Pith. sign in

REVIEW 3 major objections 4 minor 5 cited by

Boiling After the Dust Settles: Constraining First-Order Phase Transitions During Dark Energy Domination

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims current CMB temperature data cap a completed slow dark-sector phase transition at about 1% of the dark energy via anisotropic photon redshifting at a stochastic first-encounter surface.

desk verdict Novel constraints on late-time phase transitions via a first-encounter-surface mechanism that are orders of magnitude stronger than the Hubble-budget bound, but the central quadratic scaling rests on an asserted distance-matching condition; send to a referee who will push on it. read the letter →

arxiv 2509.07076 v1 pith:EZXXKBN5 submitted 2025-09-08 hep-ph astro-ph.CO

Seth Koren , Yuhsin Tsai , Runqing Wang This is my paper
classification hep-phastro-ph.CO
keywords first-orderphasetransitiondarkenergyCMBtemperatureanisotropyintegratedSachs-Wolfeeffectbubblenucleationfirst-encountersurfacevacuumlate-timecosmology
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that a first-order phase transition in the dark sector during the last few billion years—when vacuum energy already dominates—is far more constrained by CMB temperature anisotropies than by measurements of the Hubble expansion rate. The mechanism is that bubble nucleation is stochastic, so different lines of sight enter the true vacuum at slightly different redshifts; the resulting corrugated "first-encounter surface" makes CMB photons redshift by different amounts across the sky. In the minimal case where the released latent heat becomes free-streaming dark radiation, the authors derive a quadratic relation δz0 ∝ δz_pt² and project the induced redshift power spectrum onto low multipoles. Their central bound is r ≲ 10⁻⁵ (β/H⋆)², where β/H⋆ measures the transition's inverse duration in units of the Hubble rate at completion: a transition with β/H⋆ ≲ 25 can release no more than about 1% of the dark energy. This matters because Hubble-expansion measurements alone miss everything below roughly ten percent of the dark energy, so the CMB turns an otherwise nearly invisible late-time event into a testable signal.

What carries the argument

The load-bearing object is the "first-encounter surface": the corrugated surface at z̄_pt + δz_pt(θ,φ) where each CMB photon first enters the true vacuum. Two identities carry the argument: the comoving-distance matching condition χ_AO = χ_BO (Eq. 8), which cancels the linear term and leaves δz0 quadratic in δz_pt, and the projection of the resulting redshift power spectrum Pδz0(k)—built from the finite-bubble-statistics spectrum Pδt(k)—onto CMB multipoles via spherical Bessel functions (Eq. 13). The whole effect is a late-time analogue of the integrated Sachs-Wolfe effect: stochastic bubble nucleation sources metric perturbations near z̄_pt, and the second-order relation sets how strongly t

What would settle it

One decisive check is to compute or simulate photon geodesics through a stochastic bubble-nucleation history at z≈0.1–0.3 and test the paper's matching condition χ_AO = χ_BO (Eq. 8) at first order in δz_pt: any linear-in-δz_pt contribution to δz0 invalidates the quadratic formula and the derived bound. Observationally, a low-multipole (ℓ<20) CMB temperature measurement with uncertainties smaller than the predicted D_l^TT,pt for a given (r, β/H⋆, z̄_pt) would confirm or exclude the signal; an absence of the predicted r²(β/H⋆)⁻⁴ scaling would likewise settle the claim.

Watch

Extended reading notes

Core claim

Late-time first-order phase transitions leave a CMB anisotropy even if the dark radiation they release is homogeneous afterwards. Fluctuations in local transition time enter the observed photon redshift only at second order, δz0 ≈ δz_pt² rΩΛ /[(1+z̄_pt)(ΩΛ+Ωm(1+z̄_pt)³)^{3/2}], because the equality of comoving distances before and after the transition cancels the linear term. Squaring this with the finite-bubble-statistics spectrum Pδt(k) gives an induced CMB power spectrum peaked at ℓ<20 with amplitude ∝ r²(β/H⋆)⁻⁴. Equating that to the observed scalar-perturbation amplitude yields r ≲ 10⁻⁵ (β/H⋆)²: slow completed transitions are capped near 1% of dark energy, negative-vacuum endpoints requ

Load-bearing premise

The limit rests on assuming that a patchy phase transition changes only the expansion rate, not the paths photons take, so every photon that starts from the same redshift covers exactly the same spatial distance; if the transition bends photon trajectories at first order, the quadratic redshift relation and the r≲10⁻⁵(β/H⋆)² bound no longer follow.

Editorial extensions

If this is right

  • A completed slow phase transition (β/H⋆ ≲ 25) in the dark-energy-dominated era can release at most about 1% of the dark energy; anything larger would show up as an excess in the low-multipole CMB temperature spectrum.
  • Naive Hubble-expansion constraints would allow r as large as ~0.65 for a transition at z̄_pt = 0.3, while the CMB anisotropy bound is much stronger for β/H⋆ ≲ 200.
  • Negative-vacuum (r > 1) endpoints are not excluded, but only for fast transitions with β/H⋆ ≳ 300; if β/H⋆ ≲ 500, the universe must survive at least 14 Gyr before crunching.
  • Because the signal is quadratic in the transition-time fluctuation, the bound scales as r ∝ (β/H⋆)², so faster transitions evade the CMB constraint more easily.
  • The constraints are minimal: converting latent heat into free-streaming radiation homogenizes density perturbations, and the authors note that slow-moving final products would preserve perturbations and yield even stronger bounds.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An immediate extension is to compute the same first-encounter-surface signal for transitions that reheat into massive or self-interacting particles; the paper notes such cases keep density perturbations alive, so the bounds presented here should be treated as lower limits on the observable signal.
  • Because the observable is δz_pt², the induced CMB map is not Gaussian: a skewness or bispectrum search at ℓ<20 could separate a phase-transition origin from ordinary adiabatic integrated Sachs-Wolfe anisotropy.
  • The same corrugated-entry-surface logic should apply at other redshifts—for example in the 1 eV to 10 keV window where other studies bound dark-sector phase transitions—so the quadratic redshift relation offers a template for a full timeline of first-order phase-transition constraints.
  • If a late-time transition is incomplete, the anisotropy calculation does not apply as written, but photons would still cross a patchwork of false and true vacuum; quantifying that regime is the natural next step and could close the remaining allowed window.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper considers a late-time first-order phase transition in a dark sector during dark-energy domination (z ≲ 0.3), with the latent heat converted into free-streaming dark radiation. It computes CMB temperature anisotropies generated by fluctuations in the redshift at which photons enter the true vacuum, described by a spatially varying δz_pt. Using Planck 2018 data through a simplified three-bin χ² analysis, it derives an approximate upper bound r ≲ 10^{-5}(β/H_⋆)^2 on the released fraction of dark energy, and it discusses transitions to negative vacuum energy (r > 1), concluding that β/H_⋆ ≳ 300 is required and that β/H_⋆ ≲ 500 still leaves at least 14 Gyr before a crunch. The central analytic results are Eq. (9), δz_0 ∝ δz_pt^2, and Eq. (11), with the derivation in Appendix A.

Significance. Late-time FOPTs are a plausible and understudied dark-sector signature, and translating the stochastic completion time into CMB anisotropies is a fresh and potentially useful angle. If the derivation were sound, the bound r ≲ 10^{-5}(β/H_⋆)^2 would be an important, broadly applicable constraint, and the negative-vacuum/crunch discussion is a nice addition. The paper is explicit about several approximations: latent heat as free-streaming radiation, fixed Planck fiducial parameters, a three-bin χ², and the use of a published P_δt(k) from Ref. [43]. It also provides an explicit scaling relation that can be checked numerically. However, the central quantitative claim currently rests on an unproven distance-matching condition and an unjustified Gaussian truncation, so the headline numbers are not yet established.

major comments (3)
  1. [Section III, Eq. (8)] The equality χ_AO = χ_BO is asserted with the sentence that 'the total comoving distance from the same initial redshift to us must remain the same,' but no derivation is given. In the two histories being compared, H(z) differs over a finite redshift interval; a comoving distance in a modified background is not an invariant quantity, and the photon redshift is determined by the null geodesic equation, not by an independent matching condition. This condition is precisely what removes the linear-in-δz_pt term in the expansion leading to Eq. (9). If a term ∝ r δz_pt survives in δz_0, then P_{δz0}(k) scales as r^2 P_{δt}(k) rather than the convolution in Eq. (12), changing the ℓ-shape and the β/H scaling of the bound in Eq. (15). The appendix uses Eq. (8) as input and therefore does not resolve the issue. The authors should either derive Eq. (8) from a consistent gauge/matching prescription o
  2. [Appendix A, Eq. (A10)] The four-point function is truncated to products of two-point functions with the statement that only cross-correlations between x and y contribute. This is a Gaussian approximation for δz_pt. However, the text in Section III states δz_pt ≥ 0, so δz_pt cannot be an exactly Gaussian field; in a bubble-nucleation process the connected part of the four-point function is generically nonzero and can be comparable to the disconnected part at relevant scales. No estimate or bound on the connected contribution is given. Because the normalization of D_ℓ^{TT,pt}, and hence the 2σ curve in Fig. 3, depends on this truncation, the numerical results are not fully supported.
  3. [Section IV and Fig. 3] The statement that 'for β/H_⋆ ≲ 500, the universe will not crunch for at least 14 Gyr' is obtained by combining the t_end formula with the upper bounds r ≤ 2 and r ≤ 3 from the CMB anisotropy estimate. Those bounds inherit the uncertainties in Eqs. (8) and (A10). The 14-Gyr claim should therefore be presented as conditional on the anisotropy analysis, not as a robust consequence of the phase-transition dynamics alone.
minor comments (4)
  1. [Section III, Eq. (4)] The text around Eq. (4) contains an inconsistency: the fiducial values are given as ΩΛ = 0.69, Ωm = 0.31 in one place, but the duplicated passage states ΩΛ = 0.31, Ωm = 0.69. The correct values should be used consistently.
  2. [Figure 2 caption] The caption includes stray editorial text ('SK : ¯zpt, also above in Figure with r=0.1') and duplicated figure text. This should be cleaned before submission.
  3. [Section III, Eq. (14)] The three-bin χ² uses Planck error bars that are correlated and derived from a baseline cosmology. The authors acknowledge the limitation, but the resulting upper bound should be described explicitly as an order-of-magnitude estimate rather than a rigorous confidence limit.
  4. [General] The statement δz_pt ≥ 0 and the subsequent treatment of δz_pt as a Gaussian random field in Appendix A should be reconciled; this is related to the major comment on Eq. (A10).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central bound is derived from an external P_δt spectrum and a data χ², not from a fit or self-referential definition.

full rationale

The derivation chain is: (i) P_δt(k) from ref. [43] (external finite-bubble-statistics calculation), (ii) Eq. (8) matching condition defining δz0, (iii) Eq. (9) expansion giving δz0 ∝ r δz_pt², (iv) Eq. (11) power spectrum P_δz0 built from two P_δt factors, (v) Eq. (13) projection onto CMB and Eq. (14) χ² against Planck error bars, yielding Eq. (15). None of these steps fits a parameter to the target bound: r is bounded, not fitted, and P_δt is imported from a published paper, not adjusted. The one author overlap with ref. [43] (Tsai) is real, but ref. [43] is an independent parameter-free first-principles calculation with stated assumptions that do not include the present result, so it counts as real evidence and does not raise the circularity score. The distance-matching condition Eq. (8) is asserted rather than derived from perturbation theory, and the Appendix truncates the four-point function to Gaussian products (Eq. A10); these are physical/technical assumptions whose failure would change the numerical bound, but they are not circular in the sense of reducing to the output by construction. The paper also flags its own regime of validity (completed PT, gray region, free-streaming radiation), which is consistent with a non-circular derivation.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on ref. [43]'s bubble-statistics power spectrum, the distance-matching condition of Eq. (8), the Gaussian truncation of the four-point function, and the free-streaming-radiation assumption. The one manually chosen parameter that maximizes the signal is v_w=1.

free parameters (2)
  • bubble wall velocity v_w = 1 (assumed)
    Set to 1 (relativistic) for all main results; P_δt ∝ v_w^3 in Eq. (3), so this choice maximizes the CMB signal and the strength of the bounds. No scan over v_w is shown.
  • inverse transition duration β/H⋆ = N/A (scanned over 10-500)
    The bounds are quoted as a function of this parameter; it is not fitted to data but is a model parameter of the FOPT. The headline bounds are conditional on the chosen range.
assumptions (5)
  • domain assumption The comoving distance from a fixed initial redshift to the observer is invariant under the PT (Eq. 8).
    Used in Section III to derive δz0 ∝ δz_pt^2 (Eq. 9). If the PT alters the photon trajectory beyond the background expansion shift, the signal amplitude and shape change.
  • domain assumption The PT-time fluctuation field δt_c(x) is effectively Gaussian, so the four-point function in Eq. (A10) reduces to products of two-point functions.
    Appendix A: "Only the two-point correlations between perturbations at x- and y contribute..." The connected (non-Gaussian) part is dropped without an estimate of its size.
  • domain assumption The latent heat is converted to free-streaming dark radiation that homogenizes on the bubble scale immediately after the PT.
    Section III and footnote 1: this is the minimal-signal assumption; the authors note slow-moving fluids would produce larger anisotropies. The headline bounds are conditional on this choice.
  • domain assumption The power spectrum P_δt(k) from ref. [43] (Eq. 3 and Fig. 4) is valid for late-time PTs with β/H⋆≈10-500, including the sub-Hubble behavior.
    Adopted without rederivation in Section II and Appendix A. If the finite-bubble-statistics spectrum has a different normalization or shape at these redshifts, the r bounds rescale.
  • domain assumption Planck 2018 ΛCDM best-fit parameters are used and held fixed (H0=68, ΩΛ=0.69, Ωm=0.31).
    Section III: the PT signal is added incoherently to ΛCDM, justified by the claim that the allowed homogeneous redshift shift is <1%. This avoids a full cosmological fit.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Boiling After the Dust Settles: Constraining First-Order Phase Transitions During Dark Energy Domination." pith.science (2026). https://pith.science/paper/EZXXKBN5

@misc{pith2026250907076,
  author       = {Pith},
  title        = {Pith review of: Boiling After the Dust Settles: Constraining First-Order Phase Transitions During Dark Energy Domination},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EZXXKBN5}},
  note         = {Machine review of arXiv:2509.07076}
}
abstract

A first-order phase transition could occur in the late universe when vacuum energy begins dominating the energy density ($z \lesssim 0.3$) and convert some latent heat into other forms such as invisible radiation. This generic possibility also has concrete motivation in particle physics models which invoke a multitude of vacua to address theoretical puzzles. The na\"{i}ve constraint on such an event comes from measurements of the Hubble expansion rate, but this can only probe transitions involving $\mathcal{O}(10)\%$ of the dark energy. In this work, we show that significantly tighter constraints appear when accounting for phase transition fluctuations affecting CMB photon propagation anisotropically, akin to the integrated Sachs-Wolfe effect. For instance, if a completed phase transition has $\beta/H_\star\lesssim 25$, current CMB data limits the associated vacuum energy released to less than $1\%$ of the dark energy. A transition to negative vacuum energy (quasi-anti-de Sitter) is allowed only for $\beta/H_\star \gtrsim 300$. For $\beta/H_\star \lesssim 500$, the universe will not crunch for at least $14$ Gyr.

Figures

Figures reproduced from arXiv: 2509.07076 by the authors.

Figure 1
Figure 1. FIG. 1: Sketch of the origin of CMB fluctuations from a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Upper bounds on a FOPT converting a fraction [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4: Dimensionless power spectrum of PT time [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

Discussion (0). Sign in to comment.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Probing Confining Dark Sectors with Cosmological Perturbations

    hep-ph 2026-06 unverdicted novelty 6.0 of 10

    Composite dark matter from a keV-MeV confining phase transition generates curvature perturbations constrained by CMB anisotropies and Lyman-alpha forest data, offering a testable scenario even without visible sector c...

  2. Probing Confining Dark Sectors with Cosmological Perturbations

    hep-ph 2026-06 conditional novelty 6.0 of 10

    Composite dark matter from a keV–MeV confining phase transition sources an IR-enhanced curvature spectrum that competes with free-streaming suppression, yielding concrete CMB and Lyman-α bounds on transition strength ...

  3. Post-Recombination Fluctuations from a Sequestered Dark Sector

    astro-ph.CO 2026-05 unverdicted novelty 6.0 of 10

    Develops a short-timescale injection formalism for post-recombination fluctuations, derives CMB impacts from scalar/vector/tensor perturbations, and constrains sequestered dark sector phase transitions to permille-lev...

  4. Late-time Quantum Vacuum Decay and its Cosmological Implications

    astro-ph.CO 2026-05 unverdicted novelty 5.0 of 10

    Phenomenological late-time vacuum-tunneling models are fit to DESI DR2, supernova, and CMB data, allowing up to 50% vacuum-energy drop for z_t < 1 and a preferred z_t ~7 model that converts ~10% dark matter while easi...

  5. Electromagnetic Couplings of Dark Domain Walls

    hep-th 2026-02 reject novelty 4.0 of 10

    A Chern–Simons coupling between photons and a dark 3-form is claimed to rotate CMB polarization by ~10^-3 rad when light crosses dark domain walls, but the derivation has boundary-condition errors and the signal is fi...

Reference graph

Works this paper leans on

75 extracted references · 16 canonical work pages · cited by 4 Pith papers

  1. [43]

    Finite Bubble Statistics Constrain Late Cosmological Phase Transitions,

    G. Elor, R. Jinno, S. Kumar, R. McGehee, and Y. Tsai, “Finite Bubble Statistics Constrain Late Cosmological Phase Transitions,”Phys. Rev. Lett.133no. 21, (2024) 211003,arXiv:2311.16222 [hep-ph]

    arXiv 2024

  2. [1]

    Gravitational waves from first order cosmological phase transitions,

    A. Kosowsky, M. S. Turner, and R. Watkins, “Gravitational waves from first order cosmological phase transitions,”Phys. Rev. Lett.69(1992) 2026–2029

    work page 1992

  3. [2]

    Gravitational radiation from colliding vacuum bubbles,

    A. Kosowsky, M. S. Turner, and R. Watkins, “Gravitational radiation from colliding vacuum bubbles,”Phys. Rev. D45(1992) 4514–4535

    work page 1992

  4. [3]

    Gravitational radiation from colliding vacuum bubbles: envelope approximation to many bubble collisions,

    A. Kosowsky and M. S. Turner, “Gravitational radiation from colliding vacuum bubbles: envelope approximation to many bubble collisions,”Phys. Rev. D 47(1993) 4372–4391,arXiv:astro-ph/9211004

    arXiv 1993

  5. [4]

    Gravitational radiation from first order phase transitions,

    M. Kamionkowski, A. Kosowsky, and M. S. Turner, “Gravitational radiation from first order phase transitions,”Phys. Rev. D49(1994) 2837–2851, arXiv:astro-ph/9310044

    arXiv 1994

  6. [5]

    Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions,

    C. Capriniet al., “Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions,”JCAP04(2016) 001, arXiv:1512.06239 [astro-ph.CO]

    arXiv 2016

  7. [6]

    Detecting gravitational waves from cosmological phase transitions with LISA: an update,

    C. Capriniet al., “Detecting gravitational waves from cosmological phase transitions with LISA: an update,” JCAP03(2020) 024,arXiv:1910.13125 [astro-ph.CO]

    arXiv 2020

  8. [7]

    Detection of early-universe gravitational-wave signatures and fundamental physics,

    R. Caldwellet al., “Detection of early-universe gravitational-wave signatures and fundamental physics,”Gen. Rel. Grav.54no. 12, (2022) 156, arXiv:2203.07972 [gr-qc]. [8]LISACollaboration, K. G. Arunet al., “New horizons for fundamental physics with LISA,”Living Rev. Rel. 25no. 1, (2022) 4,arXiv:2205.01597 [gr-qc]. [9]LISA Cosmology W orking GroupCollabora...

    arXiv 2022

Show all 75 references
  1. [10]

    Primordial Anisotropies in the Gravitational Wave Background from Cosmological Phase Transitions,

    M. Geller, A. Hook, R. Sundrum, and Y. Tsai, “Primordial Anisotropies in the Gravitational Wave Background from Cosmological Phase Transitions,” Phys. Rev. Lett.121no. 20, (2018) 201303, arXiv:1803.10780 [hep-ph]

    2018 arXiv

  2. [11]

    Non-Gaussian stochastic gravitational waves from phase transitions,

    S. Kumar, R. Sundrum, and Y. Tsai, “Non-Gaussian stochastic gravitational waves from phase transitions,” JHEP11(2021) 107,arXiv:2102.05665 [astro-ph.CO]. [12]LISA Cosmology W orking GroupCollaboration, N. Bartoloet al., “Probing anisotropies of the Stochastic Gravitational Wav...

    2021 arXiv

  3. [13]

    Large primordial fluctuations in gravitational waves from phase transitions,

    A. Bodas and R. Sundrum, “Large primordial fluctuations in gravitational waves from phase transitions,”JHEP06(2023) 029,arXiv:2211.09301 [hep-ph]

    2023 arXiv

  4. [14]

    Unraveling cosmological anisotropies within stochastic gravitational wave backgrounds,

    Y. Cui, S. Kumar, R. Sundrum, and Y. Tsai, “Unraveling cosmological anisotropies within stochastic gravitational wave backgrounds,”JCAP10(2023) 064, arXiv:2307.10360 [astro-ph.CO]. [15]NANOGravCollaboration, Z. Arzoumanianet al., “The NANOGrav 12.5 yr Data Set: Search for an I...

    2023 arXiv

  5. [20]

    On the Evidence for a Common-spectrum Process in the Search for the Nanohertz Gravitational-wave Background with the Parkes Pulsar Timing Array,

    B. Goncharovet al., “On the Evidence for a Common-spectrum Process in the Search for the Nanohertz Gravitational-wave Background with the Parkes Pulsar Timing Array,”Astrophys. J. Lett.917 no. 2, (2021) L19,arXiv:2107.12112 [astro-ph.HE]

    2021 arXiv

  6. [21]

    Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array,

    D. J. Reardonet al., “Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array,”Astrophys. J. Lett.951no. 1, (2023) L6,arXiv:2306.16215 [astro-ph.HE]

    2023 arXiv

  7. [22]

    Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I,

    H. Xuet al., “Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I,”Res. Astron. Astrophys.23no. 7, (2023) 075024,arXiv:2306.16216 [astro-ph.HE]

    2023 arXiv

  8. [23]

    Does NANOGrav observe a dark sector phase transition?,

    T. Bringmann, P. F. Depta, T. Konstandin, K. Schmidt-Hoberg, and C. Tasillo, “Does NANOGrav observe a dark sector phase transition?,”JCAP11 7 (2023) 053,arXiv:2306.09411 [astro-ph.CO]

    2023 arXiv

  9. [24]

    Have pulsar timing array methods detected a cosmological phase transition?,

    A. Addazi, Y.-F. Cai, A. Marciano, and L. Visinelli, “Have pulsar timing array methods detected a cosmological phase transition?,”Phys. Rev. D109 no. 1, (2024) 015028,arXiv:2306.17205 [astro-ph.CO]

    2024 arXiv

  10. [25]

    Did we hear the sound of the Universe boiling? Analysis using the full fluid velocity profiles and NANOGrav 15-year data,

    T. Ghosh, A. Ghoshal, H.-K. Guo, F. Hajkarim, S. F. King, K. Sinha, X. Wang, and G. White, “Did we hear the sound of the Universe boiling? Analysis using the full fluid velocity profiles and NANOGrav 15-year data,”JCAP05(2024) 100,arXiv:2307.02259 [astro-ph.HE]

    2024 arXiv

  11. [26]

    Supercooling in radiative symmetry breaking: theory extensions, gravitational wave detection and primordial black holes,

    A. Salvio, “Supercooling in radiative symmetry breaking: theory extensions, gravitational wave detection and primordial black holes,”JCAP12(2023) 046,arXiv:2307.04694 [hep-ph]

    2023 arXiv

  12. [27]

    Origin of the Stochastic Gravitational Wave Background: First-Order Phase Transition vs. Black Hole Mergers,

    M. W. Winkler and K. Freese, “Origin of the Stochastic Gravitational Wave Background: First-Order Phase Transition vs. Black Hole Mergers,”arXiv:2401.13729 [astro-ph.CO]

    arXiv

  13. [28]

    Echoes of Self-Interacting Dark Matter from Binary Black Hole Mergers,

    A. Banik, J. H. Kim, J. S. Pi, and Y. Tsai, “Echoes of Self-Interacting Dark Matter from Binary Black Hole Mergers,”arXiv:2503.08787 [astro-ph.CO]

    arXiv

  14. [29]

    A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team,

    A. G. Riesset al., “A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team,”Astrophys. J. Lett. 934no. 1, (2022) L7,arXiv:2112.04510 [astro-ph.CO]

    2022 arXiv

  15. [30]

    The H0 Olympics: A fair ranking of proposed models,

    N. Sch¨ oneberg, G. Franco Abell´ an, A. P´ erez S´ anchez, S. J. Witte, V. Poulin, and J. Lesgourgues, “The H0 Olympics: A fair ranking of proposed models,”Phys. Rept.984(2022) 1–55,arXiv:2107.10291 [astro-ph.CO]

    2022 arXiv

  16. [31]

    New early dark energy,

    F. Niedermann and M. S. Sloth, “New early dark energy,”Phys. Rev. D103no. 4, (2021) L041303, arXiv:1910.10739 [astro-ph.CO]

    2021 arXiv

  17. [32]

    Resolving the Hubble tension with new early dark energy,

    F. Niedermann and M. S. Sloth, “Resolving the Hubble tension with new early dark energy,”Phys. Rev. D102 no. 6, (2020) 063527,arXiv:2006.06686 [astro-ph.CO]

    2020 arXiv

  18. [33]

    New Early Dark Energy as a solution to theH 0 andS 8 tensions,

    F. Niedermann and M. S. Sloth, “New Early Dark Energy as a solution to theH 0 andS 8 tensions,” arXiv:2307.03481 [hep-ph]

    arXiv

  19. [34]

    Hot new early dark energy bridging cosmic gaps: Supercooled phase transition reconciles stepped dark radiation solutions to the Hubble tension with BBN,

    M. Garny, F. Niedermann, H. Rubira, and M. S. Sloth, “Hot new early dark energy bridging cosmic gaps: Supercooled phase transition reconciles stepped dark radiation solutions to the Hubble tension with BBN,” Phys. Rev. D110no. 2, (2024) 023531, arXiv:2404.07256 [astro-ph.CO]

    2024 arXiv

  20. [35]

    Confronting cold new early dark energy and its equation of state with updated CMB, supernovae, and BAO data,

    A. Chatrchyan, F. Niedermann, V. Poulin, and M. S. Sloth, “Confronting cold new early dark energy and its equation of state with updated CMB, supernovae, and BAO data,”Phys. Rev. D111no. 4, (2025) 043536, arXiv:2408.14537 [astro-ph.CO]

    2025 arXiv

  21. [36]

    Observable CMB B-modes from Cosmological Phase Transitions,

    K. Greene, A. Ireland, G. Krnjaic, and Y. Tsai, “Observable CMB B-modes from Cosmological Phase Transitions,”arXiv:2410.23348 [astro-ph.CO]

    arXiv

  22. [37]

    Cosmological constraints on first-order phase transitions,

    Y. Bai and M. Korwar, “Cosmological constraints on first-order phase transitions,”Phys. Rev. D105no. 9, (2022) 095015,arXiv:2109.14765 [hep-ph]

    2022 arXiv

  23. [38]

    Gravitational wave generation from bubble collisions in first-order phase transitions: An analytic approach,

    C. Caprini, R. Durrer, and G. Servant, “Gravitational wave generation from bubble collisions in first-order phase transitions: An analytic approach,”Phys. Rev. D 77(2008) 124015,arXiv:0711.2593 [astro-ph]

    2008 arXiv

  24. [39]

    Gravitational waves from bubble collisions: An analytic derivation,

    R. Jinno and M. Takimoto, “Gravitational waves from bubble collisions: An analytic derivation,”Phys. Rev. D 95no. 2, (2017) 024009,arXiv:1605.01403 [astro-ph.CO]

    2017 arXiv

  25. [40]

    Gravitational waves from bubble dynamics: Beyond the Envelope,

    R. Jinno and M. Takimoto, “Gravitational waves from bubble dynamics: Beyond the Envelope,”JCAP01 (2019) 060,arXiv:1707.03111 [hep-ph]

    2019 arXiv

  26. [41]

    Dark radiation isocurvature from cosmological phase transitions,

    M. R. Buckley, P. Du, N. Fernandez, and M. J. Weikert, “Dark radiation isocurvature from cosmological phase transitions,”JCAP07(2024) 031,arXiv:2402.13309 [hep-ph]

    2024 arXiv

  27. [42]

    Constraining First-Order Phase Transitions with Curvature Perturbations,

    J. Liu, L. Bian, R.-G. Cai, Z.-K. Guo, and S.-J. Wang, “Constraining First-Order Phase Transitions with Curvature Perturbations,”Phys. Rev. Lett.130no. 5, (2023) 051001,arXiv:2208.14086 [astro-ph.CO]

    2023 arXiv

  28. [44]

    Black Holes and Gravitational Waves from Slow First-Order Phase Transitions,

    M. Lewicki, P. Toczek, and V. Vaskonen, “Black Holes and Gravitational Waves from Slow First-Order Phase Transitions,”Phys. Rev. Lett.133no. 22, (2024) 221003,arXiv:2402.04158 [astro-ph.CO]

    2024 arXiv

  29. [45]

    Numerical simulations of density perturbation and gravitational wave production from cosmological first-order phase transition,

    J. Zou, Z. Zhu, Z. Zhao, and L. Bian, “Numerical simulations of density perturbation and gravitational wave production from cosmological first-order phase transition,”arXiv:2502.20166 [hep-ph]

    arXiv

  30. [46]

    Curvature Perturbations from First-Order Phase Transitions: Implications to Black Holes and Gravitational Waves,

    G. Franciolini, Y. Gouttenoire, and R. Jinno, “Curvature Perturbations from First-Order Phase Transitions: Implications to Black Holes and Gravitational Waves,”arXiv:2503.01962 [hep-ph]

    arXiv

  31. [47]

    Oneµto rule them all: CMB spectral distortions can probe domain walls, cosmic strings and low scale phase transitions,

    N. Ramberg, W. Ratzinger, and P. Schwaller, “Oneµto rule them all: CMB spectral distortions can probe domain walls, cosmic strings and low scale phase transitions,”JCAP02(2023) 039,arXiv:2209.14313 [hep-ph]

    2023 arXiv

  32. [48]

    Bottaro, M

    S. Bottaro, M. Geller, D. Redigolo, and M. Tsurin preparation

  33. [49]

    A Mechanism for Reducing the Value of the Cosmological Constant,

    L. F. Abbott, “A Mechanism for Reducing the Value of the Cosmological Constant,”Phys. Lett. B150(1985) 427–430

    1985

  34. [50]

    Dynamical Neutralization of the Cosmological Constant,

    J. D. Brown and C. Teitelboim, “Dynamical Neutralization of the Cosmological Constant,”Phys. Lett. B195(1987) 177–182

    1987

  35. [51]

    Neutralization of the Cosmological Constant by Membrane Creation,

    J. D. Brown and C. Teitelboim, “Neutralization of the Cosmological Constant by Membrane Creation,”Nucl. Phys. B297(1988) 787–836

    1988

  36. [52]

    Four Forms and the Vanishing of the Cosmological Constant,

    M. J. Duncan and L. G. Jensen, “Four Forms and the Vanishing of the Cosmological Constant,”Nucl. Phys. B 336(1990) 100–114

    1990

  37. [53]

    Quantization of four form fluxes and dynamical neutralization of the cosmological constant,

    R. Bousso and J. Polchinski, “Quantization of four form fluxes and dynamical neutralization of the cosmological constant,”JHEP06(2000) 006, arXiv:hep-th/0004134

    2000 arXiv

  38. [54]

    Saltatory relaxation of the cosmological constant,

    J. L. Feng, J. March-Russell, S. Sethi, and F. Wilczek, “Saltatory relaxation of the cosmological constant,” Nucl. Phys. B602(2001) 307–328, arXiv:hep-th/0005276

    2001 arXiv

  39. [55]

    Field theory models for variable cosmological constant,

    G. R. Dvali and A. Vilenkin, “Field theory models for variable cosmological constant,”Phys. Rev. D64(2001) 063509,arXiv:hep-th/0102142

    2001 arXiv

  40. [56]

    Quantum-mechanical mechanism for reducing the cosmological constant,

    N. Kaloper and A. Westphal, “Quantum-mechanical mechanism for reducing the cosmological constant,” 8 Phys. Rev. D106no. 10, (2022) L101701, arXiv:2204.13124 [hep-th]

    2022 arXiv

  41. [57]

    General relativity on the multiverse and nature’s hierarchies,

    N. Kaloper, “General relativity on the multiverse and nature’s hierarchies,”Phys. Rev. D106no. 4, (2022) 044023,arXiv:2202.08860 [hep-th]

    2022 arXiv

  42. [58]

    Axion flux monodromy discharges relax the cosmological constant,

    N. Kaloper, “Axion flux monodromy discharges relax the cosmological constant,”JCAP11(2023) 032, arXiv:2307.10365 [hep-th]

    2023 arXiv

  43. [59]

    de Sitter space decay and cosmological constant relaxation in unimodular gravity with charged membranes,

    N. Kaloper, “de Sitter space decay and cosmological constant relaxation in unimodular gravity with charged membranes,”Phys. Rev. D108no. 2, (2023) 025005, arXiv:2305.02349 [hep-th]

    2023 arXiv

  44. [60]

    Discretely Evanescent Dark Energy,

    N. Kaloper, “Discretely Evanescent Dark Energy,” arXiv:2506.04317 [hep-th]

    arXiv

  45. [61]

    Cosmic attractors and gauge hierarchy,

    G. Dvali and A. Vilenkin, “Cosmic attractors and gauge hierarchy,”Phys. Rev. D70(2004) 063501, arXiv:hep-th/0304043

    2004 arXiv

  46. [62]

    Large hierarchies from attractor vacua,

    G. Dvali, “Large hierarchies from attractor vacua,” Phys. Rev. D74(2006) 025018,arXiv:hep-th/0410286

    2006 arXiv

  47. [63]

    Cosmological Relaxation of the Electroweak Scale,

    P. W. Graham, D. E. Kaplan, and S. Rajendran, “Cosmological Relaxation of the Electroweak Scale,” Phys. Rev. Lett.115no. 22, (2015) 221801, arXiv:1504.07551 [hep-ph]

    2015 arXiv

  48. [64]

    Large field excursions and approximate discrete symmetries from a clockwork axion,

    D. E. Kaplan and R. Rattazzi, “Large field excursions and approximate discrete symmetries from a clockwork axion,”Phys. Rev. D93no. 8, (2016) 085007, arXiv:1511.01827 [hep-ph]

    2016 arXiv

  49. [65]

    Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry,

    K. Choi and S. H. Im, “Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry,”JHEP01(2016) 149, arXiv:1511.00132 [hep-ph]

    2016 arXiv

  50. [66]

    Relaxion Monodromy and the Weak Gravity Conjecture,

    L. E. Ibanez, M. Montero, A. Uranga, and I. Valenzuela, “Relaxion Monodromy and the Weak Gravity Conjecture,”JHEP04(2016) 020, arXiv:1512.00025 [hep-th]

    2016 arXiv

  51. [67]

    Is the Relaxion an Axion?,

    R. S. Gupta, Z. Komargodski, G. Perez, and L. Ubaldi, “Is the Relaxion an Axion?,”JHEP02(2016) 166, arXiv:1509.00047 [hep-ph]

    2016 arXiv

  52. [68]

    Relaxation from particle production,

    A. Hook and G. Marques-Tavares, “Relaxation from particle production,”JHEP12(2016) 101, arXiv:1607.01786 [hep-ph]

    2016 arXiv

  53. [69]

    Irrational axions as a solution of the strong CP problem in an eternal universe,

    T. Banks, M. Dine, and N. Seiberg, “Irrational axions as a solution of the strong CP problem in an eternal universe,”Phys. Lett. B273(1991) 105–110, arXiv:hep-th/9109040

    1991 arXiv

  54. [70]

    A Vacuum accumulation solution to the strong CP problem,

    G. Dvali, “A Vacuum accumulation solution to the strong CP problem,”Phys. Rev. D74(2006) 025019, arXiv:hep-th/0510053

    2006 arXiv

  55. [71]

    Landscaping the Strong CP Problem,

    N. Kaloper and J. Terning, “Landscaping the Strong CP Problem,”JHEP03(2019) 032,arXiv:1710.01740 [hep-th]

    2019 arXiv

  56. [72]

    A Quantal Theory of Restoration of Strong CP Symmetry,

    N. Kaloper, “A Quantal Theory of Restoration of Strong CP Symmetry,”arXiv:2505.04690 [hep-ph]

    arXiv

  57. [73]

    An Alternative to Axion,

    N. Kaloper, “An Alternative to Axion,” arXiv:2504.21078 [hep-ph]

  58. [74]

    Origin of the Gravitational Constant and Particle Masses in Scale Invariant Scalar - Tensor Theory,

    Y. Fujii, “Origin of the Gravitational Constant and Particle Masses in Scale Invariant Scalar - Tensor Theory,”Phys. Rev. D26(1982) 2580

    1982

  59. [75]

    COSMOLOGICAL CONSTANT DAMPING BY UNSTABLE SCALAR FIELDS,

    L. H. Ford, “COSMOLOGICAL CONSTANT DAMPING BY UNSTABLE SCALAR FIELDS,”Phys. Rev. D35(1987) 2339

    1987

  60. [76]

    Cosmological Consequences of a Rolling Homogeneous Scalar Field,

    B. Ratra and P. J. E. Peebles, “Cosmological Consequences of a Rolling Homogeneous Scalar Field,” Phys. Rev. D37(1988) 3406

    1988

  61. [77]

    Cosmology and the Fate of Dilatation Symmetry,

    C. Wetterich, “Cosmology and the Fate of Dilatation Symmetry,”Nucl. Phys. B302(1988) 668–696, arXiv:1711.03844 [hep-th]. [78]DESICollaboration, M. Abdul Karimet al., “DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints,” arXiv:2503.14...

    1988 arXiv

  62. [79]

    Nucleation of cosmological phase transitions,

    C. J. Hogan, “Nucleation of cosmological phase transitions,”Physics Letters B133no. 3, (1983) 172–176.https://www.sciencedirect.com/science/ article/pii/0370269383905531

    1983

  63. [80]

    Nucleation and bubble growth in a first-order cosmological electroweak phase transition,

    K. Enqvist, J. Ignatius, K. Kajantie, and K. Rummukainen, “Nucleation and bubble growth in a first-order cosmological electroweak phase transition,” Phys. Rev. D45(May, 1992) 3415–3428.https: //link.aps.org/doi/10.1103/PhysRevD.45.3415

    1992 doi

  64. [81]

    Numerical simulations of acoustically generated gravitational waves at a first order phase transition,

    M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, “Numerical simulations of acoustically generated gravitational waves at a first order phase transition,”Phys. Rev. D92no. 12, (2015) 123009, arXiv:1504.03291 [astro-ph.CO]

    2015 arXiv

  65. [82]

    Cosmological phase transitions: From perturbative particle physics to gravitational waves,

    P. Athron, C. Bal´ azs, A. Fowlie, L. Morris, and L. Wu, “Cosmological phase transitions: From perturbative particle physics to gravitational waves,”Progress in Particle and Nuclear Physics135(2024) 104094. https://www.sciencedirect.com/science/article/ pii/S0146641023000753. ...

    2024 arXiv

  66. [85]

    Perturbations of a cosmological model and angular variations of the microwave background,

    R. K. Sachs and A. M. Wolfe, “Perturbations of a cosmological model and angular variations of the microwave background,”Astrophys. J.147(1967) 73–90. [86]DESICollaboration, K. Lodhaet al., “Extended Dark Energy analysis using DESI DR2 BAO measurements,” arXiv:2503.14743 [astro...

    1967 arXiv

  67. [88]

    De Sitter Space and the Swampland,

    G. Obied, H. Ooguri, L. Spodyneiko, and C. Vafa, “De Sitter Space and the Swampland,”arXiv:1806.08362 [hep-th]. 9 0.1 0.5 1 5 10 0.001 0.005 0.010 0.050 0.100 0.500 1 FIG. 4: Dimensionless power spectrum of PT time fluctuations from [43], rescaled by (β/H ⋆)2, plotted vs. the ...

    arXiv

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.