Pith. sign in

REVIEW 4 major objections 5 minor 58 references

A bubble of lower dark energy density can reproduce DESI's BAO features, but the CMB excludes the parameters that do so.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 15:33 UTC pith:IHAOM3NC

load-bearing objection Useful toy-model study of a dark-energy bubble; the distance-measure machinery is solid, the DESI 'alignment' is qualitative and tuned, and the off-centre CMB redshift calculation looks unfinished — the kSZ-based exclusion should be rechecked. the 4 major comments →

arxiv 2607.18376 v1 pith:IHAOM3NC submitted 2026-07-20 astro-ph.CO

Dark Energy Bubble as Dynamical Dark Energy: Properties and CMB Constraints

Batia Friedman-Shaw , Matthew C. Johnson , Katherine J. Mack This is my paper
classification astro-ph.CO
keywords dark energyvacuum decaycosmological phase transitionbubble cosmologybaryon acoustic oscillationsAlcock–Paczynski testkinetic Sunyaev–Zel'dovich effectCMB constraints
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper takes the DESI hint of evolving dark energy at face value and asks whether it could come not from a homogeneous dark-energy equation of state but from a spatial bubble of lower vacuum energy that nucleated late in cosmic history. It constructs a toy cosmology from two flat FLRW patches joined by a thin bubble wall, derives the resulting redshift, distance, sound-horizon, and Hubble-parameter relations, and compares them with BAO and CMB data. The central result is double-sided: with the bubble nucleating at redshift about 1.4 and carrying about 10 percent less vacuum energy, the model produces Alcock–Paczynski distortions that mirror the DESI DR2 measurements; but the same bubble generates a CMB dipole, a kinetic Sunyaev–Zel'dovich signal, a velocity-reconstruction monopole, and a shifted sound-horizon distance, which together exclude the DESI-matching parameter region at 2σ. A sympathetic reader should take away that spatially varying dark energy is a physically motivated and calculable alternative to evolving w(a), but in its simplest single-bubble form it fails the CMB tests.

Core claim

The paper's central claim is that a single vacuum bubble—a spherical region whose vacuum energy density is a fraction β of the exterior value, nucleated at redshift z_nuc—predicts sharp, localized features in the Alcock–Paczynski BAO stretch parameters. When β≈0.9 and z_nuc≈1.4, the binned parallel and perpendicular stretches qualitatively track the DESI DR2 measurements. However, the same geometry forces an off-centre observer to see an angle-dependent CMB redshift; the induced dipole, the remote-dipole kSZ contribution, the velocity-reconstruction monopole, and the modified distance to last scattering all constrain the bubble, and the DESI-matching region of parameter space is excluded to

What carries the argument

The construction is a matched pair of flat FLRW spacetimes joined by Israel junction conditions across a spherical thin wall; in the relevant regime the wall becomes ultra-relativistic almost immediately, so it is treated as an outgoing null shell. All observables are built from the wall-crossing map between the two charts: photons acquire a redshift jump at the wall, which shows up as a step in the effective Hubble parameter H_eff(z) = (dr/dz)^{-1}; a discontinuity in comoving distance; and a residual in the BAO stretch parameters. The same map, computed for lines of sight at arbitrary angle, yields the direction-dependent CMB redshift at the centre of the constraint analysis.

Load-bearing premise

Everything hinges on treating the bubble wall as infinitely thin and moving at the speed of light from the moment it forms; if the real wall is slower, thicker, or interacts with matter, the sharp distance features and the CMB exclusion both change.

What would settle it

A measurement of the CMB kSZ amplitude at ℓ≈3000 with sensitivity below about one μK² would settle the central conflict: the paper predicts a bubble-induced contribution roughly two orders of magnitude above the quoted upper limit for the DESI-matching parameters. A clean non-detection confirms the negative conclusion; an elevated signal reopens the explanation. On the BAO side, a survey with narrow redshift bins around z≈1.4 would resolve the predicted step in α_⊥.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • For β≈0.9 and z_nuc≈1.4, the model's binned α_∥ and α_⊥ track the reported BAO measurements from DESI DR2.
  • The CMB dipole forces the observer to lie close to the bubble centre; larger displacements are ruled out.
  • The kSZ constraint is the most restrictive: the bubble-induced contribution at ℓ≈3000 exceeds the current upper bound by about two orders of magnitude for the DESI-like parameters.
  • Combining dipole, kSZ, velocity-monopole, and sound-horizon distance constraints excludes the DESI-like parameter region at 2σ; the surviving bubbles are too small or late to affect the BAO redshift range.
  • The model gives different parallel and perpendicular stretch behaviour, something a homogeneous w(a) dark energy cannot do, so AP measurements can serve as a discriminating test for spatial variation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Editorial extension: If the wall has finite thickness or moves subluminally, the redshift jump is smoothed and the CMB exclusion could weaken; rerunning the same distance and kSZ calculations for a thick or slow wall is the natural next test of whether some form of the bubble can survive.
  • Editorial extension: The Snell's-law bending derived for non-central observers implies a direction-dependent magnification of background sources; this is a testable lensing signature that the paper does not pursue.
  • Editorial extension: The strongest constraint (kSZ) is sourced by remote observers seeing anisotropic CMBs; in a multi-bubble or percolating transition the distant dipole field would be even richer, so the constraints are likely to strengthen, but the AP-feature idea transfers to those settings.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper studies a toy model in which dark energy is a metastable vacuum that has partially decayed in a spherical region ('bubble') of lower dark energy density, embedded in an exterior flat ΛCDM cosmology. The authors use Israel junction conditions and approximate the bubble wall as an outgoing null hypersurface. They derive the redshift, comoving distance, angular-diameter distance, sound-horizon scale, and effective Hubble parameter in this piecewise-FLRW spacetime. They then compute Alcock–Paczynski BAO stretch parameters and compare them with DESI, finding qualitative resemblance for a bubble nucleating at z_nuc ≈ 1.4 with interior/exterior vacuum ratio β ≈ 0.9. They also derive CMB constraints — dipole, kinetic Sunyaev–Zel'dovich (kSZ), velocity-reconstruction monopole, and sound-horizon calibration — and conclude that the CMB excludes the parameter region that produces the DESI-like features. The paper positions this as a useful toy model for spatially varying dynamical dark energy, not as a viable explanation of current data.

Significance. If the central claims were robust, the paper would provide a concrete and instructive example of how spatial variation in dark energy can produce distinctive distance and BAO signatures, and a cautionary demonstration that such models are strongly constrained by CMB anisotropy. The geometric derivation of the angular-diameter distance for a central observer (Appendix C) is careful, and the paper is unusually transparent about its idealizations (thin wall, null trajectory, spherical symmetry, no matter–wall interactions). However, several load-bearing points are not yet adequately supported: the off-centre redshift calculation omits the angle-dependent wall frequency shift that Appendix E itself derives; the exterior cosmology and the early-universe sound-horizon input are mutually inconsistent; and the kSZ constraint is computed with a homogeneous estimator applied to a single, deterministic bubble. As it stands, the qualitative DESI 'alignment' is not a prediction, and the quantitative exclusion region could change under corrected calculations. With revision, the model could still serve as a useful toy.

major comments (4)
  1. [Appendix D, Eq. (D.9); Appendix E, Eq. (E.5)] The redshift z(θ) for off-centre observers is computed with the middle factor in Eq. (D.9) taken as the radial wall time-coordinate Jacobian dt_-/dt_+, and the text asserts that photon deflection 'is not needed.' But Appendix E derives Snell's law ω_+ sinθ_+ = ω_- sinθ_- (Eq. E.5), which shows that the frequency shift across a moving thin wall depends on the photon's incidence angle. For oblique crossings the wall frequency ratio is not the time-coordinate ratio; the continuity of the pulled-back momentum along the null generator gives an additional factor depending on the angles. This correction is not negligible for remote observers inside the bubble used in Sec. 3.3.1, whose displacement from the bubble centre can be comparable to the wall radius. Since the dipole constraint (Eq. 3.3) and the kSZ remote-dipole field (Eq. 3.11) both rely on z(θ), the exclusion region in Fig. 12 may shi
  2. [Sec. 2.4; Sec. 3.3.3] The exterior flat ΛCDM cosmology is fixed at (h, Ω_M,0) = (0.6736, 0.2892), the lower 1σ DESI value, while the sound-horizon calculation uses the Planck physical densities ω_b = 0.02237, ω_c = 0.1200. With h = 0.6736 those Planck densities imply Ω_m,0 ≈ 0.314, not 0.2892. Thus the expansion history used for bubble distances and the early-time expansion history used for r_d and r_s cannot both follow from the same Friedmann equation if the exterior is a single FLRW cosmology. This inconsistency affects the BAO stretch predictions (Sec. 3.2), the sound-horizon constraint (Sec. 3.3.3), and hence the exclusion plot in Fig. 12. The paper should either adopt a self-consistent set of parameters or explicitly model and justify the transition between the early- and late-time expansion histories.
  3. [Sec. 3.2, Fig. 2] The abstract's claim of 'strikingly well' alignment with DESI is not supported by a likelihood or a prior predictive statement. The parameters β = 0.9, z_nuc = 1.4, and the choice Ω_M,0 = 0.2892 are selected to produce the features, and the text admits there is no quantitative goodness-of-fit. As a result, the resemblance in Fig. 2 is an input selection rather than an independent output. The paper should either perform a quantitative fit and show the likelihood surface over β and z_nuc, or explicitly label the comparison as an illustrative coincidence and temper the language in the abstract and Sec. 3.2.
  4. [Sec. 3.3.1, Eq. (3.11)] The kSZ constraint is computed with the homogeneous estimator C_l^vv of Ref. [57], which assumes a statistically homogeneous remote-dipole field whose correlations are set by the matter power spectrum P_k. In the bubble model, the remote dipole v_dip(r) is a single deterministic, spatially localized profile that is nonzero only inside the bubble. The contribution of such a single bubble to the CMB temperature power spectrum is not generally equal to the homogeneous C_l^vv, and the SPT-3G upper limit on the kSZ power amplitude may not directly apply. Since the kSZ constraint is the strongest one driving Fig. 12, the authors should either compute the actual single-bubble kSZ angular pattern or justify in detail why the homogeneous formula is applicable in this setting.
minor comments (5)
  1. [Fig. 12] The shaded regions for the three constraints (reconstructed velocity monopole, CMB distance, kSZ auto-power) are not clearly distinguished. The caption says 'Excluded by all at 2σ,' but the individual 1σ and 2σ contours should be labeled or use distinct styles.
  2. [Eq. (A.7)] There appears to be a mismatched parenthesis/square root in the displayed equation for dR/dt; please check the typesetting.
  3. [Sec. 3.1, Eq. (3.3)] The dipole projection uses a Legendre weighting; please define the convention explicitly so the reader can verify the normalization, e.g., v_dip = (3/4π) ∫ (ΔT/T) cosθ dΩ or the equivalent.
  4. [Fig. 15 caption / Appendix D] The caption states that deflection 'is not needed,' which is confusing immediately before Appendix E derives Snell's law. Even if the angle-dependent frequency shift were negligible for the central observer, the caption should be reconciled with the content of Appendix E.
  5. [Sec. 2.5.1, Eq. (2.11)] The notation for the wall-crossing time t_c^± and the time mapping t_-(t_+) could be introduced more explicitly; currently the reader must infer the numerical procedure from the accompanying text.

Circularity Check

1 steps flagged

DESI-like AP alignment is partly retrospective parameter choice, but the central CMB-exclusion result is independent and self-contained.

specific steps
  1. fitted input called prediction [Sec. 3.2 (Comparison with DESI BAO Features), around Eq. (3.5); see also Sec. 2.4 and Fig. 2]
    "For the illustrative comparison below, we use the lower 1σ value of the DESI-inferred ΩM,0, which gives a good match to the observed trend."

    The paper's abstract and Fig. 2 describe 'model predictions of Alcock–Paczynski distortion' that 'align strikingly well' with DESI, but the alignment is obtained by choosing ΩM,0 at the lower 1σ DESI value and then selecting beta=0.9, znuc=1.4 to produce the sharp features. These are inputs chosen to match the target data, not outputs of an independent parameter-free prediction. The paper itself labels the comparison 'feature-level' and 'qualitative', which reduces the severity, but the claimed 'prediction' is partly retrospective. The central exclusion claim does not depend on this step.

full rationale

The central result of the paper is the exclusion, by CMB data (dipole, kSZ, velocity monopole, sound-horizon distance), of the parameter region that reproduces the DESI-like BAO features. That exclusion is computed from external measurements and analytic junction-condition geometry; it does not reduce to the model's own inputs. The only near-circular element is the 'striking alignment' of the AP stretch features: ΩM,0 = 0.2892, beta=0.9, and znuc=1.4 are hand-selected to make the curves resemble DESI, and the paper explicitly says no goodness-of-fit is assessed. The Appendix D statement that photon deflection is not needed for z(theta) is a robustness/correctness concern (especially in light of the Snell's-law result in Appendix E), not a circularity of the derivation's logic. No load-bearing self-citation chain is used: Ref. [57] is by a co-author but provides a published formula applied here, not the result being derived. Overall the paper is not circular where it matters; it earns a mild score only because part of the advertised DESI alignment is input-selected rather than independently predicted.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The paper's parameter space is {β, z_nuc, observer position} plus the hand-picked exterior ΩM,0. These are phenomenological inputs; the central exclusion is computed with them as inputs. No new particles, forces, or conserved quantities are introduced.

free parameters (4)
  • β (interior/exterior vacuum energy ratio) = 0.9 (illustrative; scanned 0–1)
    Model parameter controlling dark-energy contrast; hand-picked to 0.9 in Fig. 2 and the star in Fig. 12 to reproduce DESI-like AP features.
  • z_nuc (nucleation redshift) = 1.4 (illustrative)
    Model parameter setting when the bubble forms; chosen so the wall crosses the DESI redshift range.
  • Ω_M,0 exterior = 0.2892
    Chosen as the lower 1σ value of DESI DR2 to give a better qualitative fit to DESI BAO stretch (Sec. 2.4, Sec. 3.2).
  • Observer displacement from centre = ≈0 (central observer)
    Constrained by CMB dipole; the paper then assumes approximately central observer for BAO and CMB calculations.
axioms (6)
  • standard math Flat FLRW metrics inside and outside, joined via Israel junction conditions
    Sec. 2.1; standard general relativity.
  • ad hoc to paper Wall reaches ultra-relativistic speed on scales smaller than probed and is approximated as an outgoing null trajectory
    Sec. 2.2, Appendix A; load-bearing idealization for all distance measures and CMB constraints.
  • domain assumption Matter density is continuous at nucleation
    Sec. 2.3; chosen matching prescription; if false, interior matter content differs.
  • domain assumption Pre-recombination physics is unchanged; z_ls=1089.92 and Planck sound-horizon inputs are used
    Sec. 2.4; needed for CMB distance and sound-horizon constraints.
  • domain assumption Perfectly spherical bubble and no matter-wall interactions
    Sec. 4; acknowledged idealizations; would alter kSZ and BAO features.
  • standard math Null-shell Barrabès–Israel formalism applies across the wall
    Appendix C; used to derive DA = areal radius for central observers.

pith-pipeline@v1.3.0-alltime-deepseek · 25831 in / 11843 out tokens · 100800 ms · 2026-08-01T15:33:14.917801+00:00 · methodology

0 comments
read the original abstract

Recent DESI results are in tension with the constant dark energy density predicted by the $\Lambda$CDM model. If dark energy is associated with the vacuum energy of a scalar field in a metastable state, it will undergo a first-order phase transition through the nucleation of bubbles containing a reduced dark energy density. In this paper, we explore the consequences of this model, where dark energy density varies in both space and time. We model a single bubble spacetime using the Israel junction conditions and derive each of the usual distance measures in this inhomogeneous cosmology. We find that the model predictions of Alcock-Paczynski distortion have features that align strikingly well with the DESI measurements if the dark energy phase transition occurred at roughly a redshift of 1.4 and if the bubble of lower dark energy density has roughly 10$\%$ less dark energy density than the outer cosmology. Despite this feature, we find that the dark energy bubble is heavily constrained by the CMB which excludes the region of parameter space that reproduces the DESI BAO measurements. Still, the peculiar features in the distance measurements of the dark energy bubble cosmology serve as a useful toy model to motivate and inform future work in the currently poorly explored area of spatially varying dynamical dark energy.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

58 extracted references · 24 linked inside Pith

  1. [1]

    Abdul-Karim et al.,Data release 1 of the Dark Energy Spectroscopic Instrument, 2025, [2503.14745]

    DESI Collaboration, M. Abdul-Karim et al.,Data release 1 of the Dark Energy Spectroscopic Instrument, 2025, [2503.14745]

    Pith/arXiv arXiv 2025

  2. [2]

    Abdul-Karim et al.,DESI DR2 results

    M. Abdul-Karim et al.,DESI DR2 results. II. measurements of baryon acoustic oscillations and cosmological constraints,Phys. Rev. D112(2025)

    2025

  3. [3]

    Louis et al.,The Atacama Cosmology Telescope: DR6 power spectra, likelihoods, andΛCDM parameters, 2025, [2503.14452]

    T. Louis et al.,The Atacama Cosmology Telescope: DR6 power spectra, likelihoods, andΛCDM parameters, 2025, [2503.14452]. – 25 –

    Pith/arXiv arXiv 2025

  4. [4]

    Aghanim et al.,Planck 2018 results

    N. Aghanim et al.,Planck 2018 results. VI. cosmological parameters,Astron. Astrophys.641 (2020) A6

    2018

  5. [5]

    Aghanim et al.,Planck 2018 results

    N. Aghanim et al.,Planck 2018 results. I. overview and the cosmological legacy of Planck, Astron. Astrophys.641(2020) A1

    2018

  6. [6]

    Camphuis et al.,SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G main field,Phys

    E. Camphuis et al.,SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G main field,Phys. Rev. D113 (2026)

    2019

  7. [7]

    DES Collaboration, T. M. C. Abbott et al.,The Dark Energy Survey: Cosmology results with 1500 new high-redshift type Ia supernovae using the full five-year dataset, 2025, [2401.02929]

    Pith/arXiv arXiv 2025

  8. [8]

    Rubin et al.,Union through UNITY: Cosmology with 2,000 SNe using a unified bayesian framework, 2025, [2311.12098]

    D. Rubin et al.,Union through UNITY: Cosmology with 2,000 SNe using a unified bayesian framework, 2025, [2311.12098]

    Pith/arXiv arXiv 2025

  9. [9]

    Brout et al.,The Pantheon+ analysis: Cosmological constraints,Astrophys

    D. Brout et al.,The Pantheon+ analysis: Cosmological constraints,Astrophys. J.938(2022) 110

    2022

  10. [10]

    Chevallier and D

    M. Chevallier and D. Polarski,Accelerating universes with scaling dark matter,Int. J. Mod. Phys. D10(2001) 213

    2001

  11. [11]

    E. V. Linder,Exploring the expansion history of the universe,Phys. Rev. Lett.90(2003) 091301

    2003

  12. [12]

    Marra, L

    V. Marra, L. Amendola, I. Sawicki and W. Valkenburg,Cosmic variance and the measurement of the local Hubble parameter,Phys. Rev. Lett.110(2013) 241305

    2013

  13. [13]

    García-Bellido and T

    J. García-Bellido and T. Haugbølle,Confronting Lemaître–Tolman–Bondi models with observational cosmology,JCAP2008(2008) 003

    2008

  14. [14]

    Alnes, M

    H. Alnes, M. Amarzguioui and Ø. Grøn,Inhomogeneous alternative to dark energy?,Phys. Rev. D73(2006) 083519

    2006

  15. [15]

    Célérier,Do we really see a cosmological constant in the supernovae data?,Astronomy & Astrophysics353(2000) 63 [astro-ph/9907206]

    M.-N. Célérier,Do we really see a cosmological constant in the supernovae data?,Astronomy & Astrophysics353(2000) 63 [astro-ph/9907206]

    Pith/arXiv arXiv 2000

  16. [16]

    Coleman,Fate of the false vacuum: Semiclassical theory,Phys

    S. Coleman,Fate of the false vacuum: Semiclassical theory,Phys. Rev. D15(1977) 2929

    1977

  17. [17]

    C. G. Callan and S. Coleman,Fate of the false vacuum. II. first quantum corrections,Phys. Rev. D16(1977) 1762

    1977

  18. [18]

    Coleman and F

    S. Coleman and F. De Luccia,Gravitational effects on and of vacuum decay,Phys. Rev. D21 (1980) 3305

    1980

  19. [19]

    A. H. Guth and E. J. Weinberg,Could the universe have recovered from a slow first-order phase transition?,Nucl. Phys. B212(1983) 321

    1983

  20. [20]

    Weinberg,The cosmological constant problem,Rev

    S. Weinberg,The cosmological constant problem,Rev. Mod. Phys.61(1989) 1

    1989

  21. [21]

    Bousso and J

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

    Pith/arXiv arXiv 2000

  22. [22]

    Susskind,The anthropic landscape of string theory, 2003, [hep-th/0302219]

    L. Susskind,The anthropic landscape of string theory, 2003, [hep-th/0302219]

    Pith/arXiv arXiv 2003

  23. [23]

    Cabibbo, L

    N. Cabibbo, L. Maiani, G. Parisi and R. Petronzio,Bounds on the fermions and Higgs-boson masses in grand unified theories,Nucl. Phys. B158(1979) 295

    1979

  24. [24]

    Isidori, G

    G. Isidori, G. Ridolfi and A. Strumia,On the metastability of the Standard Model vacuum, Nucl. Phys. B609(2001) 387 [hep-ph/0104016]

    Pith/arXiv arXiv 2001

  25. [25]

    Degrassi, S

    G. Degrassi, S. Di Vita, J. Elias-Miro, J. R. Espinosa, G. F. Giudice, G. Isidori et al.,Higgs mass and vacuum stability in the Standard Model at NNLO,JHEP08(2012) 098 [1205.6497]

    Pith/arXiv arXiv 2012

  26. [26]

    Buttazzo, G

    D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giudice, F. Sala, A. Salvio et al.,Investigating the near-criticality of the Higgs boson,JHEP2013(2013) 89 [1307.3536]. – 26 –

    Pith/arXiv arXiv 2013

  27. [27]

    Markkanen, A

    T. Markkanen, A. Rajantie and S. Stopyra,Cosmological aspects of Higgs vacuum metastability,Front. Astron. Space Sci.5(2018) 40 [1809.06923]

    Pith/arXiv arXiv 2018

  28. [28]

    L. F. Abbott,A mechanism for reducing the value of the cosmological constant,Phys. Lett. B 150(1985) 427

    1985

  29. [29]

    J. D. Brown and C. Teitelboim,Neutralization of the cosmological constant by membrane creation,Nucl. Phys. B297(1988) 787

    1988

  30. [30]

    J. L. Feng, J. March-Russell, S. Sethi and F. Wilczek,Saltatory relaxation of the cosmological constant,Nucl. Phys. B602(2001) 307

    2001

  31. [31]

    S. B. Giddings,The fate of four dimensions,Phys. Rev. D68(2003) 026006 [hep-th/0303031]

    Pith/arXiv arXiv 2003

  32. [32]

    S. B. Giddings and R. C. Myers,Spontaneous decompactification,Phys. Rev. D70(2004) 046005 [hep-th/0404220]

    Pith/arXiv arXiv 2004

  33. [33]

    D. N. Page,Is our universe likely to decay within 20 billion years?,Phys. Rev. D78(2008) 063535 [hep-th/0610079]

    Pith/arXiv arXiv 2008

  34. [34]

    Aguirre,Eternal inflation, past and future, 2007, [0712.0571], DOI

    A. Aguirre,Eternal inflation, past and future, 2007, [0712.0571], DOI

    Pith/arXiv arXiv 2007

  35. [35]

    Banks and M

    T. Banks and M. Johnson,Regulating eternal inflation, 2005, [hep-th/0512141]

    Pith/arXiv arXiv 2005

  36. [36]

    Aguirre, T

    A. Aguirre, T. Banks and M. Johnson,Regulating eternal inflation. II. The great divide,JHEP 08(2006) 065 [hep-th/0603107]

    Pith/arXiv arXiv 2006

  37. [37]

    Rudelius,Conditions for (no) eternal inflation,JCAP08(2019) 009 [1905.05198]

    T. Rudelius,Conditions for (no) eternal inflation,JCAP08(2019) 009 [1905.05198]

    Pith/arXiv arXiv 2019

  38. [38]

    Sakai and K.-i

    N. Sakai and K.-i. Maeda,Junction conditions of Friedmann–Robertson–Walker spacetimes, Phys. Rev. D50(1994) 5425

    1994

  39. [39]

    Pen and P

    U.-L. Pen and P. Zhang,Observational consequences of dark energy decay,Phys. Rev. D89 (2014) 063009

    2014

  40. [40]

    U.-L. Pen, A. Loeb and N. Turok,Gamma-ray bursts from baryon decay in neutron stars, Astrophys. J.509(1998) 537 [astro-ph/9712178]

    Pith/arXiv arXiv 1998

  41. [41]

    Aguirre and M

    A. Aguirre and M. C. Johnson,Dynamics and instability of false vacuum bubbles,Phys. Rev. D 72(2005) 103525

    2005

  42. [42]

    Aguirre and M

    A. Aguirre and M. C. Johnson,Two tunnels to inflation,Phys. Rev. D73(2006) 123529

    2006

  43. [43]

    M. C. Johnson, M. B. Paranjape, A. Savard and N. Tapia-Arellano,Stable thin-wall negative-mass bubbles in de Sitter spacetime,Gen. Rel. Grav.52(2020)

    2020

  44. [44]

    V. A. Berezin, V. A. Kuzmin and I. I. Tkachev,Dynamics of bubbles in general relativity,Phys. Rev. D36(1987) 2919

    1987

  45. [45]

    Sato,Motion of a shell at metric junction,Prog

    H. Sato,Motion of a shell at metric junction,Prog. Theor. Phys.76(1986) 1250

    1986

  46. [46]

    Aurilia, M

    A. Aurilia, M. Palmer and E. Spallucci,Evolution of bubbles in a vacuum,Phys. Rev. D40 (1989) 2511

    1989

  47. [47]

    S. K. Blau, E. I. Guendelman and A. H. Guth,Dynamics of false-vacuum bubbles,Phys. Rev. D35(1987) 1747

    1987

  48. [48]

    Shafieloo, D

    A. Shafieloo, D. K. Hazra, V. Sahni and A. A. Starobinsky,Metastable dark energy with radioactive-like decay,Mon. Not. Roy. Astron. Soc.473(2018) 2760 [1610.05192]

    Pith/arXiv arXiv 2018

  49. [49]

    X. Li, A. Shafieloo, V. Sahni and A. A. Starobinsky,Revisiting metastable dark energy and tensions in the estimation of cosmological parameters,Astrophys. J.887(2019) 153 [1904.03790]

    Pith/arXiv arXiv 2019

  50. [50]

    Y. Bai, S. Lu and N. Orlofsky,Late-time quantum vacuum decay and its cosmological implications, 2026, [2605.30259]. – 27 –

    Pith/arXiv arXiv 2026

  51. [51]

    D. J. Fixsen,The temperature of the cosmic microwave background,Astrophys. J.707(2009) 916

    2009

  52. [52]

    Alam et al.,The clustering of galaxies in the completed SDSS-III baryon oscillation spectroscopic survey: Cosmological analysis of the DR12 galaxy sample,Mon

    S. Alam et al.,The clustering of galaxies in the completed SDSS-III baryon oscillation spectroscopic survey: Cosmological analysis of the DR12 galaxy sample,Mon. Not. Roy. Astron. Soc.470(2017) 2617

    2017

  53. [53]

    Beutler et al.,The 6dF galaxy survey: Baryon acoustic oscillations and the local Hubble constant,Mon

    F. Beutler et al.,The 6dF galaxy survey: Baryon acoustic oscillations and the local Hubble constant,Mon. Not. Roy. Astron. Soc.416(2011) 3017

    2011

  54. [54]

    S. Alam et al.,Completed SDSS-IV extended baryon oscillation spectroscopic survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory,Phys. Rev. D103(2021) 083533

    2021

  55. [55]

    R. A. Sunyaev and Y. B. Zeldovich,The observations of relic radiation as a test of the nature of X-ray radiation from the Clusters of Galaxies,Comments on Astrophysics and Space Physics 4(1972) 173

    1972

  56. [56]

    Birkinshaw,The Sunyaev–Zel’dovich effect,Phys

    M. Birkinshaw,The Sunyaev–Zel’dovich effect,Phys. Rept.310(1999) 97

    1999

  57. [57]

    Bloch and M

    R. Bloch and M. C. Johnson,Kinetic Sunyaev–Zel’dovich velocity reconstruction from Planck and unWISE, 2024, [2405.00809]

    Pith/arXiv arXiv 2024

  58. [58]

    Poisson,A reformulation of the Barrabès–Israel null-shell formalism, 2002, [gr-qc/0207101]

    E. Poisson,A reformulation of the Barrabès–Israel null-shell formalism, 2002, [gr-qc/0207101]. Appendix A Bubble Wall Velocity Derivation Using Eq. (8) from Ref. [38] for a flat FLRW cosmology wherer=χ, we see that dR dτ =γ(v+HR) ± ,(A.1) whereγ= dt dτ = 1√ 1−v2. Note thatv=a(dr/dt)is the bubble wall’s peculiar velocity relative to the background expansio...

    Pith/arXiv arXiv 2002