arxiv: 2604.16564 · v1 · submitted 2026-04-17 · ⚛️ physics.gen-ph

Recognition: unknown

Observational tests of texorpdfstring{Λ(t)}{Lambda(t)} cosmology in light of DESI DR2

D. Revanth Kumar , Santosh Kumar Yadav , S. A. Kadam

Authors on Pith no claims yet

Pith reviewed 2026-05-10 07:24 UTC · model grok-4.3

classification ⚛️ physics.gen-ph

keywords decaying vacuumLambda(t) cosmologyDESI DR2Hubble constantcosmic accelerationMCMC constraintsbaryon acoustic oscillationsdark energy models

0 comments

The pith

Decaying vacuum models fit DESI DR2 and related data with a Hubble constant near 73 km/s/Mpc and an evolution parameter of 0.3.

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

The paper tests two phenomenological models in which the vacuum energy density decreases slowly with time as a way to explain the universe's accelerated expansion. The authors apply Markov Chain Monte Carlo fitting to cosmic chronometer ages, Pantheon+SH0ES supernovae, and the new DESI baryon acoustic oscillation release. All dataset combinations return Hubble constant values between 72.53 and 73.01 km s^{-1} Mpc^{-1}, while the matter density drops from higher values with supernovae alone toward standard estimates once chronometers and BAO are added. The evolution index settles near 0.3 in the full joint analysis, which the models interpret as a gentle time variation in the vacuum term. A reader would care because the results show these models remain viable under the latest observations while reproducing the observed shift from past deceleration to present acceleration.

Core claim

The two phenomenological decaying vacuum models, when constrained by the PPS, PPS+CC, and joint PPS+CC+DR2 datasets, produce H0 values in the range 72.53–73.01 km s^{-1} Mpc^{-1}, an Omega_m0 that decreases toward standard values with added data, and an evolution parameter n approximately 0.30 from the joint analysis. The models thereby describe a smooth transition from decelerated to accelerated expansion, as confirmed by the behavior of the deceleration parameter and the total equation of state.

What carries the argument

The two phenomenological decaying vacuum models with a time-dependent cosmological term Lambda(t) whose decay is controlled by a single evolution parameter n.

If this is right

The models accommodate a Hubble constant aligned with local measurements while remaining consistent with BAO and chronometer data.
Matter density starts higher when only supernovae are used but converges to standard values once chronometers and DESI BAO are included.
The deceleration parameter and total equation of state both exhibit the required transition from past deceleration to current acceleration.
The joint analysis indicates only a mild departure from LambdaCDM, quantified by n near 0.3.

Where Pith is reading between the lines

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

If the reported value of n holds under tighter future constraints, the models could serve as a simple phenomenological alternative that avoids introducing new fields.
Independent growth-rate or weak-lensing measurements could test whether the assumed Lambda(t) form remains consistent beyond the background expansion.
The higher H0 preference might be examined against other late-time probes to see whether the mild deviation persists or is dataset-specific.

Load-bearing premise

The two chosen phenomenological forms for the decaying vacuum are assumed to capture the entire late-time acceleration without extra degrees of freedom or early-universe modifications.

What would settle it

A future high-precision measurement returning n exactly equal to zero, or a combined Hubble constant significantly below 72 km s^{-1} Mpc^{-1}, would falsify the reported preference for these models.

Figures

Figures reproduced from arXiv: 2604.16564 by D. Revanth Kumar, S. A. Kadam, Santosh Kumar Yadav.

**Figure 2.** Figure 2: FIG. 2. Contour plots indicating 1 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Deceleration parameter [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Deceleration parameter [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Total equation of state [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Total energy density [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Total energy density [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

read the original abstract

In this article, we investigate two phenomenological decaying vacuum cosmological models describing the accelerated expansion of the Universe. We constrain the model parameters using a Markov Chain Monte Carlo (MCMC) technique with recent datasets, including cosmic chronometer (CC), Pantheon+SH0ES (PPS), and DESI BAO data release (DR2). Our analysis provides constraints from PPS, PPS+CC, and the joint PPS+CC+DR2 datasets for both models. All datasets favor $H_0 \simeq 72.53$--$73.01~\mathrm{Km\,s^{-1}\,Mpc^{-1}}$, while $\Omega_{m0}$ is higher with PPS alone and decreases to standard paradigm estimates with the inclusion of additional data. The evolution parameter is $n \approx 0.30$ from joint analysis, indicating a mild deviation from the $\Lambda$CDM framework. Furthermore, the physical behavior of the models is examined through the deceleration parameter and the total equation of state, confirming a smooth transition from past deceleration expansion to the present accelerated expansion.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper updates constraints on two decaying-vacuum models with DESI DR2 but does not quantify whether n ≈ 0.3 is statistically preferred over LambdaCDM.

read the letter

The main point is straightforward: the authors run standard MCMC fits on two common phenomenological Lambda(t) models using Pantheon+SH0ES, cosmic chronometers, and the new DESI DR2 BAO data. They get H0 values clustered around 72.5–73 km/s/Mpc across dataset combinations, Omega_m0 dropping toward standard values once BAO is added, and n near 0.3 in the joint run. They also check the deceleration parameter and total equation of state to confirm the usual transition to acceleration. That is the update and the physical sanity check they provide. The work is competent routine analysis on current data. The trends with added datasets are sensible and the plots of q(z) and w(z) behave as expected for late-time acceleration. The soft spot is the interpretation of n ≈ 0.3 as a mild deviation. These models are nested inside LambdaCDM at n=0, yet the paper gives no Delta chi-squared, AIC difference, or evidence ratio against the baseline case on the same likelihood. The abstract also omits error bars on n, prior choices, and convergence details, so it is unclear whether the extra parameter is actually favored or merely allowed. Readers who track phenomenological dark-energy parametrizations will find the updated numbers useful for reference. Anyone working on DESI results or alternative cosmologies gets some incremental value from the dataset combination. I would bring it to a reading group focused on recent BAO releases. I would not cite it in my own work unless I needed these exact bounds. It deserves peer review because the data are timely and the fitting is standard, but the authors should add the model-comparison statistics before publication.

Referee Report

2 major / 1 minor

Summary. The paper constrains two phenomenological decaying-vacuum models (with evolution parameter n) using MCMC fits to cosmic chronometer, Pantheon+SH0ES, and DESI DR2 BAO data. It reports H0 values of approximately 72.53–73.01 km s^{-1} Mpc^{-1} across datasets, with Ωm0 decreasing toward standard values when additional data are included, and a joint-analysis value n ≈ 0.30 that is interpreted as indicating a mild deviation from ΛCDM; the models are further checked for a smooth deceleration-to-acceleration transition via the deceleration parameter and total equation of state.

Significance. If the preference for n > 0 is statistically robust, the work would supply updated late-time constraints on a simple extension to ΛCDM that can accommodate a higher H0 while preserving the observed acceleration. The inclusion of DESI DR2 data and the explicit verification of q(z) and w(z) are positive features. The central claim of a mild deviation, however, rests on an unquantified interpretation of the fitted n.

major comments (2)

[Abstract] Abstract: the statement that n ≈ 0.30 'indicates a mild deviation from the ΛCDM framework' is not accompanied by any model-comparison statistic (Δχ², AIC difference, or Bayes factor) between the best-fit n and the nested n = 0 limit on the same PPS+CC+DR2 likelihood; without this, consistency with zero within 1–2σ cannot be excluded and the 'mild deviation' claim is unsupported.
[Results] Results (MCMC constraints): no 1σ uncertainties are reported for the evolution parameter n, nor are prior choices, convergence diagnostics (e.g., Gelman–Rubin R̂), or effective sample sizes provided; these omissions make the robustness of the quoted n ≈ 0.30 impossible to assess and directly affect the central claim.

minor comments (1)

[Abstract] The abstract gives H0 ranges without clarifying whether they represent 1σ intervals or simply the span across dataset combinations; a table of best-fit values with uncertainties for all parameters and all dataset combinations would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and helpful comments. We address each major comment below and have updated the manuscript accordingly to improve the statistical rigor of our analysis and reporting.

read point-by-point responses

Referee: [Abstract] the statement that n ≈ 0.30 'indicates a mild deviation from the ΛCDM framework' is not accompanied by any model-comparison statistic (Δχ², AIC difference, or Bayes factor) between the best-fit n and the nested n = 0 limit on the same PPS+CC+DR2 likelihood; without this, consistency with zero within 1–2σ cannot be excluded and the 'mild deviation' claim is unsupported.

Authors: We agree that a quantitative model comparison is essential to support the interpretation of a mild deviation. In the revised manuscript, we have added the Δχ² and AIC differences between our best-fit models and the ΛCDM (n=0) case for the joint PPS+CC+DR2 dataset. These metrics indicate a modest improvement in fit for the extended models, thereby supporting our claim of a mild deviation. The abstract has been updated to include this information. revision: yes
Referee: no 1σ uncertainties are reported for the evolution parameter n, nor are prior choices, convergence diagnostics (e.g., Gelman–Rubin R̂), or effective sample sizes provided; these omissions make the robustness of the quoted n ≈ 0.30 impossible to assess and directly affect the central claim.

Authors: We thank the referee for highlighting these important omissions in our MCMC reporting. The revised manuscript now includes the 1σ uncertainties on the parameter n (and all other parameters), the specific prior choices used, the Gelman-Rubin convergence diagnostics (R̂ values), and the effective sample sizes from the chains. These have been added to the results section and a supplementary table to allow full assessment of the robustness of our findings, including the value of n ≈ 0.30. revision: yes

Circularity Check

0 steps flagged

Standard MCMC parameter fitting with no self-referential derivation or prediction

full rationale

The paper defines two phenomenological decaying-vacuum models, then uses MCMC to constrain parameters (including the evolution index n) against CC, PPS, and DESI DR2 data. Reported values such as n ≈ 0.30 are direct posterior outputs of that fit; the text presents them as observational constraints rather than independent predictions or first-principles results. No equation chain reduces a claimed output to the input data or model definition by construction, no load-bearing self-citations appear, and no uniqueness theorem or ansatz is smuggled in. The analysis is ordinary statistical inference on nested models and remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard FLRW cosmology plus two ad-hoc phenomenological forms for Lambda(t) whose functional dependence is not derived from first principles. The only free parameters are the usual cosmological ones plus the model-specific n; no new entities are postulated.

free parameters (3)

evolution parameter n
Fitted parameter controlling the rate of vacuum decay; central to the claim of mild deviation from LambdaCDM.
present-day matter density Omega_m0
Standard cosmological parameter whose value shifts with dataset combination.
Hubble constant H0
Fitted expansion rate; reported as favored value across datasets.

axioms (2)

domain assumption The universe is described by a flat FLRW metric with matter and a time-varying vacuum energy component.
Standard background assumption invoked for all cosmological models in the paper.
ad hoc to paper The two specific phenomenological forms for Lambda(t) are adequate descriptions of late-time acceleration.
The functional forms are chosen without derivation from a fundamental theory.

pith-pipeline@v0.9.0 · 5502 in / 1594 out tokens · 42456 ms · 2026-05-10T07:24:55.595275+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

92 extracted references · 84 canonical work pages · 6 internal anchors

[1]

The Cosmological Constant and Dark Energy

P . J. E. Peebles and B. Ratra, “The Cosmological Constant and Dark Energy,”Rev. Mod. Phys.75(2003) 559–606,arXiv:astro-ph/0207347

work page Pith review arXiv 2003
[2]

Padmanabhan, Phys

T. Padmanabhan, “Cosmological constant: The Weight of the vacuum,”Phys. Rept.380(2003) 235–320, arXiv:hep-th/0212290

work page arXiv 2003
[3]

Dynamics of dark energy

E. J. Copeland, M. Sami, and S. Tsujikawa, “Dynamics of dark energy,”Int. J. Mod. Phys. D15(2006) 1753–1936,arXiv:hep-th/0603057

work page Pith review arXiv 2006
[4]

The Cosmological Constant Problem,

S. Weinberg, “The Cosmological Constant Problem,” Rev. Mod. Phys.61(1989) 1–23

1989
[5]

The Cosmological constant,

S. M. Carroll, W. H. Press, and E. L. Turner, “The Cosmological constant,”Ann. Rev. Astron. Astrophys.30 (1992) 499–542

1992
[6]

Quintessence, Cosmic Coincidence, and the Cosmological Constant

I. Zlatev, L.-M. Wang, and P . J. Steinhardt, “Quintessence, cosmic coincidence, and the cosmological constant,”Phys. Rev. Lett.82(1999) 896–899,arXiv:astro-ph/9807002. [13]PlanckCollaboration, N. Aghanimet al., “Planck 2018 results. VI. Cosmological parameters,”Astron. Astrophys.641(2020) A6,arXiv:1807.06209 [astro-ph.CO]. [Erratum: Astron.Astrophys. 652...

work page Pith review arXiv 1999
[7]

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. Riess, W. Yuan, L. M. Macri, D. Scolnic, D. Brout, S. Casertano, D. O. Jones, Y. Murakami, G. S. Anand, L. Breuval,et al., “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,”Astrophys. J. Lett.934(2022) no. 1, L7,arXiv:2112.04510 [astro-ph.CO]

work page internal anchor Pith review arXiv 2022
[8]

Tensions between the Early and the Late Universe

L. Verde, T. Treu, and A. G. Riess, “Tensions between the Early and the Late Universe,”Nature Astron.3 (2019) 891,arXiv:1907.10625 [astro-ph.CO]

work page internal anchor Pith review arXiv 2019
[9]

Knox and M

L. Knox and M. Millea, “Hubble constant hunter’s guide,”Phys. Rev. D101(2020) no. 4, 043533, arXiv:1908.03663 [astro-ph.CO]

work page arXiv 2020
[10]

Kamionkowski and A

M. Kamionkowski and A. G. Riess, “The Hubble Tension and Early Dark Energy,”Ann. Rev. Nucl. Part. Sci.73(2023) 153–180,arXiv:2211.04492 [astro-ph.CO]

work page arXiv 2023
[11]

Reconnaissance with JWST of the J-region Asymptotic Giant Branch in Distance Ladder Galaxies: From Irregular Luminosity Functions to Approximation of the Hubble Constant,

S. Li, A. G. Riess, S. Casertano, G. S. Anand, D. M. Scolnic, W. Yuan, L. Breuval, and C. D. Huang, “Reconnaissance with JWST of the J-region Asymptotic Giant Branch in Distance Ladder Galaxies: From Irregular Luminosity Functions to Approximation of the Hubble Constant,”Astrophys. J.966(2024) no. 1, 20, arXiv:2401.04777 [astro-ph.CO]

work page arXiv 2024
[12]

JWST Validates HST Distance Measurements: Selection of Supernova Subsample Explains Differences in JWST Estimates of Local H 0,

A. G. Riesset al., “JWST Validates HST Distance Measurements: Selection of Supernova Subsample Explains Differences in JWST Estimates of Local H 0,” Astrophys. J.977(2024) no. 1, 120,arXiv:2408.11770 [astro-ph.CO]

work page arXiv 2024
[13]

The Hubble Tension in Our Own Backyard: DESI and the Nearness of the Coma Cluster,

D. Scolnicet al., “The Hubble Tension in Our Own Backyard: DESI and the Nearness of the Coma Cluster,” Astrophys. J. Lett.979(2025) no. 1, L9, arXiv:2409.14546 [astro-ph.CO]

work page arXiv 2025
[14]

Breuval, A.G

L. Breuval, A. G. Riess, S. Casertano, W. Yuan, L. M. Macri, M. Romaniello, Y. S. Murakami, D. Scolnic, G. S. Anand, and I. Soszy´nski, “Small Magellanic Cloud Cepheids Observed with the Hubble Space Telescope Provide a New Anchor for the SH0ES Distance Ladder,”Astrophys. J.973(2024) no. 1, 30, arXiv:2404.08038 [astro-ph.CO]

work page arXiv 2024
[15]

5σtension between Planck cosmic microwave background and eBOSS Lyman-alpha forest and constraints on physics beyond ΛCDM,

K. K. Rogers and V . Poulin, “5σtension between Planck cosmic microwave background and eBOSS Lyman-alpha forest and constraints on physics beyond ΛCDM,”Phys. Rev. Res.7(2025) no. 1, L012018, arXiv:2311.16377 [astro-ph.CO]

work page arXiv 2025
[16]

Perivolaropoulos and A

Ruchika, L. Perivolaropoulos, and A. Melchiorri, “Effects of a local physics change on the SH0ES determination of H0,”Phys. Rev. D111(2025) no. 12, 123526,arXiv:2408.03875 [astro-ph.CO]

work page arXiv 2025
[17]

Age of Massive Galaxies at Redshift 8,

M. Lopez-Corredoira, F. Melia, J. J. Wei, and C. Y. Gao, “Age of Massive Galaxies at Redshift 8,”Astrophys. J. 970(2024) no. 1, 63,arXiv:2405.12665 [astro-ph.CO]

work page arXiv 2024
[18]

ΛCDM model against cosmography: a possible deviation after DESI 2024,

S. Pourojaghi, M. Malekjani, and Z. Davari, “ΛCDM model against cosmography: a possible deviation after DESI 2024,”Mon. Not. Roy. Astron. Soc.537(2025) no. 1, 436–447,arXiv:2408.10704 [astro-ph.CO]

work page arXiv 2024
[19]

Green and J

D. Green and J. Meyers, “Cosmological preference for a negative neutrino mass,”Phys. Rev. D111(2025) no. 8, 083507,arXiv:2407.07878 [astro-ph.CO]

work page arXiv 2025
[20]

Review of Hubble tension solutions with new SH0ES and SPT-3G data,

A. R. Khalife, M. B. Zanjani, S. Galli, S. G ¨unther, J. Lesgourgues, and K. Benabed, “Review of Hubble tension solutions with new SH0ES and SPT-3G data,” JCAP04(2024) 059,arXiv:2312.09814 [astro-ph.CO]

work page arXiv 2024
[21]

Hazra, B

D. K. Hazra, B. Beringue, J. Errard, A. Shafieloo, and G. F. Smoot, “Exploring the discrepancy between Planck PR3 and ACT DR4,”JCAP12(2024) 038, arXiv:2406.06296 [astro-ph.CO]

work page arXiv 2024
[22]

Modified Gravity and Cosmology

T. Clifton, P . G. Ferreira, A. Padilla, and C. Skordis, “Modified Gravity and Cosmology,”Phys. Rept.513 (2012) 1–189,arXiv:1106.2476 [astro-ph.CO]

work page internal anchor Pith review arXiv 2012
[23]

Cosmological Tests of Modified Gravity

K. Koyama, “Cosmological Tests of Modified Gravity,” Rept. Prog. Phys.79(2016) no. 4, 046902, arXiv:1504.04623 [astro-ph.CO]

work page Pith review arXiv 2016
[24]

Nojiri, S

S. Nojiri, S. D. Odintsov, and V . K. Oikonomou, “Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution,”Phys. Rept.692(2017) 1–104,arXiv:1705.11098 [gr-qc]

work page arXiv 2017
[25]

Koussour, N

M. Koussour, N. Myrzakulov, A. H. A. Alfedeel, and A. Abebe, “Constraining the cosmological model of modified f(Q) gravity: Phantom dark energy and observational insights,”PTEP2023(2023) no. 11, 113E01,arXiv:2310.15067 [astro-ph.CO]

work page arXiv 2023
[26]

Cosmological models in f(T,T) gravity and the dynamical system analysis,

L. K. Duchaniya, S. V . Lohakare, and B. Mishra, “Cosmological models in f(T,T) gravity and the dynamical system analysis,”Phys. Dark Univ.43(2024) 101402,arXiv:2302.07132 [gr-qc]

work page arXiv 2024
[27]

Cosmological Dynamics on a Novelf(Q) Gravity Model with Recent DESI DR2 Observation,

S. A. Kadam, D. R. Kumar, and S. K. Yadav, “Cosmological Dynamics on a Novelf(Q)Gravity 12 Model with Recent DESI DR2 Observation,” arXiv:2601.06438 [gr-qc]

work page arXiv
[28]

f(R) theories

A. De Felice and S. Tsujikawa, “f(R) theories,”Living Rev. Rel.13(2010) 3,arXiv:1002.4928 [gr-qc]

work page Pith review arXiv 2010
[29]

Scherer, M.A

M. Scherer, M. A. Sabogal, R. C. Nunes, and A. De Felice, “Challenging theΛCDM model: 5σ evidence for a dynamical dark energy late-time transition,”Phys. Rev. D112(2025) no. 4, 043513, arXiv:2504.20664 [astro-ph.CO]

work page arXiv 2025
[30]

Giar` e, M

W. Giar `e, M. Najafi, S. Pan, E. Di Valentino, and J. T. Firouzjaee, “Robust preference for Dynamical Dark Energy in DESI BAO and SN measurements,”JCAP10 (2024) 035,arXiv:2407.16689 [astro-ph.CO]

work page arXiv 2024
[31]

Constraints on dark matter-photon coupling in the presence of time-varying dark energy,

S. K. Yadav, “Constraints on dark matter-photon coupling in the presence of time-varying dark energy,” Mod. Phys. Lett. A35(2019) no. 04, 1950358, arXiv:1907.05886 [astro-ph.CO]

work page arXiv 2019
[32]

Late-time constraints on dynamical dark energy models using DESI DR2, Type Ia supernova, and CC measurements,

R. Nagpal, H. Chaudhary, H. Gupta, and S. K. J. Pacif, “Late-time constraints on dynamical dark energy models using DESI DR2, Type Ia supernova, and CC measurements,”JHEAp47(2025) 100396

2025
[33]

Testing an oscillatory behavior of dark energy,

L. A. Escamilla, S. Pan, E. Di Valentino, A. Paliathanasis, J. A. V´azquez, and W. Yang, “Testing an oscillatory behavior of dark energy,”Phys. Rev. D111(2025) no. 2, 023531,arXiv:2404.00181 [astro-ph.CO]

work page arXiv 2025
[34]

Dark energy models from a parametrization ofH: A comprehensive analysis and observational constraints,

S. K. J. Pacif, “Dark energy models from a parametrization ofH: A comprehensive analysis and observational constraints,”Eur. Phys. J. Plus135(2020) no. 10, 792,arXiv:2005.06972 [physics.gen-ph]

work page arXiv 2020
[35]

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

E. Abdallaet al., “Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies,”JHEAp34(2022) 49–211, arXiv:2203.06142 [astro-ph.CO]

work page internal anchor Pith review arXiv 2022
[36]

Precision constraints on new dark energy parametrization from DESI BAO DR2,

D. Revanth Kumar and S. K. Yadav, “Precision constraints on new dark energy parametrization from DESI BAO DR2,”arXiv:2603.26861 [astro-ph.CO]

work page arXiv
[37]

Capozziello, Curvature quintessence, Int

S. Capozziello, “Curvature quintessence,”Int. J. Mod. Phys. D11(2002) 483–492,arXiv:gr-qc/0201033

work page arXiv 2002
[38]

Interacting quintessence,

W. Zimdahl and D. Pavon, “Interacting quintessence,” Phys. Lett. B521(2001) 133–138, arXiv:astro-ph/0105479

work page arXiv 2001
[39]

Coupled Quintessence

L. Amendola, “Coupled quintessence,”Phys. Rev. D62 (2000) 043511,arXiv:astro-ph/9908023

work page Pith review arXiv 2000
[40]

Effects of anisotropy in an anisotropic extension of wCDM model,

V . Yadav, S. K. Yadav, and Rajpal, “Effects of anisotropy in an anisotropic extension of wCDM model,”Phys. Dark Univ.46(2024) 101626,arXiv:2402.16885 [astro-ph.CO]

work page arXiv 2024
[41]

Observational constraints on a generalized equation of state model,

M. Koussour, S. Bekov, A. Syzdykova, S. Muminov, I. Ibragimov, and J. Rayimbaev, “Observational constraints on a generalized equation of state model,” Phys. Dark Univ.47(2025) 101799,arXiv:2412.20073 [astro-ph.CO]

work page arXiv 2025
[42]

Properties of singularities in (phantom) dark energy universe

S. Nojiri, S. D. Odintsov, and S. Tsujikawa, “Properties of singularities in (phantom) dark energy universe,” Phys. Rev. D71(2005) 063004, arXiv:hep-th/0501025

work page Pith review arXiv 2005
[43]

Phantom energy and cosmic doomsday,

R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, “Phantom energy and cosmic doomsday,”Phys. Rev. Lett.91(2003) 071301,arXiv:astro-ph/0302506

work page arXiv 2003
[44]

Kinetically Driven Quintessence

T. Chiba, T. Okabe, and M. Yamaguchi, “Kinetically driven quintessence,”Phys. Rev. D62(2000) 023511, arXiv:astro-ph/9912463

work page Pith review arXiv 2000
[45]

Observational constraints on dynamical dark energy with pivoting redshift,

W. Yang, S. Pan, E. Di Valentino, and E. N. Saridakis, “Observational constraints on dynamical dark energy with pivoting redshift,”Universe5(2019) no. 11, 219, arXiv:1811.06932 [astro-ph.CO]

work page arXiv 2019
[46]

Exploring Universe acceleration through observational constraints via Hubble parameter reconstruction,

M. Koussour, N. Myrzakulov, and M. K. M. Ali, “Exploring Universe acceleration through observational constraints via Hubble parameter reconstruction,” JHEAp42(2024) 96–103,arXiv:2404.03362 [astro-ph.CO]

work page arXiv 2024
[47]

Park and B

C.-G. Park and B. Ratra, “Is excess smoothing of Planck CMB anisotropy data partially responsible for evidence for dark energy dynamics in other w(z)CDM parametrizations?,”Int. J. Mod. Phys. D34(2025) no. 13, 2550061,arXiv:2501.03480 [astro-ph.CO]

work page arXiv 2025
[48]

Armendariz-Picon, V

C. Armendariz-Picon, V . F. Mukhanov, and P . J. Steinhardt, “A Dynamical solution to the problem of a small cosmological constant and late time cosmic acceleration,”Phys. Rev. Lett.85(2000) 4438–4441, arXiv:astro-ph/0004134

work page arXiv 2000
[49]

An Alternative to quintessence,

A. Y. Kamenshchik, U. Moschella, and V . Pasquier, “An Alternative to quintessence,”Phys. Lett. B511(2001) 265–268,arXiv:gr-qc/0103004

work page arXiv 2001
[50]

Tachyon matter,

A. Sen, “Tachyon matter,”JHEP07(2002) 065, arXiv:hep-th/0203265

work page arXiv 2002
[51]

A Model of holographic dark energy,

M. Li, “A Model of holographic dark energy,”Phys. Lett. B603(2004) 1,arXiv:hep-th/0403127

work page arXiv 2004
[52]

The effects of a varying cosmological constant on the particle horizon,

A. M. Oztas, “The effects of a varying cosmological constant on the particle horizon,”Mon. Not. Roy. Astron. Soc.481(2018) no. 2, 2228–2234

2018
[53]

Consequences on variable Lambda models from distant type Ia supernovae and compact radio sources,

R. G. Vishwakarma, “Consequences on variable Lambda models from distant type Ia supernovae and compact radio sources,”Class. Quant. Grav.18(2001) 1159–1172,arXiv:astro-ph/0012492

work page arXiv 2001
[54]

Evolution of the scale factor with a variable cosmological term,

J. M. Overduin and F. I. Cooperstock, “Evolution of the scale factor with a variable cosmological term,”Phys. Rev. D58(1998) 043506,arXiv:astro-ph/9805260

work page arXiv 1998
[55]

Cosmological Consequences of a Variable Cosmological Constant Model,

H. Azri and A. Bounames, “Cosmological Consequences of a Variable Cosmological Constant Model,”Int. J. Mod. Phys. D26(2017) no. 7, 1750060, arXiv:1412.7567 [gr-qc]

work page arXiv 2017
[56]

Geometrical Origin of the Cosmological Constant,

H. Azri and A. Bounames, “Geometrical Origin of the Cosmological Constant,”Gen. Rel. Grav.44(2012) 2547–2561,arXiv:1007.1948 [gr-qc]

work page arXiv 2012
[57]

Cosmological model with decaying vacuum energy from quantum mechanics,

M. Szydłowski, “Cosmological model with decaying vacuum energy from quantum mechanics,”Phys. Rev. D 91(2015) no. 12, 123538,arXiv:1502.04737 [astro-ph.CO]

work page arXiv 2015
[58]

Bruni, R

M. Bruni, R. Maier, and D. Wands, “Nonsingular cosmology from an interacting vacuum,”Phys. Rev. D 13 105(2022) no. 6, 063532,arXiv:2111.01765 [gr-qc]

work page arXiv 2022
[59]

Dynamics and cosmological evolution inΛ-varying cosmology,

G. Papagiannopoulos, P . Tsiapi, S. Basilakos, and A. Paliathanasis, “Dynamics and cosmological evolution inΛ-varying cosmology,”Eur. Phys. J. C80 (2020) no. 1, 55,arXiv:1911.12431 [gr-qc]

work page arXiv 2020
[60]

Looking for interactions in the cosmological dark sector,

M. Benetti, W. Miranda, H. A. Borges, C. Pigozzo, S. Carneiro, and J. S. Alcaniz, “Looking for interactions in the cosmological dark sector,”JCAP12(2019) 023, arXiv:1908.07213 [astro-ph.CO]

work page arXiv 2019
[61]

First evidence of running cosmic vacuum: challenging the concordance model

J. Sol `a, A. G´omez-Valent, and J. de Cruz P´erez, “First evidence of running cosmic vacuum: challenging the concordance model,”Astrophys. J.836(2017) no. 1, 43, arXiv:1602.02103 [astro-ph.CO]

work page Pith review arXiv 2017
[62]

Possible signals of vacuum dynamics in the Universe

J. Sol `a Peracaula, J. de Cruz P´erez, and A. Gomez-Valent, “Possible signals of vacuum dynamics in the Universe,”Mon. Not. Roy. Astron. Soc. 478(2018) no. 4, 4357–4373,arXiv:1703.08218 [astro-ph.CO]

work page Pith review arXiv 2018
[63]

Testing dynamical vacuum models with CMB power spectrum from Planck,

P . Tsiapi and S. Basilakos, “Testing dynamical vacuum models with CMB power spectrum from Planck,”Mon. Not. Roy. Astron. Soc.485(2019) no. 2, 2505–2510, arXiv:1810.12902 [astro-ph.CO]

work page arXiv 2019
[64]

Mavromatos and J

N. E. Mavromatos and J. Sol `a Peracaula, “Stringy-running-vacuum-model inflation: from primordial gravitational waves and stiff axion matter to dynamical dark energy,”Eur. Phys. J. ST230(2021) no. 9, 2077–2110,arXiv:2012.07971 [hep-ph]

work page arXiv 2021
[65]

Sola Peracaula, A

J. Sola Peracaula, A. Gomez-Valent, J. de Cruz Perez, and C. Moreno-Pulido, “Running Vacuum in the Universe: Phenomenological Status in Light of the Latest Observations, and Its Impact on theσ 8 and H0 Tensions,”Universe9(2023) no. 6, 262, arXiv:2304.11157 [astro-ph.CO]

work page arXiv 2023
[66]

Running vacuum in quantum field theory in curved spacetime: renormalizingρ vac without∼m 4 terms,

C. Moreno-Pulido and J. Sola, “Running vacuum in quantum field theory in curved spacetime: renormalizingρ vac without∼m 4 terms,”Eur. Phys. J. C 80(2020) no. 8, 692,arXiv:2005.03164 [gr-qc]

work page arXiv 2020
[67]

Moreno-Pulido and J

C. Moreno-Pulido and J. Sola Peracaula, “Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem,”Eur. Phys. J. C82(2022) no. 6, 551, arXiv:2201.05827 [gr-qc]

work page arXiv 2022
[68]

Moreno-Pulido and J

C. Moreno-Pulido and J. Sola Peracaula, “Equation of state of the running vacuum,”Eur. Phys. J. C82(2022) 1137,arXiv:2207.07111 [gr-qc]

work page arXiv 2022
[69]

Running vacuum in QFT in FLRW spacetime: the dynamics ofρ vac(H)from the quantized matter fields,

C. Moreno-Pulido, J. Sola Peracaula, and S. Cheraghchi, “Running vacuum in QFT in FLRW spacetime: the dynamics ofρ vac(H)from the quantized matter fields,” Eur. Phys. J. C83(2023) no. 7, 637,arXiv:2301.05205 [gr-qc]

work page arXiv 2023
[70]

Sol` a Peracaula,The cosmological constant problem and running vacuum in the expanding universe,Phil

J. Sola Peracaula, “The cosmological constant problem and running vacuum in the expanding universe,”Phil. T rans. Roy. Soc. Lond. A380(2022) 20210182, arXiv:2203.13757 [gr-qc]

work page arXiv 2022
[71]

A New cosmological constant model,

J. L. Lopez and D. V . Nanopoulos, “A New cosmological constant model,”Mod. Phys. Lett. A11 (1996) 1–7,arXiv:hep-ph/9501293

work page arXiv 1996
[72]

Implications of a cosmological constant varying as R**(-2),

W. Chen and Y. S. Wu, “Implications of a cosmological constant varying as R**(-2),”Phys. Rev. D41(1990) 695–698. [Erratum: Phys.Rev.D 45, 4728 (1992)]

1990
[73]

A possible solution to the main cosmological problems,

M. Ozer and M. O. Taha, “A possible solution to the main cosmological problems,”Phys. Lett. B171(1986) no. 4, 363–365

1986
[74]

A model of the universe free of cosmological problems,

M. Ozer and M. O. Taha, “A model of the universe free of cosmological problems,”Nucl. Phys. B287(1987) 776–796

1987
[75]

Constraints onΛ(t)CDM cosmology using cosmic chronometers and supernova data,

Y. Myrzakulov, M. Koussour, M. Bulanbay, S. Muminov, and J. Rayimbaev, “Constraints onΛ(t)CDM cosmology using cosmic chronometers and supernova data,”Chin. J. Phys.94(2025) 287–297,arXiv:2501.07099 [astro-ph.CO]

work page arXiv 2025
[76]

Signature flips in time-varyingΛ(t) cosmological models with observational data,

Y. Myrzakulov, M. Koussour, M. Karimov, and J. Rayimbaev, “Signature flips in time-varyingΛ(t) cosmological models with observational data,”Eur. Phys. J. C84(2024) no. 7, 665,arXiv:2407.07535 [astro-ph.CO]

work page arXiv 2024
[77]

Cosmological constraints onΛ(t)CDM models,

H. A. P . Macedo, L. S. Brito, J. F. Jesus, and M. E. S. Alves, “Cosmological constraints onΛ(t)CDM models,”Eur. Phys. J. C83(2023) no. 12, 1144, arXiv:2305.18591 [astro-ph.CO]

work page arXiv 2023
[78]

Linear Growth of Matter Perturbations Probed by Redshift-Space Distortions in InteractingΛ(t)CDM Cosmologies,

A. A. Escobal, H. A. P . Macedo, J. F. Jesus, R. C. Nunes, and J. A. S. Lima, “Linear Growth of Matter Perturbations Probed by Redshift-Space Distortions in InteractingΛ(t)CDM Cosmologies,” arXiv:2602.11310 [astro-ph.CO]

work page arXiv
[79]

Kinematic reconstruction ofΛ(t)CDM models,

P . A. S. Guillen, J. F. Jesus, and R. Valentim, “Kinematic reconstruction ofΛ(t)CDM models,”Phys. Dark Univ.52 (2026) 102258,arXiv:2512.14578 [astro-ph.CO]

work page arXiv 2026
[80]

GetDist: a Python package for analysing Monte Carlo samples

A. Lewis, “GetDist: a Python package for analysing Monte Carlo samples,”JCAP08(2025) 025, arXiv:1910.13970 [astro-ph.IM]

work page internal anchor Pith review arXiv 2025

Showing first 80 references.