Is Dark Energy an Effective Manifestation of Non-equilibrium Thermodynamics? -- Insights from DESI

Emmanuel N. Saridakis; Jaume de Haro; Sauvik Bhattacharjee; Sudip Halder; Supriya Pan

REVIEW 3 major objections 5 minor 2 cited by

Is Dark Energy an Effective Manifestation of Non-equilibrium Thermodynamics? -- Insights from DESI

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Cosmic acceleration can arise from adiabatic particle creation in the dark matter sector, and the fitted creation rates are non-zero at many standard deviations across CC, supernova, and DESI BAO data.

desk verdict A competent background study whose headline claim is not supported by its own results: Model I is LambdaCDM in disguise, Model II is only mildly preferred by a few dataset combos, and no perturbation test is attempted. read the letter →

arxiv 2507.15575 v2 pith:EBG7UEDU submitted 2025-07-21 astro-ph.CO gr-qc

Sauvik Bhattacharjee , Sudip Halder , Jaume de Haro , Supriya Pan , Emmanuel N. Saridakis This is my paper

classification astro-ph.COgr-qc PACS 98.80.-k95.35.+d95.36.+x

keywords darkenergyadiabaticparticlecreationpressuredynamicalmatterDESIBAOΛCDMcosmologycosmicaccelerationbackground

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

The paper proposes that the late-time accelerated expansion of the universe need not be caused by dark energy or modified gravity: it can emerge from adiabatic particle creation in the dark matter sector, which generates a negative 'creation pressure' that pushes the expansion. The authors study two creation rates, $\Gamma = 3\alpha H(\rho_{c,0}/\rho_{\rm dm})$ and $\Gamma = 3\alpha H(\rho_{c,0}/\rho_{\rm dm})^l$, and show by dynamical-systems analysis that both reproduce the radiation-to-matter-to-acceleration sequence of $\Lambda$CDM. Fitting to Cosmic Chronometers, three supernova samples, and DESI BAO DR1/DR2, they find the creation amplitude $\alpha$ is non-zero at many standard deviations in both models. Model I is statistically indistinguishable from $\Lambda$CDM, while Model II is preferred over $\Lambda$CDM when DESI BAO data are included, consistent with DESI's own hints of dynamical dark energy. A sympathetic reader would care because a positive creation rate with no cosmological constant is a genuinely different physical mechanism that current expansion data do not exclude.

What carries the argument

The load-bearing mechanism is the adiabatic creation pressure $p_c = -(\Gamma/3H)\rho_{\rm dm}$, derived from the thermodynamic relation for a fluid whose particle number changes isentropically; it modifies only the dark matter continuity equation while the total stress-energy tensor stays conserved. The two rates studied are $\Gamma = 3\alpha H(\rho_{c,0}/\rho_{\rm dm})$ (Model I) and $\Gamma = 3\alpha H(\rho_{c,0}/\rho_{\rm dm})^l$ (Model II), which admit exact analytic solutions for $\rho_{\rm dm}$ whose constant asymptotic piece acts as an effective cosmological constant. The phase-space analysis in variables $(\Omega_{\rm dm}, \Omega_r, \xi = H_0/(H_0+H))$ shows that the physically accepted branch always flows from a radiation-dominated unstable point through a decelerating matter era to a stable de Sitter-like attractor, while phantom-like branches suffer early acceleration and are discarded.

What would settle it

A concrete test is to compute the linear matter growth predicted by the modified dark-matter continuity equation with the best-fit parameters and compare it against redshift-space distortion measurements such as $f\sigma_8(z)$; if the creation pressure suppresses or enhances structure growth beyond what current clustering data allow, the models would be ruled out despite their good background fit. A full CMB likelihood analysis that includes the effective dark-matter equation of state would settle the question.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the observed background expansion is consistent with a universe in which dark matter particles are continually created by the gravitational field, and that this creation is what accelerates the expansion at late times. The creation process enters as a creation pressure $p_c = -(\Gamma/3H)\rho_{\rm dm}$ in the dark matter continuity equation $\dot{\rho}_{\rm dm} + 3H\rho_{\rm dm} = \Gamma\rho_{\rm dm}$, which is equivalent to giving dark matter a dynamical equation of state $w_{\rm dm} = -\Gamma/3H$. For Model I this equation solves exactly to $\rho_{\rm dm} = \alpha\rho_{c,0} + (\rho_{{\rm dm},0}-\alpha\rho_{c,0})(1+z)^3$, whose constant piece plays precisely the role of a cosmological constant, so the model reproduces $\Lambda$CDM's expansion history with no vacuum energy at all. Model II generalizes this with an exponent and, fitted to DESI BAO DR2 combined with supernova samples, prefers $l \neq 1$, a genuine departure from $\Lambda$CDM, while still describing the full thermal history from radiation domination through matter-dominated deceleration to a de Sitter-like attractor. The authors conclude that matter creation is an observationally viable alternative to both dark energy and modified gravity at the background level.

Load-bearing premise

The whole analysis lives at the background level: the paper assumes that the same creation process, once perturbations are included, will not alter the growth of cosmic structure in a way that contradicts CMB or galaxy-clustering observations, a check the authors explicitly defer to future work.

Editorial extensions

If this is right

Late-time cosmic acceleration can be produced without a cosmological constant or modified gravity, purely by a positive particle-creation rate in the dark matter sector.
Both models require $\alpha \neq 0$ at many standard deviations, so matter creation is strongly favoured over no creation; Model I is statistically equivalent to $\Lambda$CDM while Model II is preferred over $\Lambda$CDM when DESI BAO data are included.
The preference for $l \neq 1$ in Model II with DESI DR2 data gives a physical interpretation of DESI's dynamical dark energy hint: what looks like evolving dark energy could be an emergent creation pressure.
Data combinations involving the DESY5 supernova sample push the inferred $H_0$ to about 70 km/s/Mpc, suggesting matter creation could ease the Hubble tension, although only a perturbation-level analysis can confirm this.
The phase-space analysis shows which branches of Model II are physically viable: only the $\Lambda$CDM-like branch survives, since phantom-like branches suffer unacceptably early acceleration.

Reading between the lines

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

The decisive arena for these models is perturbative: the effective dark-matter equation of state $w_{\rm dm} = -\Gamma/3H$ will change the sound speed and growth of dark-matter fluctuations, so CMB lensing, $f\sigma_8$ data, and the matter power spectrum should discriminate matter-creation cosmologies from $\Lambda$CDM even where the background fits are identical.
The near-degeneracy of Model I with $\Lambda$CDM suggests current background probes are close to their limit for detecting creation; the testable distinction shifts to non-linear structure, gravitational lensing, and the dark-matter halo mass function.
A model-agnostic check would be to promote $\alpha$ or $l$ to functions of redshift and compare against the DESI $(w_0, w_a)$ contours, which would show whether the creation-pressure interpretation is kinematically distinct from evolving dark-energy parameterizations.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, this is a careful, reproducible background-level study of adiabatic matter creation models. The analytic solutions in the appendices are clean, the MCMC uses public likelihoods, and the phase-space analysis is thorough. Model II, the power-law generalization of the LJO rate, is the genuinely new piece, and the DESI DR2 constraints on it are new. Second, the headline claim does not survive contact with the paper's own tables. Model I is exactly LambdaCDM with alpha playing the role of Omega_Lambda (Eq. 34), so its "evidence of matter creation at many standard deviations" is just evidence for a constant energy density. That is not a flaw in the math, but it is a flaw in how the result is framed. The abstract also overstates Model II: only three of nine dataset combinations give Delta chi2 > 3.84, and the BIC favors LambdaCDM in eight of nine. "When DESI data are included" is doing a lot of work.

The stress-test note is fair, and I do not think it overreaches. The modified dark-matter conservation equation (21) will change perturbation growth. The paper explicitly defers perturbation analysis and CMB confrontation in Section VI, which is honest, but the title and abstract imply an alternative to dark energy, not a background degeneracy. Without growth or CMB constraints, these models are not alternatives; they are reparameterizations with a promising extension that needs testing.

What the paper does well: the generalized creation rate, the phase-space stability analysis (including the tricky l<0 and l=0 cases), and the data confrontation itself are all solid. The authors correctly note that l=1 recovers LambdaCDM and that the perturbation analysis is future work.

The soft spots are interpretive and proportionate: the Model I equivalence is not highlighted enough, the abstract oversells Model II, and the missing perturbation analysis is a load-bearing gap, not a minor omission. These are addressable in revision.

Verdict: this deserves a serious referee. The model space and the DESI DR2 constraints are worth having in the literature, and the analysis is reproducible. A good referee should ask for a corrected abstract, an explicit statement that alpha in Model I is a relabeling of Omega_Lambda, and a clear caveat that physical viability requires perturbation-level testing. I would send it out.

Referee Report

3 major / 5 minor

Summary. The manuscript investigates two adiabatic matter-creation cosmologies as alternatives to dark energy and modified gravity, motivated by the recent DESI DR2 BAO data. Model I uses the Lima-Jesus-Oliveira creation rate Gamma = 3 alpha H (rho_c0/rho_dm), while Model II generalizes it to Gamma = 3 alpha H (rho_c0/rho_dm)^l. The paper derives analytical solutions for the dark-matter density and Hubble rate, performs a dynamical-system analysis for both models (including sub-cases of l), and fits the models to Cosmic Chronometer, Pantheon+, DESY5, Union3, and DESI DR1/DR2 data using MCMC. The authors report evidence for matter creation at many standard deviations in both models, find Model I statistically equivalent to LambdaCDM, and claim that for DESI-including datasets Model II is favored over LambdaCDM. The paper explicitly states that perturbation-level analysis and CMB confrontation are left to future work.

Significance. If the results held, the paper would provide a background-level proof of concept that adiabatic particle creation can mimic LambdaCDM and, for l != 1, produce a dynamical dark-energy-like expansion. The analytical solutions and dynamical-system classification are carried out carefully, and the observational analysis uses standard public likelihoods with transparent MCMC implementation and model-comparison tables. The main significance is limited by two facts: for Model I the Friedmann equation is exactly LambdaCDM with alpha playing the role of Omega_Lambda, so the reported 'evidence of matter creation' is a restatement of evidence for a cosmological-constant-like term; and the physical viability of the models as alternatives to dark energy is not tested at the perturbation level. The paper is honest about this limitation, but the abstract and conclusions currently claim more than the background analysis can support.

major comments (3)

[III.A, Eq. (34), and V.A] The claim that Model I shows 'evidence of matter creation at many standard deviations' is not supported by the model structure. Substituting the analytical solution (33) into the Friedmann equation yields Eq. (34), which is exactly the LambdaCDM expansion history with alpha playing the role of Omega_Lambda. Consequently, the posteriors in Table IV measure a cosmological-constant-like energy density, not a particle-creation mechanism; the same applies to Model II at l = 1 and, via Omega_eff^Lambda approximately alpha^(1/l) in Eq. (40), approximately for general l. The abstract should be rewritten to avoid implying that a detection of alpha != 0 constitutes evidence for the creation process itself.
[VI, Eqs. (21)-(24)] The viability of the models as alternatives to dark energy is not established without a perturbation analysis. The creation pressure p_c = -Gamma rho_dm/(3H) enters the second Friedmann equation, and the modified dark-matter continuity equation (21) changes the perturbed conservation laws; linearizing the rates in Eqs. (32) and (37) introduces delta-Gamma contributions that can modify the growth of structure, possibly in a scale-dependent way, and can produce instabilities or altered f sigma_8 values. Since the paper explicitly defers this analysis ('one should extend the analysis beyond the background level...'), the headline claim that matter creation is a viable alternative to dark energy is currently a background degeneracy statement. I request either a quantitative perturbation analysis (e.g., growth index, f sigma_8, CMB TT/TE/EE, lensing) or a substantial toning-down of the physical-viability claims.
[Abstract and V.B / Table VII] The abstract's statement that 'when DESI data are included matter creation Model II is favoured over LambdaCDM' is stronger than the results. In Table VII only three of the nine dataset combinations satisfy Delta chi^2_min > 3.84, and only CC+U3+D-DR2 has a positive Delta BIC, with Delta BIC = 0.28, which is weak evidence. The body correctly describes the outcome as 'a mixed picture.' The abstract and the concluding paragraph should be revised to reflect that Model II is preferred only in some DESI-including combinations and only by LRT/AIC, not by BIC for most combinations.

minor comments (5)

[III.B, Table II] The entries for the 0<l<1 case contain two points labeled B1, and the text refers to both as 'B1'; renumber the second as B2 and adjust the discussion accordingly.
[IV.3] The DESI DR2 description says 13 data points from 7 redshift bins, but the text earlier mentions 7 redshift bins with D_M/r_d, D_H/r_d, and D_V/r_d; clarify the exact counting.
[V.B] The likelihood-ratio-test threshold reference [152,153] is nonstandard; cite a standard statistics reference for the chi-square threshold.
[Tables IV-VII] The notation 'D-DR1' and 'D-DR2' is confusing; use 'DESI-DR1' and 'DESI-DR2' consistently.
[IV, priors] The MCMC prior l ~ U(-1,1.2) includes the l<0 region that Section III.B.3 identifies as 'not physically interesting' because of early acceleration; if these regions are excluded on physical grounds, the prior should be truncated to l>0 to avoid mixing theoretically disfavored solutions with the fitted posterior.

Circularity Check

1 steps flagged · score 6.0 of 10

The 'evidence of matter creation' is the ΛCDM constant term relabeled: for Model I the fitted α is exactly Ω_Λ by Eq. (34), so the headline detection is a relabeling, not an independent result.

renaming known result [Section V.A (parameter interpretation) and Section III.A, Eq. (34)]
"Recall that for both the models, α̸= 0 indicates the evidence of matter creation ... The first Friedmann equation (23) can be written as (H/H0)^2 = α+(Ω_dm,0−α)(1+z)^3+Ω_b,0(1+z)^3+Ω_r,0(1+z)^4."

Model I's rate (32), Γ=3αHρ_c0/ρ_dm, converts the DM continuity equation into dρ_dm/dt+3Hρ_dm=3αHρ_c0, whose solution (33) is ρ_dm=(ρ_dm,0−αρ_c0)a^−3+αρ_c0. Substituting into the Friedmann equation gives Eq. (34), which is exactly ΛCDM with α playing the role of Ω_Λ. The parameter α fitted to CC, SNIa, and DESI-BAO data is therefore not an independent 'matter creation' amplitude; it is the same constant energy-density term already present in ΛCDM. The abstract's claim 'we find evidence of matter creation at many standard deviations' is logically the same statement as 'the data prefer a non-zero cosmological constant,' merely relabeled as a creation-rate parameter.

full rationale

The paper's thermodynamic setup, continuity equations, and dynamical-system analysis are internally self-contained, and the model is not derived from a self-citation chain: the core creation-rate ansätze trace to external work by Lima et al., and the authors' self-citations appear mainly as methodological references (e.g., [117,118]) or related-model studies, none of which is load-bearing for the central claim. The main circular element is at the interpretation level: because Model I's expansion history is mathematically identical to ΛCDM with α=Ω_Λ, the fitted 'evidence of matter creation' is the known cosmological-constant evidence under a new parameter name. The paper itself acknowledges this mimicry ('the above solution naturally generates a constant term which resembles a cosmological constant term') and that Model I is statistically equivalent to ΛCDM, but the abstract nevertheless presents the non-zero α of both models as evidence for matter creation. This is a partial circularity: a fitted parameter that is, by construction, the ΛCDM constant-density parameter is relabeled as a detection of a new physical mechanism. The acknowledged absence of a perturbation analysis (Section VI) is a completeness and viability gap rather than a circularity, and it does not further increase the circularity score.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The paper does not introduce new particles, forces, or conserved quantities; the matter creation process is adopted from prior work. The central claim rests on the phenomenological creation rates and the assumption that the background-only analysis is sufficient, plus the standard FLRW/GR framework.

free parameters (4)

alpha (creation rate amplitude) = 0.65-0.72 depending on dataset (e.g., 0.670 +/- 0.018 for CC+PP in Model I)
Amplitude of the creation rate in Eqs. (32) and (37); effectively becomes the constant energy density term in the Friedmann equation. Fitted to all datasets.
l (power-law exponent) = 0.65-0.89 depending on dataset (e.g., 0.830 +0.220/-0.170 for CC+PP in Model II)
Exponent in the generalized creation rate (37); controls deviation from LambdaCDM (l=1). Fitted to data.
H0 = ~67.7-70.5 km/s/Mpc
Hubble constant, fitted jointly.
M (SNIa absolute magnitude) = 23.78-23.81
Nuisance parameter in the SNIa likelihood, fitted.

assumptions (7)

standard math FLRW metric and general relativity with minimal matter coupling
Section II, Eqs. (1)-(2).
domain assumption Creation pressure ansatz p_c = -(Gamma/(3H))(rho_dm+p_dm) and adiabaticity (alpha=1 in Eq. 13)
Section II, Eqs. (13)-(17), adopted from Calvao-Lima-Waga; not derived in this paper.
ad hoc to paper Specific creation rate choices Gamma=3*alpha*H*(rho_c0/rho_dm) and Gamma=3*alpha*H*(rho_c0/rho_dm)^l
Eqs. (32) and (37); phenomenological choices that guarantee a constant term in the dark matter density, producing acceleration.
domain assumption Radiation and baryons follow standard conservation laws with no interaction with dark matter
Eqs. (19)-(20).
domain assumption Dark matter equilibrium pressure is zero
Section II, p_dm=0 in Eq. (17).
standard math The physical domain 0 <= x <= 1, 0 <= y <= 1, 0 <= xi <= 1, x+y <= 1 and positive invariance
Section III, Eq. (28); used for phase-space analysis.
ad hoc to paper Perturbations around the background are not treated and are assumed not to invalidate the model
Section VI leaves perturbation analysis to future work; this is an unstated assumption of the paper's viability claim.

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Cite this review

Pith. "Pith review of Is Dark Energy an Effective Manifestation of Non-equilibrium Thermodynamics? -- Insights from DESI." pith.science (2026). https://pith.science/paper/EBG7UEDU

@misc{pith2026250715575,
  author       = {Pith},
  title        = {Pith review of: Is Dark Energy an Effective Manifestation of Non-equilibrium Thermodynamics? -- Insights from DESI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EBG7UEDU}},
  note         = {Machine review of arXiv:2507.15575}
}

abstract

We investigate the background cosmological expansion on the onset of cosmological homogeneous matter creation scenario, a dynamical dark matter approach ($w_{\rm dm} \neq 0$), and an alternative approach to both dark energy and modified gravity theories, after the recent DESI DR2-BAO release. We consider that the total matter sector consists of three independently evolving components, namely, radiation, baryons, and dark matter, with the latter being governed by an adiabatic matter creation process, affects the background homogeneously, leads to a modified continuity equation. Though the total stress-energy tensor is conserved the only violation of the conservation law in the dark matter sector is coming from the creation pressure, and under a proper choice of dark-matter particle creation rate one can obtain the present accelerating phase as well as the past thermal history of the Universe. We study two specific matter creation rates. By applying the dynamical-system analysis we show that both Model I and Model II can mimic a $\Lambda$CDM-like behavior. Furthermore, we perform a detailed observational confrontation using a series of latest observational datasets including Cosmic Chronometers (CC), Supernovae Type Ia (SNIa) (Pantheon+, DESY5 and Union3 samples) and DESI Baryon Acoustic Oscillations (BAO) (DR1 and DR2 samples). In both Model I and Model II we find evidence of matter creation at many standard deviations. Finally, applying the AIC and BIC information criteria we find that Model I is statistically equivalent with $\Lambda$CDM scenario, while Model II shows a mixed picture, namely for most datasets $\Lambda$CDM scenario is favoured, however when DESI data are included matter creation Model II is favoured over $\Lambda$CDM paradigm.

Figures

Figures reproduced from arXiv: 2507.15575 by the authors.

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

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

Figures from the paper (7 more)

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: we show the evolution of the density parameters and the deceleration parameter. The fact that q becomes negative very early, i.e. the system exhibits an early acFIG. 10. Summary plot of the obtained results. The horizontal and vertical directions are the deceleration…

**Figure 11.** Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

**Figure 12.** Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]

**Figure 14.** Figure 14: FIG. 14. Posterior distributions and two-dimensional joint likelihood contours for different supernovae data with the DESI [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]

**Figure 15.** Figure 15: FIG. 15. Posterior distributions and two-dimensional joint likelihood contours for different supernovae data with the DESI [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]

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Works this paper leans on

159 extracted references · 18 canonical work pages · cited by 2 Pith papers

[1]

Case0< l <1 In this parametric domain the system (41) possesses only one singularity atξ= 1. Multiplying with (1−ξ) 2l yields the autonomous system x′ =xy(1−ξ) 2l + 3αx1−l(1−x)ξ 2l,(43a) y′ =y (y−1)(1−ξ) 2l −3αx 1−lξ2l ,(43b) ξ′ = 3 2 ξ(1−ξ) h 1 + y 3 (1−ξ) 2l −αx 1−lξ2l i .(43c) From the above dynamical system we acquire the follow- ing invariant manifol...
[2]

In contrast to the previous case,x= 0 does not form an invariant manifold

Casel >1 In this case the system (41) simplifies as x′ =xly(1−ξ) 2l + 3α(1−x)ξ 2l,(44a) y′ =y xl−1(y−1)(1−ξ) 2l −3αξ 2l ,(44b) ξ′ = 3 2 ξ(1−ξ) h xl−1 1 + y 3 (1−ξ) 2l −αξ 2l i .(44c) The planesy= 0,ξ= 0,ξ= 1 andx+y= 1 constitute the invariant manifolds in the phase space. In contrast to the previous case,x= 0 does not form an invariant manifold. However, ...
[3]

The criti- cal points and their properties are presented in Table II

Casel <0 In this case the autonomous system takes the form x′ =xyξ −2l + 3αx1−l(1−x)(1−ξ) 2l,(45a) y′ =y (y−1)ξ 2l −3αx 1−l(1−ξ) 2l ,(45b) ξ′ = 3 2 ξ(1−ξ) h (1 + y 3 )ξ2l −αx 1−l(1−ξ) 2l i ,(45c) and the planesx= 0,y= 0,ξ= 0,ξ= 1 and x+y= 1 constitute invariant manifolds, making the phase space domainRpositively invariant. The criti- cal points and their ...
[4]

Triangle

Casel= 0 In the casel= 0 the autonomous system simplifies significantly, since Γ = 3αH, namely it becomes x′ =xy+ 3αx(1−x),(46a) y′ =y(y−1−3αx),(46b) ξ′ = 3 2 ξ(1−ξ) 1 + y 3 −αx .(46c) The reduced system possesses five invariant manifolds, namelyx= 0,y= 0,ξ= 0,ξ= 1 andx+y= 1, ensuring that the phase space domainRagain remains positively invariant. In Tabl...
[5]

Theχ 2 is defined as,χ 2 = P i HCC,i−Hmodel,i σi 2 , where ‘i’ denotes the redshift values

Hubble data from Cosmic Chronometers (CC): We use 34 measurements of the Hubble parame- ter at different redshifts using the CC approach, displayed in Table III. Theχ 2 is defined as,χ 2 = P i HCC,i−Hmodel,i σi 2 , where ‘i’ denotes the redshift values
[6]

A way of making Europe

Type Ia Supernovae (SNIa): We use three distinct 11 z H(z)σ H(z) Ref. z H(z)σ H(z) Ref. 0.07 69.0 19.6 [120] 0.48 97.0 62.0 [121] 0.09 69.0 12.0 [122] 0.5929 104.0 13.0 [123] 0.12 68.6 26.2 [120] 0.6797 92.0 8.0 [123] 0.17 83.0 8.0 [124] 0.75 98.8 33.6 [125] 0.1791 75.0 4.0 [123] 0.7812 105.0 12.0 [123] 0.1993 75.0 5.0 [123] 0.80 113.1 25.22 [126] 0.20 72...

arXiv 1993
[7]

Di Valentino, O

E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri, D. F. Mota, A. G. Riess, and J. Silk, In the realm of the Hubble tension—a review of solutions, Class. Quant. Grav.38, 153001 (2021), arXiv:2103.01183 [astro-ph.CO]

arXiv 2021
[8]

Perivolaropoulos and F

L. Perivolaropoulos and F. Skara, Challenges for ΛCDM: An update, New Astron. Rev.95, 101659 (2022), arXiv:2105.05208 [astro-ph.CO]

arXiv 2022

Show all 159 references

[9]

Sch¨ oneberg, G

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, 1 (2022), arXiv:2107.10291 [astro-ph.CO]

2022 arXiv
[10]

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

2022 arXiv
[11]

Kamionkowski and A

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

2023 arXiv
[12]

E. Di Valentinoet al.(CosmoVerse), The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics (2025), arXiv:2504.01669 [astro-ph.CO]

2025 arXiv
[13]

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

2003 arXiv
[14]

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

2006 arXiv
[15]

Bamba, S

K. Bamba, S. Capozziello, S. Nojiri, and S. D. Odintsov, Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests, As- trophys. Space Sci.342, 155 (2012), arXiv:1205.3421 [gr-qc]

2012 arXiv
[16]

Perlmutter, M

S. Perlmutter, M. S. Turner, and M. J. White, Con- straining dark energy with SNe Ia and large scale struc- ture, Phys. Rev. Lett.83, 670 (1999), arXiv:astro- ph/9901052

1999
[17]

Boisseau, G

B. Boisseau, G. Esposito-Farese, D. Polarski, and A. A. Starobinsky, Reconstruction of a scalar tensor theory of gravity in an accelerating universe, Phys. Rev. Lett.85, 2236 (2000), arXiv:gr-qc/0001066

2000 arXiv
[18]

Amendola, Coupled quintessence, Phys

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

2000 arXiv
[19]

Parker and A

L. Parker and A. Raval, Nonperturbative effects of vac- uum energy on the recent expansion of the universe, Phys. Rev. D60, 063512 (1999), [Erratum: Phys.Rev.D 67, 029901 (2003)], arXiv:gr-qc/9905031

1999 arXiv
[20]

R. R. Caldwell, A Phantom menace?, Phys. Lett. B545, 23 (2002), arXiv:astro-ph/9908168

2002 arXiv
[21]

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

2001 arXiv
[22]

Padmanabhan, Accelerated expansion of the universe driven by tachyonic matter, Phys

T. Padmanabhan, Accelerated expansion of the universe driven by tachyonic matter, Phys. Rev. D66, 021301 (2002), arXiv:hep-th/0204150

2002 arXiv
[23]

Cardenas, T

R. Cardenas, T. Gonzalez, Y. Leiva, O. Martin, and I. Quiros, A model of the universe including dark energy accounted for by both a quintessence field and a (neg- ative) cosmological constant, Phys. Rev. D67, 083501 (2003), arXiv:astro-ph/0206315

2003 arXiv
[24]

Khoury and A

J. Khoury and A. Weltman, Chameleon cosmol- ogy, Phys. Rev. D69, 044026 (2004), arXiv:astro- ph/0309411

2004
[25]

Khoury and A

J. Khoury and A. Weltman, Chameleon fields: Awaiting surprises for tests of gravity in space, Phys. Rev. Lett. 93, 171104 (2004), arXiv:astro-ph/0309300

2004 arXiv
[26]

Li, A Model of holographic dark energy, Phys

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

2004 arXiv
[27]

Wang and X.-H

P. Wang and X.-H. Meng, Can vacuum decay in our uni- verse?, Class. Quant. Grav.22, 283 (2005), arXiv:astro- ph/0408495

2005
[28]

Y.-F. Cai, E. N. Saridakis, M. R. Setare, and J.-Q. Xia, Quintom Cosmology: Theoretical implications and ob- servations, Phys. Rept.493, 1 (2010), arXiv:0909.2776 [hep-th]

2010 arXiv
[29]

Uggla, Global cosmological dynamics for the scalar field representation of the modified Chaplygin gas, Phys

C. Uggla, Global cosmological dynamics for the scalar field representation of the modified Chaplygin gas, Phys. Rev. D88, 064040 (2013), arXiv:1308.5838 [astro- ph.CO]

2013 arXiv
[30]

B. C. Paul and P. Thakur, Observational constraints on modified Chaplygin gas from cosmic growth, JCAP11, 052 (2013), arXiv:1306.4808 [astro-ph.CO]

2013 arXiv
[31]

G. S. Sharov, Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state, JCAP06, 023 (2016), arXiv:1506.05246 [gr-qc]

2016 arXiv
[32]

Leanizbarrutia, A

I. Leanizbarrutia, A. Rozas-Fern´ andez, and I. Tereno, Cosmological constraints on a unified dark matter- energy scalar field model with fast transition, Phys. Rev. D96, 023503 (2017), arXiv:1706.01706 [astro-ph.CO]

2017 arXiv
[33]

Lombriser, C

L. Lombriser, C. Dalang, J. Kennedy, and A. Tay- lor, Inherently stable effective field theory for dark energy and modified gravity, JCAP01, 041 (2019), arXiv:1810.05225 [astro-ph.CO]

2019 arXiv
[34]

S. Pan, J. de Haro, W. Yang, and J. Amor´ os, Under- standing the phenomenology of interacting dark energy scenarios and their theoretical bounds, Phys. Rev. D 101, 123506 (2020), arXiv:2001.09885 [gr-qc]

2020 arXiv
[35]

R. G. Landim, Fractional dark energy: Phantom be- havior and negative absolute temperature, Phys. Rev. D104, 103508 (2021), arXiv:2106.15415 [gr-qc]

2021 arXiv
[36]

Artymowski, I

M. Artymowski, I. Ben-Dayan, and U. Kumar, More on emergent dark energy from unparticles, Phys. Rev. D 106, 083502 (2022), arXiv:2111.09946 [astro-ph.CO]

2022 arXiv
[37]

W. Yang, S. Pan, E. Di Valentino, O. Mena, and A. Mel- chiorri, 2021-H0 odyssey: closed, phantom and inter- acting dark energy cosmologies, JCAP10, 008 (2021), arXiv:2101.03129 [astro-ph.CO]

2021 arXiv
[38]

Oriti and X

D. Oriti and X. Pang, Phantom-like dark en- ergy from quantum gravity, JCAP12, 040 (2021), arXiv:2105.03751 [gr-qc]

2021 arXiv
[39]

E. M. Teixeira, B. J. Barros, V. M. C. Fer- reira, and N. Frusciante, Dissecting kinetically coupled quintessence: phenomenology and observational tests, JCAP11, 059 (2022), arXiv:2207.13682 [astro-ph.CO]

2022 arXiv
[40]

B.-H. Lee, W. Lee, E. ´O. Colg´ ain, M. M. Sheikh- Jabbari, and S. Thakur, Is local H 0 at odds with dark energy EFT?, JCAP04, 004 (2022), arXiv:2202.03906 [astro-ph.CO]

2022 arXiv
[41]

Ballardini, A

M. Ballardini, A. G. Ferrari, and F. Finelli, Phantom scalar-tensor models and cosmological tensions, JCAP 04, 029 (2023), arXiv:2302.05291 [astro-ph.CO]. 21

2023 arXiv
[42]

S. S. da Costa, D. R. da Silva, ´A. S. de Jesus, N. Pinto- Neto, and F. S. Queiroz, The H 0 trouble: confronting non-thermal dark matter and phantom cosmology with the CMB, BAO, and Type Ia supernovae data, JCAP 04, 035 (2024), arXiv:2311.07420 [astro-ph.CO]

2024 arXiv
[43]

Forconi, W

M. Forconi, W. Giar` e, O. Mena, Ruchika, E. Di Valentino, A. Melchiorri, and R. C. Nunes, A double take on early and interacting dark energy from JWST, JCAP05, 097 (2024), arXiv:2312.11074 [astro-ph.CO]

2024 arXiv
[44]

M. A. van der Westhuizen and A. Abebe, Interact- ing dark energy: clarifying the cosmological implica- tions and viability conditions, JCAP01, 048 (2024), arXiv:2302.11949 [gr-qc]

2024 arXiv
[45]

J. M. Cline, M. Puel, T. Toma, and Q. S. Wang, Phan- tom fluid cosmology: Impact of a phantom hidden sec- tor on cosmological observables, Phys. Rev. D108, 095033 (2023), arXiv:2308.12989 [hep-ph]

2023 arXiv
[46]

Patil, Ruchika, and S

T. Patil, Ruchika, and S. Panda, Coupled quintessence scalar field model in light of observational datasets, JCAP05, 033 (2024), arXiv:2307.03740 [astro-ph.CO]

2024 arXiv
[47]

Giar` e, M

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

2024 arXiv
[48]

Notari, M

A. Notari, M. Redi, and A. Tesi, Consistent theories for the DESI dark energy fit, JCAP11, 025 (2024), arXiv:2406.08459 [astro-ph.CO]

2024 arXiv
[49]

Giar` e, M

W. Giar` e, M. A. Sabogal, R. C. Nunes, and E. Di Valentino, Interacting Dark Energy after DESI Baryon Acoustic Oscillation Measurements, Phys. Rev. Lett.133, 251003 (2024), arXiv:2404.15232 [astro- ph.CO]

2024 arXiv
[50]

Christiansen, F

Ø. Christiansen, F. Hassani, and D. F. Mota, Environ- mental cosmic acceleration from a phase transition in the dark sector, JCAP01, 043 (2025), arXiv:2405.00668 [astro-ph.CO]

2025 arXiv
[51]

Silva, M

E. Silva, M. A. Sabogal, M. Scherer, R. C. Nunes, E. Di Valentino, and S. Kumar, New constraints on interacting dark energy from DESI DR2 BAO observations, Phys. Rev. D111, 123511 (2025), arXiv:2503.23225 [astro-ph.CO]

2025 arXiv
[52]

M. A. Sabogal, E. Silva, R. C. Nunes, S. Kumar, and E. Di Valentino, Sign switching in dark sector cou- pling interactions as a candidate for resolving cosmo- logical tensions, Phys. Rev. D111, 043531 (2025), arXiv:2501.10323 [astro-ph.CO]

2025 arXiv
[53]

Nojiri and S

S. Nojiri and S. D. Odintsov, Introduction to modified gravity and gravitational alternative for dark energy, eConfC0602061, 06 (2006), arXiv:hep-th/0601213

2006 arXiv
[54]

De Felice and S

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

2010 arXiv
[55]

Clifton, P

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

2012 arXiv
[56]

Y.-F. Cai, S. Capozziello, M. De Laurentis, and E. N. Saridakis, f(T) teleparallel gravity and cosmology, Rept. Prog. Phys.79, 106901 (2016), arXiv:1511.07586 [gr- qc]

2016 arXiv
[57]

Nojiri, S

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

2017 arXiv
[58]

Bahamonde, K

S. Bahamonde, K. F. Dialektopoulos, C. Escamilla- Rivera, G. Farrugia, V. Gakis, M. Hendry, M. Hohmann, J. Levi Said, J. Mifsud, and E. Di Valentino, Teleparallel gravity: from theory to cosmology, Rept. Prog. Phys.86, 026901 (2023), arXiv:2106.13793 [gr-qc]

2023 arXiv
[59]

Heisenberg, Review on f(Q) gravity, Phys

L. Heisenberg, Review on f(Q) gravity, Phys. Rept. 1066, 1 (2024), arXiv:2309.15958 [gr-qc]

2024 arXiv
[60]

Nojiri and S

S. Nojiri and S. D. Odintsov, Modified gravity with neg- ative and positive powers of the curvature: Unification of the inflation and of the cosmic acceleration, Phys. Rev. D68, 123512 (2003), arXiv:hep-th/0307288

2003 arXiv
[61]

A. D. Dolgov and M. Kawasaki, Can modified gravity explain accelerated cosmic expansion?, Phys. Lett. B 573, 1 (2003), arXiv:astro-ph/0307285

2003 arXiv
[62]

S. M. Carroll, A. De Felice, V. Duvvuri, D. A. Eas- son, M. Trodden, and M. S. Turner, The Cosmology of generalized modified gravity models, Phys. Rev. D71, 063513 (2005), arXiv:astro-ph/0410031

2005 arXiv
[63]

Cognola, E

G. Cognola, E. Elizalde, S. Nojiri, S. D. Odintsov, and S. Zerbini, Dark energy in modified Gauss-Bonnet grav- ity: Late-time acceleration and the hierarchy problem, Phys. Rev. D73, 084007 (2006), arXiv:hep-th/0601008

2006 arXiv
[64]

Ferraro and F

R. Ferraro and F. Fiorini, Modified teleparallel grav- ity: Inflation without inflaton, Phys. Rev. D75, 084031 (2007), arXiv:gr-qc/0610067

2007 arXiv
[65]

P. S. Apostolopoulos, N. Brouzakis, N. Tetradis, and E. Tzavara, Modified brane cosmologies with induced gravity, arbitrary matter content and a Gauss-Bonnet term in the bulk, Phys. Rev. D76, 084029 (2007), arXiv:0708.0469 [hep-th]

2007 arXiv
[66]

T. P. Sotiriou and V. Faraoni, Modified gravity with R-matter couplings and (non-)geodesic motion, Class. Quant. Grav.25, 205002 (2008), arXiv:0805.1249 [gr- qc]

2008 arXiv
[67]

Harko, Modified gravity with arbitrary coupling be- tween matter and geometry, Phys

T. Harko, Modified gravity with arbitrary coupling be- tween matter and geometry, Phys. Lett. B669, 376 (2008), arXiv:0810.0742 [gr-qc]

2008 arXiv
[68]

Bamba, C.-Q

K. Bamba, C.-Q. Geng, S. Nojiri, and S. D. Odintsov, Crossing of the phantom divide in modified gravity, Phys. Rev. D79, 083014 (2009), arXiv:0810.4296 [hep- th]

2009 arXiv
[69]

Elizalde, S

E. Elizalde, S. Nojiri, S. D. Odintsov, and D. Saez- Gomez, Unifying inflation with dark energy in modified F(R) Horava-Lifshitz gravity, Eur. Phys. J. C70, 351 (2010), arXiv:1006.3387 [hep-th]

2010 arXiv
[70]

Tsujikawa, Modified gravity models of dark energy, Lect

S. Tsujikawa, Modified gravity models of dark energy, Lect. Notes Phys.800, 99 (2010), arXiv:1101.0191 [gr- qc]

2010 arXiv
[71]

Martinelli, E

M. Martinelli, E. Calabrese, F. De Bernardis, A. Mel- chiorri, L. Pagano, and R. Scaramella, Constraining Modified Gravity with Euclid, Phys. Rev. D83, 023012 (2011), arXiv:1010.5755 [astro-ph.CO]

2011 arXiv
[72]

Harko, F

T. Harko, F. S. N. Lobo, S. Nojiri, and S. D. Odintsov, f(R, T) gravity, Phys. Rev. D84, 024020 (2011), arXiv:1104.2669 [gr-qc]

2011 arXiv
[73]

Martinelli, A

M. Martinelli, A. Melchiorri, O. Mena, V. Salvatelli, and Z. Girones, Future constraints on the Hu-Sawicki mod- ified gravity scenario, Phys. Rev. D85, 024006 (2012), arXiv:1109.4736 [astro-ph.CO]

2012 arXiv
[74]

Borowiec, M

A. Borowiec, M. Kamionka, A. Kurek, and M. Szyd- lowski, Cosmic acceleration from modified gravity with Palatini formalism, JCAP02, 027 (2012), arXiv:1109.3420 [gr-qc]

2012 arXiv
[75]

Li, G.-B

B. Li, G.-B. Zhao, R. Teyssier, and K. Koyama, 22 ECOSMOG: An Efficient Code for Simulating Modified Gravity, JCAP01, 051 (2012), arXiv:1110.1379 [astro- ph.CO]

2012 arXiv
[76]

Brax, A.-C

P. Brax, A.-C. Davis, and B. Li, Modified Grav- ity Tomography, Phys. Lett. B715, 38 (2012), arXiv:1111.6613 [astro-ph.CO]

2012 arXiv
[77]

D. S. Y. Mak, E. Pierpaoli, F. Schmidt, and N. Ma- cellari, Constraints on Modified Gravity from Sunyaev- Zeldovich Cluster Surveys, Phys. Rev. D85, 123513 (2012), arXiv:1111.1004 [astro-ph.CO]

2012 arXiv
[78]

Basilakos and A

S. Basilakos and A. Pouri, The growth index of mat- ter perturbations and modified gravity, Mon. Not. Roy. Astron. Soc.423, 3761 (2012), arXiv:1203.6724 [astro- ph.CO]

2012 arXiv
[79]

Di Valentino, A

E. Di Valentino, A. Melchiorri, V. Salvatelli, and A. Silvestri, Parametrised modified gravity and the CMB Bispectrum, Phys. Rev. D86, 063517 (2012), arXiv:1204.5352 [astro-ph.CO]

2012 arXiv
[80]

Gao, Generalized modified gravity with the second order acceleration equation, Phys

C. Gao, Generalized modified gravity with the second order acceleration equation, Phys. Rev. D86, 103512 (2012), arXiv:1208.2790 [gr-qc]

2012 arXiv
[81]

Briscese, A

F. Briscese, A. Marcian` o, L. Modesto, and E. N. Saridakis, Inflation in (Super-)renormalizable Gravity, Phys. Rev. D87, 083507 (2013), arXiv:1212.3611 [hep- th]

2013 arXiv
[82]

Clemson and K

T. Clemson and K. Koyama, The Distinguishability of Interacting Dark Energy from Modified Gravity, JCAP 01, 010 (2013), arXiv:1209.2618 [astro-ph.CO]

2013 arXiv
[83]

Chakraborty, An alternative f(R, T) gravity theory and the dark energy problem, Gen

S. Chakraborty, An alternative f(R, T) gravity theory and the dark energy problem, Gen. Rel. Grav.45, 2039 (2013), arXiv:1212.3050 [physics.gen-ph]

2013 arXiv
[84]

P. Brax, C. van de Bruck, S. Clesse, A.-C. Davis, and G. Sculthorpe, Early Modified Gravity: Implica- tions for Cosmology, Phys. Rev. D89, 123507 (2014), arXiv:1312.3361 [astro-ph.CO]

2014 arXiv
[85]

C. D. Leonard, T. Baker, and P. G. Ferreira, Explor- ing degeneracies in modified gravity with weak lens- ing, Phys. Rev. D91, 083504 (2015), arXiv:1501.03509 [astro-ph.CO]

2015 arXiv
[86]

R. C. Nunes, S. Pan, and E. N. Saridakis, New ob- servational constraints on f(T) gravity from cosmic chronometers, JCAP08, 011 (2016), arXiv:1606.04359 [gr-qc]

2016 arXiv
[87]

R. C. Nunes, S. Pan, E. N. Saridakis, and E. M. C. Abreu, New observational constraints onf(R) grav- ity from cosmic chronometers, JCAP01, 005 (2017), arXiv:1610.07518 [astro-ph.CO]

2017 arXiv
[88]

R. C. Nunes, S. Pan, and E. N. Saridakis, New observational constraints onf(T) gravity through gravitational-wave astronomy, Phys. Rev. D98, 104055 (2018), arXiv:1810.03942 [gr-qc]

2018 arXiv
[89]

Samart, B

D. Samart, B. Silasan, and P. Channuie, Cosmological dynamics of interacting dark energy and dark matter in viable models of f(R) gravity, Phys. Rev. D104, 063517 (2021), arXiv:2104.12687 [gr-qc]

2021 arXiv
[90]

Lymperis, Late-time cosmology with phantom dark-energy in f(Q) gravity, JCAP11, 018 (2022), arXiv:2207.10997 [gr-qc]

A. Lymperis, Late-time cosmology with phantom dark-energy in f(Q) gravity, JCAP11, 018 (2022), arXiv:2207.10997 [gr-qc]

2022 arXiv
[91]

F. B. M. d. Santos, Updating constraints on phan- tom crossing f(T) gravity, JCAP06, 039 (2023), arXiv:2211.16370 [astro-ph.CO]

2023 arXiv
[92]

Kumar, R

S. Kumar, R. C. Nunes, S. Pan, and P. Yadav, New late-time constraints on f(R) gravity, Phys. Dark Univ. 42, 101281 (2023), arXiv:2301.07897 [astro-ph.CO]

2023 arXiv
[93]

A. G. Ferrari, M. Ballardini, F. Finelli, and D. Paoletti, Scalar-tensor gravity and DESI 2024 BAO data, Phys. Rev. D111, 083523 (2025), arXiv:2501.15298 [astro- ph.CO]

2025 arXiv
[94]

Ayuso, M

I. Ayuso, M. Bouhmadi-L´ opez, C.-Y. Chen, X. Y. Chew, K. Dialektopoulos, and Y. C. Ong, Insights inf(Q) cosmology: the relevance of the connection (2025), arXiv:2506.03506 [gr-qc]

2025
[95]

Y. Yang, X. Ren, B. Wang, Y.-F. Cai, and E. N. Sari- dakis, Data reconstruction of the dynamical connection function in f(Q) cosmology, Mon. Not. Roy. Astron. Soc. 533, 2232 (2024), arXiv:2404.12140 [astro-ph.CO]

2024 arXiv
[96]

P. Xia, D. Zhang, X. Ren, B. Wang, and Y. C. Ong, Constraining the linear scalar perturbation theory of Cotton gravity, Phys. Rev. D111, 023526 (2025), arXiv:2405.07209 [astro-ph.CO]

2025 arXiv
[97]

Steigman, R

G. Steigman, R. C. Santos, and J. A. S. Lima, An Ac- celerating Cosmology Without Dark Energy, JCAP06, 033 (2009), arXiv:0812.3912 [astro-ph]

2009 arXiv
[98]

J. A. S. Lima, F. E. Silva, and R. C. Santos, Accelerating Cold Dark Matter Cosmology (Ω Λ ≡0), Class. Quant. Grav.25, 205006 (2008), arXiv:0807.3379 [astro-ph]

2008 arXiv
[99]

J. A. S. Lima, J. F. Jesus, and F. A. Oliveira, CDM Accelerating Cosmology as an Alternative to LCDM model, JCAP11, 027 (2010), arXiv:0911.5727 [astro- ph.CO]

2010 arXiv
[100]

J. A. S. Lima, J. F. Jesus, and F. A. Oliveira, Note on ’Continuous matter creation and the acceleration of the universe: the growth of density fluctuations’, Gen. Rel. Grav.43, 1883 (2011), arXiv:1012.5069 [astro-ph.CO]

2011 arXiv
[101]

J. F. Jesus, F. A. Oliveira, S. Basilakos, and J. A. S. Lima, Newtonian Perturbations on Models with Mat- ter Creation, Phys. Rev. D84, 063511 (2011), arXiv:1105.1027 [astro-ph.CO]

2011 arXiv
[102]

J. A. S. Lima, S. Basilakos, and F. E. M. Costa, New Cosmic Accelerating Scenario without Dark Energy, Phys. Rev. D86, 103534 (2012), arXiv:1205.0868 [astro- ph.CO]

2012 arXiv
[103]

J. A. S. Lima, L. L. Graef, D. Pavon, and S. Basi- lakos, Cosmic acceleration without dark energy: Back- ground tests and thermodynamic analysis, JCAP10, 042 (2014), arXiv:1406.5538 [gr-qc]

2014 arXiv
[104]

J. A. S. Lima and I. Baranov, Gravitationally In- duced Particle Production: Thermodynamics and Kinetic Theory, Phys. Rev. D90, 043515 (2014), arXiv:1411.6589 [gr-qc]

2014 arXiv
[105]

Chakraborty, S

S. Chakraborty, S. Pan, and S. Saha, A third alterna- tive to explain recent observations: Future deceleration, Phys. Lett. B738, 424 (2014), arXiv:1411.0941 [gr-qc]

2014 arXiv
[106]

J. A. S. Lima, R. C. Santos, and J. V. Cunha, Is ΛCDM an effective CCDM cosmology?, JCAP03, 027 (2016), arXiv:1508.07263 [gr-qc]

2016 arXiv
[107]

Baranov and J

I. Baranov and J. A. S. Lima, Gravitationally Induced Particle Production and its Impact on the WIMP Abun- dance, Phys. Lett. B751, 338 (2015), arXiv:1505.02743 [gr-qc]

2015 arXiv
[108]

de Haro and S

J. de Haro and S. Pan, Gravitationally induced adiabatic particle production: From Big Bang to de Sitter, Class. Quant. Grav.33, 165007 (2016), arXiv:1512.03100 [gr-qc]

2016 arXiv
[109]

S. Pan, J. de Haro, A. Paliathanasis, and R. J. Slagter, Evolution and Dynamics of a Matter creation model, Mon. Not. Roy. Astron. Soc.460, 1445 (2016), arXiv:1601.03955 [gr-qc]. 23

2016 arXiv
[110]

Paliathanasis, J

A. Paliathanasis, J. D. Barrow, and S. Pan, Cosmo- logical solutions with gravitational particle production and nonzero curvature, Phys. Rev. D95, 103516 (2017), arXiv:1610.02893 [gr-qc]

2017 arXiv
[111]

S. Pan, J. D. Barrow, and A. Paliathanasis, Two-fluid solutions of particle-creation cosmologies, Eur. Phys. J. C79, 115 (2019), arXiv:1812.05493 [gr-qc]

2019 arXiv
[112]

Elizalde, M

E. Elizalde, M. Khurshudyan, and S. D. Odintsov, Can we learn from matter creation to solve theH 0 tension problem?, Eur. Phys. J. C84, 782 (2024), arXiv:2407.20285 [gr-qc]

2024 arXiv
[113]

Kuzmin and I

V. Kuzmin and I. Tkachev, Ultrahigh-energy cosmic rays, superheavy long living particles, and matter creation after inflation, JETP Lett.68, 271 (1998), arXiv:hep-ph/9802304

1998 arXiv
[114]

Y. Ema, K. Nakayama, and Y. Tang, Production of Purely Gravitational Dark Matter, JHEP09, 135, arXiv:1804.07471 [hep-ph]

arXiv
[115]

Shiu and L.-T

G. Shiu and L.-T. Wang, D matter, Phys. Rev. D69, 126007 (2004), arXiv:hep-ph/0311228

2004 arXiv
[116]

Y. Ema, K. Nakayama, and Y. Tang, Production of purely gravitational dark matter: the case of fermion and vector boson, JHEP07, 060, arXiv:1903.10973 [hep-ph]

1903 arXiv
[117]

S. K. Modak, Cosmological Particle Creation Beyond de Sitter, Int. J. Mod. Phys. D28, 1930015 (2019), arXiv:1905.04111 [gr-qc]

2019 arXiv
[118]

C. M. Muller, Cosmological bounds on the equation of state of dark matter, Phys. Rev. D71, 047302 (2005), arXiv:astro-ph/0410621

2005 arXiv
[119]

Armendariz-Picon and J

C. Armendariz-Picon and J. T. Neelakanta, How Cold is Cold Dark Matter?, JCAP03, 049 (2014), arXiv:1309.6971 [astro-ph.CO]

2014 arXiv
[120]

Gariazzo, M

S. Gariazzo, M. Escudero, R. Diamanti, and O. Mena, Cosmological searches for a noncold dark matter compo- nent, Phys. Rev. D96, 043501 (2017), arXiv:1704.02991 [astro-ph.CO]

2017 arXiv
[121]

M. Kopp, C. Skordis, D. B. Thomas, and S. Ili´ c, Dark Matter Equation of State through Cosmic History, Phys. Rev. Lett.120, 221102 (2018), arXiv:1802.09541 [astro-ph.CO]

2018 arXiv
[122]

M. O. Calvao, J. A. S. Lima, and I. Waga, On the thermodynamics of matter creation in cosmology, Phys. Lett. A162, 223 (1992)

1992
[123]

Leon and E

G. Leon and E. N. Saridakis, Dynamical behav- ior in mimetic F(R) gravity, JCAP04, 031 (2015), arXiv:1501.00488 [gr-qc]

2015 arXiv
[124]

Leon and E

G. Leon and E. N. Saridakis, Dynamical analysis of generalized Galileon cosmology, JCAP03, 025 (2013), arXiv:1211.3088 [astro-ph.CO]

2013 arXiv
[125]

Aghanimet al.(Planck), Planck 2018 results

N. Aghanimet al.(Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

2020 arXiv
[126]

Zhang, H

C. Zhang, H. Zhang, S. Yuan, T.-J. Zhang, and Y.-C. Sun, Four new observationalH(z) data from luminous red galaxies in the Sloan Digital Sky Survey data re- lease seven, Res. Astron. Astrophys.14, 1221 (2014), arXiv:1207.4541 [astro-ph.CO]

2014 arXiv
[127]

Stern, R

D. Stern, R. Jimenez, L. Verde, M. Kamionkowski, and S. A. Stanford, Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measure- ments, JCAP02, 008 (2010), arXiv:0907.3149 [astro- ph.CO]

2010 arXiv
[128]

Jimenez, L

R. Jimenez, L. Verde, T. Treu, and D. Stern, Con- straints on the equation of state of dark energy and the Hubble constant from stellar ages and the CMB, Astrophys. J.593, 622 (2003), arXiv:astro-ph/0302560

2003 arXiv
[129]

Moresco, L

M. Moresco, L. Verde, L. Pozzetti, R. Jimenez, and A. Cimatti, New constraints on cosmological parame- ters and neutrino properties using the expansion rate of the Universe to z˜1.75, JCAP07, 053 (2012), arXiv:1201.6658 [astro-ph.CO]

2012 arXiv
[130]

Simon, L

J. Simon, L. Verde, and R. Jimenez, Constraints on the redshift dependence of the dark energy potential, Phys. Rev. D71, 123001 (2005), arXiv:astro-ph/0412269

2005 arXiv
[131]

Borghi, M

N. Borghi, M. Moresco, and A. Cimatti, Toward a Bet- ter Understanding of Cosmic Chronometers: A New Measurement of H(z) at z∼0.7, Astrophys. J. Lett. 928, L4 (2022), arXiv:2110.04304 [astro-ph.CO]

2022 arXiv
[132]

K. Jiao, N. Borghi, M. Moresco, and T.-J. Zhang, New Observational H(z) Data from Full-spectrum Fitting of Cosmic Chronometers in the LEGA-C Survey, Astro- phys. J. Suppl.265, 48 (2023), arXiv:2205.05701 [astro- ph.CO]

2023 arXiv
[133]

Moresco, L

M. Moresco, L. Pozzetti, A. Cimatti, R. Jimenez, C. Maraston, L. Verde, D. Thomas, A. Citro, R. To- jeiro, and D. Wilkinson, A 6% measurement of the Hubble parameter atz∼0.45: direct evidence of the epoch of cosmic re-acceleration, JCAP05, 014 (2016), arXiv:1601.01701 [astro-ph.CO]

2016 arXiv
[134]

Tomasetti, M

E. Tomasetti, M. Moresco, N. Borghi, K. Jiao, A. Cimatti, L. Pozzetti, A. C. Carnall, R. J. McLure, and L. Pentericci, A new measurement of the expan- sion history of the Universe at z = 1.26 with cosmic chronometers in V ANDELS, Astron. Astrophys.679, A96 (2023), arXiv:2305.1...

2023 arXiv
[135]

Moresco, Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z ∼2, Mon

M. Moresco, Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z ∼2, Mon. Not. Roy. Astron. Soc.450, L16 (2015), arXiv:1503.01116 [astro-ph.CO]

2015 arXiv
[136]

A. L. Ratsimbazafy, S. I. Loubser, S. M. Craw- ford, C. M. Cress, B. A. Bassett, R. C. Nichol, and P. V¨ ais¨ anen, Age-dating Luminous Red Galax- ies observed with the Southern African Large Tele- scope, Mon. Not. Roy. Astron. Soc.467, 3239 (2017), arXiv:1702.00418 [astro-ph.CO]

2017 arXiv
[137]

Broutet al., The Pantheon+ Analysis: Cosmo- logical Constraints, Astrophys

D. Broutet al., The Pantheon+ Analysis: Cosmo- logical Constraints, Astrophys. J.938, 110 (2022), arXiv:2202.04077 [astro-ph.CO]

2022 arXiv
[138]

A. G. Riesset al., A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 M pc−1 Uncertainty from the Hubble Space Tele- scope and the SH0ES Team, Astrophys. J. Lett.934, L7 (2022), arXiv:2112.04510 [astro-ph.CO]

2022 arXiv
[139]

T. M. C. Abbottet al.(DES), The Dark Energy Sur- vey: Cosmology Results with∼1500 New High-redshift Type Ia Supernovae Using the Full 5 yr Data Set, Astro- phys. J. Lett.973, L14 (2024), arXiv:2401.02929 [astro- ph.CO]

2024 arXiv
[140]

Vincenziet al.(DES), The Dark Energy Survey Supernova Program: Cosmological Analysis and Sys- tematic Uncertainties, Astrophys

M. Vincenziet al.(DES), The Dark Energy Survey Supernova Program: Cosmological Analysis and Sys- tematic Uncertainties, Astrophys. J.975, 86 (2024), arXiv:2401.02945 [astro-ph.CO]

2024 arXiv
[141]

B. O. S´ anchezet al.(DES), The Dark Energy Survey Supernova Program: Light Curves and 5 Yr Data Re- lease, Astrophys. J.975, 5 (2024), arXiv:2406.05046 [astro-ph.CO]. 24

2024 arXiv
[142]

Rubinet al., Union Through UNITY: Cosmology with 2,000 SNe Using a Unified Bayesian Framework, ApJ (2023), arXiv:2311.12098 [astro-ph.CO]

D. Rubinet al., Union Through UNITY: Cosmology with 2,000 SNe Using a Unified Bayesian Framework, ApJ (2023), arXiv:2311.12098 [astro-ph.CO]

2023 arXiv
[143]

A. G. Adameet al.(DESI), DESI 2024 III: Baryon Acoustic Oscillations from Galaxies and Quasars, astro- ph.CO (2024), arXiv:2404.03000

2024 arXiv
[144]

A. G. Adameet al.(DESI), DESI 2024 IV: Baryon Acoustic Oscillations from the Lyman Alpha Forest, astro-ph.CO (2024), arXiv:2404.03001

2024 arXiv
[145]

Cortˆ es and A

M. Cortˆ es and A. R. Liddle, Interpreting DESI’s evi- dence for evolving dark energy, JCAP12, 007 (2024), arXiv:2404.08056 [astro-ph.CO]

2024 arXiv
[146]

A. G. Adameet al.(DESI), DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations, astro-ph.CO (2024), arXiv:2404.03002

2024 arXiv
[147]

Abdul Karimet al.(DESI), DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cos- mological Constraints, (2025), arXiv:2503.14738 [astro- ph.CO]

M. Abdul Karimet al.(DESI), DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cos- mological Constraints, (2025), arXiv:2503.14738 [astro- ph.CO]

2025 arXiv
[148]

Foreman-Mackey, D

D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, emcee: The MCMC Hammer, Publ. As- tron. Soc. Pac.125, 306 (2013), arXiv:1202.3665 [astro- ph.IM]

2013 arXiv
[149]

Goodman and J

J. Goodman and J. Weare, Ensemble samplers with affine invariance, Commun. Appl. Math. Comput. Sc. 5, 65 (2010)

2010
[150]

Gelman and D

A. Gelman and D. B. Rubin, A single series from the gibbs sampler provides a false sense of security, in Bayesian Statistics 4: Proceedings of the Fourth Va- lencia International Meeting, Dedicated to the memory of Morris H. DeGroot, 1931–1989(Oxford University Press, 1992)

1931
[151]

Lewis, GetDist: a Python package for analysing Monte Carlo samples (2019), arXiv:1910.13970 [astro- ph.IM]

A. Lewis, GetDist: a Python package for analysing Monte Carlo samples (2019), arXiv:1910.13970 [astro- ph.IM]

2019 arXiv
[152]

Navaset al.(Particle Data Group), Review of particle physics, Phys

S. Navaset al.(Particle Data Group), Review of particle physics, Phys. Rev. D110, 030001 (2024)

2024
[153]

Akaike, A new look at the statistical model identi- fication, IEEE Transactions on Automatic Control19, 716 (1974)

H. Akaike, A new look at the statistical model identi- fication, IEEE Transactions on Automatic Control19, 716 (1974)

1974
[154]

Schwarz, Estimating the Dimension of a Model, The Annals of Statistics6, 461 (1978)

G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics6, 461 (1978)

1978
[155]

Trotta, Bayes in the sky: Bayesian inference and model selection in cosmology, Contemp

R. Trotta, Bayes in the sky: Bayesian inference and model selection in cosmology, Contemp. Phys.49, 71 (2008), arXiv:0803.4089 [astro-ph]

2008 arXiv
[156]

K. P. Burnham and D. R. Anderson,Model Selection and Multimodel Inference: A Practical Information- Theoretic Approach, 2nd ed. (Springer-Verlag, New York, 2002)

2002
[157]

R. E. Kass and A. E. Raftery, Bayes Factors, J. Am. Statist. Assoc.90, 773 (1995)

1995
[158]

Montanari and E

A. Montanari and E. Moulin, The Dark Matter Mystery (2024) see, pg. 123

2024
[159]

Corstanjeet al., Depth of shower maximum and mass composition of cosmic rays from 50 PeV to 2 EeV mea- sured with the LOF AR radio telescope, Phys

A. Corstanjeet al., Depth of shower maximum and mass composition of cosmic rays from 50 PeV to 2 EeV mea- sured with the LOF AR radio telescope, Phys. Rev. D 103, 102006 (2021), see, pg. 11, arXiv:2103.12549 [astro- ph.HE]

2021 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Case0< l <1 In this parametric domain the system (41) possesses only one singularity atξ= 1. Multiplying with (1−ξ) 2l yields the autonomous system x′ =xy(1−ξ) 2l + 3αx1−l(1−x)ξ 2l,(43a) y′ =y (y−1)(1−ξ) 2l −3αx 1−lξ2l ,(43b) ξ′ = 3 2 ξ(1−ξ) h 1 + y 3 (1−ξ) 2l −αx 1−lξ2l i .(43c) From the above dynamical system we acquire the follow- ing invariant manifol...

[2] [2]

In contrast to the previous case,x= 0 does not form an invariant manifold

Casel >1 In this case the system (41) simplifies as x′ =xly(1−ξ) 2l + 3α(1−x)ξ 2l,(44a) y′ =y xl−1(y−1)(1−ξ) 2l −3αξ 2l ,(44b) ξ′ = 3 2 ξ(1−ξ) h xl−1 1 + y 3 (1−ξ) 2l −αξ 2l i .(44c) The planesy= 0,ξ= 0,ξ= 1 andx+y= 1 constitute the invariant manifolds in the phase space. In contrast to the previous case,x= 0 does not form an invariant manifold. However, ...

[3] [3]

The criti- cal points and their properties are presented in Table II

Casel <0 In this case the autonomous system takes the form x′ =xyξ −2l + 3αx1−l(1−x)(1−ξ) 2l,(45a) y′ =y (y−1)ξ 2l −3αx 1−l(1−ξ) 2l ,(45b) ξ′ = 3 2 ξ(1−ξ) h (1 + y 3 )ξ2l −αx 1−l(1−ξ) 2l i ,(45c) and the planesx= 0,y= 0,ξ= 0,ξ= 1 and x+y= 1 constitute invariant manifolds, making the phase space domainRpositively invariant. The criti- cal points and their ...

[4] [4]

Triangle

Casel= 0 In the casel= 0 the autonomous system simplifies significantly, since Γ = 3αH, namely it becomes x′ =xy+ 3αx(1−x),(46a) y′ =y(y−1−3αx),(46b) ξ′ = 3 2 ξ(1−ξ) 1 + y 3 −αx .(46c) The reduced system possesses five invariant manifolds, namelyx= 0,y= 0,ξ= 0,ξ= 1 andx+y= 1, ensuring that the phase space domainRagain remains positively invariant. In Tabl...

[5] [5]

Theχ 2 is defined as,χ 2 = P i HCC,i−Hmodel,i σi 2 , where ‘i’ denotes the redshift values

Hubble data from Cosmic Chronometers (CC): We use 34 measurements of the Hubble parame- ter at different redshifts using the CC approach, displayed in Table III. Theχ 2 is defined as,χ 2 = P i HCC,i−Hmodel,i σi 2 , where ‘i’ denotes the redshift values

[6] [6]

A way of making Europe

Type Ia Supernovae (SNIa): We use three distinct 11 z H(z)σ H(z) Ref. z H(z)σ H(z) Ref. 0.07 69.0 19.6 [120] 0.48 97.0 62.0 [121] 0.09 69.0 12.0 [122] 0.5929 104.0 13.0 [123] 0.12 68.6 26.2 [120] 0.6797 92.0 8.0 [123] 0.17 83.0 8.0 [124] 0.75 98.8 33.6 [125] 0.1791 75.0 4.0 [123] 0.7812 105.0 12.0 [123] 0.1993 75.0 5.0 [123] 0.80 113.1 25.22 [126] 0.20 72...

arXiv 1993

[7] [7]

Di Valentino, O

E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri, D. F. Mota, A. G. Riess, and J. Silk, In the realm of the Hubble tension—a review of solutions, Class. Quant. Grav.38, 153001 (2021), arXiv:2103.01183 [astro-ph.CO]

arXiv 2021

[8] [8]

Perivolaropoulos and F

L. Perivolaropoulos and F. Skara, Challenges for ΛCDM: An update, New Astron. Rev.95, 101659 (2022), arXiv:2105.05208 [astro-ph.CO]

arXiv 2022