient is exactly the “drive vs. infall balance” the birth-run paper’s longevity claim has to demonstrate quantitatively, run by run — this entry stays open (not settled) until that demonstration exists on a gate-clean run.

Source ↗
@article{eardley1974,
  author  = {Eardley, Douglas M.},
  title   = {Death of White Holes in the Early Universe},
  journal = {Physical Review Letters},
  volume  = {33},
  number  = {7},
  pages   = {442--444},
  year    = {1974},
  doi     = {10.1103/PhysRevLett.33.442}
}
Singular hypersurfaces and thin shells in general relativity (1966) supports strong settled

Israel, W. · 1966

The foundational result for treating a boundary between two regions of spacetime as a physical object in its own right: given a thin shell of stress-energy, the jump in the surrounding geometry’s extrinsic curvature across it is fixed by the shell’s own stress (the “Israel junction condition”). Every thin-brane picture in the brane-world literature — including WHD’s own earlier thin-shell treatment of the boundary — is built on this result.

Connection to WHD. WHD’s thick-wall paper (thick-wall-brane) explicitly moves away from treating Israel’s condition as an input: once the wall is numerically resolved rather than assumed thin, the junction condition becomes something the resolved layer either reproduces or doesn’t, in the appropriate thin limit — a derived check, not a boundary condition imposed by hand. This entry is marked supports because that check is only meaningful as a check against Israel’s own result — the thick-wall picture doesn’t discard this paper, it demotes it from assumption to consistency requirement.

Source ↗
@article{israel1966,
  author  = {Israel, W.},
  title   = {Singular hypersurfaces and thin shells in general relativity},
  journal = {Il Nuovo Cimento B},
  volume  = {44},
  number  = {1},
  pages   = {1--14},
  year    = {1966},
  note    = {Erratum: Nuovo Cim. B 48, 463 (1967)},
  doi     = {10.1007/BF02710419}
}
A Large Mass Hierarchy from a Small Extra Dimension (1999) context moderate settled

Randall, Lisa and Sundrum, Raman · 1999

The paper that made “our universe as a brane in a higher-dimensional bulk, with a Z2 orbifold identification across the extra dimension” a standard tool in theoretical physics, using it to address the electroweak hierarchy problem via a warped extra dimension.

Connection to WHD. Filed as context rather than supports or threatens: WHD borrows the vocabulary (a brane as a Z2-orbifold fixed locus in a bulk) but not the mechanism — WHD’s motivation is not the hierarchy problem, its extra dimension is not necessarily warped in the Randall–Sundrum sense, and the brane here is derived as a resolved field- theoretic kink rather than posited as a delta-function source. Useful orientation for a reader asking “haven’t I seen ‘brane plus Z2 mirror’ before?” — the answer is yes, and this is where; the physics content each program builds on top of that shared vocabulary is otherwise independent.

Source ↗
@article{randallsundrum1999,
  author  = {Randall, Lisa and Sundrum, Raman},
  title   = {A Large Mass Hierarchy from a Small Extra Dimension},
  journal = {Physical Review Letters},
  volume  = {83},
  number  = {17},
  pages   = {3370--3373},
  year    = {1999},
  eprint  = {hep-ph/9905221},
  archivePrefix = {arXiv},
  doi     = {10.1103/PhysRevLett.83.3370}
}
Rolling Tachyon (2002) supports moderate

Sen, Ashoke · 2002

Works out the dynamics of an open-string tachyon rolling off the unstable maximum of its potential toward its true vacuum, on an unstable D-brane — the archetypal “rolling tachyon” that gives brane–antibrane tachyon condensation its modern, quantitatively tractable form.

Connection to WHD. This is the direct technical ancestor of the UV completion paper’s central, most falsifiable claim: that the Higgs-like field in WHD’s low-energy description is an open-string tachyon of exactly this kind, with its mass fixed by the string tension rather than chosen. Marked supports at moderate strength (not strong) because Sen’s result establishes that this kind of rolling-tachyon dynamics is well-posed and well-studied — it does not by itself establish that WHD’s specific brane–antibrane construction is the one nature selects, which is exactly the “realizable, not proven selected” caveat the UV completion paper states about itself.

Source ↗
@article{sen2002,
  author  = {Sen, Ashoke},
  title   = {Rolling Tachyon},
  journal = {Journal of High Energy Physics},
  volume  = {2002},
  number  = {04},
  pages   = {048},
  year    = {2002},
  eprint  = {hep-th/0203211},
  archivePrefix = {arXiv},
  doi     = {10.1088/1126-6708/2002/04/048}
}
An SU(2) Anomaly (1982) supports strong settled

Witten, Edward · 1982

Shows that an SU(2) gauge theory with an odd number of doublet (spin-1/2) fermion representations is mathematically inconsistent — the path integral measure changes sign under a large gauge transformation, a global anomaly that has nothing to do with the more familiar perturbative (triangle) anomalies. The practical consequence: any consistent SU(2) gauge theory with chiral doublets must have an even number of them.

Connection to WHD. This is the load-bearing mathematical fact behind the UV completion candidate’s family-count argument: WHD’s SU(2) gauge sector, if realized as a genuine consistent gauge theory (string-embedded or otherwise), cannot have an odd number of chiral doublet families — the minimum consistent with observing chiral matter at all is two. This is not a numerology coincidence dressed up after the fact; it’s a 40-year-old, well-established consistency theorem being applied to a specific construction. Marked settled because the anomaly result itself is not in question — what remains open (tracked separately, open status elsewhere) is whether WHD’s specific brane construction is the right object to apply it to.

Source ↗
@article{witten1982anomaly,
  author  = {Witten, Edward},
  title   = {An SU(2) Anomaly},
  journal = {Physics Letters B},
  volume  = {117},
  number  = {5},
  pages   = {324--328},
  year    = {1982},
  doi     = {10.1016/0370-2693(82)90728-6}
}