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The paper shows that sign-changing dark energy is governed by the regular combinations ρ+p and ρ+3p, not by the ratio w=p/ρ, and that a smooth density zero forces a kinematic pole in w with a universal residue.

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2026-08-01 16:21 UTC pith:5FD3KE6Y

load-bearing objection Solid, honest paper on ratio-free diagnostics for sign-changing dark energy: local theorems hold, the q-zero count is conditional, and Eq. (74) has a typo.

arxiv 2607.18008 v1 pith:5FD3KE6Y submitted 2026-07-20 gr-qc astro-ph.CO

Defocusing dark energy: Raychaudhuri diagnostics beyond w<-1/3 and the phantom divide

\"Ozg\"ur Akarsu , Antonio De Felice , N. Merve Uzun This is my paper
classification gr-qc astro-ph.CO MSC 83F0583C05 PACS 98.80.-k95.36.+x
keywords dark energyequation of statephantom divideRaychaudhuri equationsign-changing dark energy densitynull energy conditionactive gravitational mass densitydeceleration parameter
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper's central claim is that the standard equation-of-state parameter w=p/ρ fails as a diagnostic when an effective dark-energy sector's density changes sign, and that the two combinations that actually appear in Einstein's equations—I=ρ+p and M=ρ+3p—should replace it. For a smooth negative-to-positive density crossing of finite odd order, the authors prove I and M are negative around the crossing while w blows up with a pole whose residue n(1+z†)/3 is fixed by the crossing redshift and the order of the zero alone. This implies that repulsion, acceleration, phantom-like behavior, and NEC violation are four distinct notions; in particular, a sector can already be repulsive while its density is negative, so w<-1/3 is only a positive-branch proxy. The paper matters because current data analyses allow effective DE densities to cross zero, and ratio-based landmarks like the phantom divide would mislabel such histories.

Core claim

For a separately conserved effective dark-energy sector whose density crosses zero smoothly from negative to positive at redshift z† with finite odd order n, the paper proves that I_de=ρ_de+p_de and M_de=ρ_de+3p_de are negative in a punctured neighborhood of the crossing and non-positive at the crossing itself, while the ratio w_de=p_de/ρ_de develops a pole with the universal residue n(1+z†)/3. Because M_de is the quantity entering the Raychaudhuri source, the sector is already Raychaudhuri-repulsive on the negative-density side whenever it is attractive at high redshift, and the familiar conditions w<-1/3 and w=-1 are only branch-dependent ratio representations of M_de<0 and I_de=0. Under t

What carries the argument

The central object is the active gravitational mass density M=ρ+3p, selected by the Raychaudhuri equation via ä/a=-(4πG/3)Σ(ρ_i+3p_i), together with the inertial mass density I=ρ+p, which the continuity equation fixes through ρ'=3(1+z)^{-1}I. The local theorem is a Taylor-expansion identity: for ρ_de≈A(z-z†)^n with n odd and A<0, both I_de and M_de inherit a negative sign from the even power (z-z†)^{n-1}, while w_de behaves as n(1+z†)/[3(z-z†)], giving a pole whose residue depends only on n and z†. The global one-or-three counting is a Rolle's-theorem argument: with at most two stationary points of M_tot, there can be at most three sign-changing zeros of q.

Load-bearing premise

The main claims assume a smooth, separately conserved dark-energy sector whose density crosses zero with a finite odd order; the one-or-three counting additionally assumes that M_tot has at most two stationary points in the post-recombination interval and that each sign switch generates at most one negative impulse.

What would settle it

Compute M_tot(z)=ρ_m(z)+(1+z)ρ'_de(z)-2ρ_de(z) for any proposed smooth, separately conserved sign-switching profile. If a profile in the stated single-impulse class has M_tot with at most two stationary points but q has more than three sign-changing zeros, the counting theorem fails. Equivalently, a numerically reconstructed H(z) with ρ_de crossing zero near z≈2 that yields five sign-changing q=0 crossings would falsify the claimed one-or-three pattern.

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

If this is right

  • w=p/ρ is a branch-dependent coordinate; across a density zero the regular separators are I=0 (sector NEC boundary) and M=0 (repulsion boundary).
  • Any smooth negative-to-positive crossing of order n produces a pole in w with residue n(1+z†)/3, so a detected pole is a kinematic signature of the crossing rather than a stress-energy singularity.
  • If the sector is attractive at high redshift, repulsion onset occurs at some z_rep>z† on the negative-density side, so the sector is already Raychaudhuri-repulsive while ρ_de<0.
  • A sufficiently sharp crossing can create a transient acceleration window with the ordering z_rep>z_begin>z†>z_end>z_late; under the stated conditions q has either one or three sign-changing zeros.
  • Linear perturbations can be formulated without dividing by ρ or I, so density zeros are kinematically regular; microphysical stability remains a property of the chosen completion.

Where Pith is reading between the lines

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

  • One testable extension: a measured pole in w at known z† directly yields the order n of the density zero through the residue formula, giving a kinematic classifier for reconstructed histories.
  • If reconstructions that let ρ_de cross zero near z≈2 are correct, this paper predicts a separate repulsion-onset redshift z_rep>z† and, for sharp transitions, an intermediate acceleration window; checking this ordering in H(z) reconstructions would discriminate sign-switching histories from smooth positive-density histories.
  • The ratio-safe perturbation formulation suggests Boltzmann implementations could evolve unnormalized density and momentum perturbations through ρ=0 without special prescriptions at the crossing; the remaining obstacle is microphysical closure, not kinematic regularity.
  • The one-or-three q-crossing count rests on a stationary-point bound that may fail for oscillatory or multi-impulse profiles; the bound itself could be tested by scanning the single-impulse profile class for counterexamples.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 2 minor

Summary. The paper argues that the usual dark-energy equation-of-state parameter w is a branch-dependent proxy that fails when an effective DE density crosses zero, and proposes organizing sector-level statements around the signed density ρ_de and the two field-equation-selected combinations I_de = ρ_de + p_de and M_de = ρ_de + 3p_de. For a separately conserved sector with a smooth negative-to-positive density crossing of finite odd order n at z†, it proves that I_de and M_de are negative in a punctured neighborhood and non-positive at the crossing, while w_de develops a kinematic pole with universal residue n(1+z†)/3. It further shows that if M_de > 0 at sufficiently high redshift, continuity implies a repulsion-onset redshift z_rep > z†; derives the exact range of ρ'_de(z†) for acceleration at the crossing with the total NEC satisfied; and, under stated single-impulse and stationary-point assumptions, proves that the deceleration parameter has either one or three sign-changing zeros. These results are illustrated with a smooth ΛsCDM profile, an exponential infrared f(T) model, and the minimal phantom brane, with ΛCDM and CPL as reference histories. A ratio-safe linear perturbation formulation in unnormalized stress–energy variables is also presented.

Significance. If the results hold — and the local crossing theorems appear straightforward and correct — the paper provides a clean, branch-independent diagnostic framework that is directly relevant to current analyses of sign-changing effective DE histories such as ΛsCDM. The universal residue of the w pole, the exact acceleration-with-NEC window, and the analytic uniqueness of the phantom-brane q=0 crossing are concrete, checkable contributions. The paper is honest about the conditional nature of the q=0 counting result, and the worked examples are explicitly illustrative rather than parameter-inference claims. The perturbation section usefully separates kinematic regularity from microphysical stability. Overall this is a valuable conceptual clarification, though it does not by itself vindicate any particular sign-switching model.

minor comments (2)
  1. [Sec. VA, Eqs. (73) and (74)] There is a factor typo in the two displayed inequalities. As printed, Eq. (73) reads ΩΛs0/η tanh(ηz†) > Ωm0(1+z†)^2, which for η=5, ΩΛs0=0.7, Ωm0=0.3, z†=2 gives 0.14 > 2.7, contradicting the text that η=5 satisfies the intermediate acceleration condition. The correct factor is ΩΛs0 η / tanh(ηz†), and Eq. (74) should be adjusted accordingly: Ωm0(1+z†)^2 < ΩΛs0 η/tanh(ηz†) ≤ 3Ωm0(1+z†)^2. With this correction the stated range 3.9 ≲ η ≲ 11.6 follows.
  2. [Sec. IVB] The one-or-three q=0 counting relies on two assumptions: each sign switch generates at most one localized negative impulse in M_de(z), and M_tot(z) has at most two stationary points in the post-recombination interval. These are stated clearly, but they are not derived from the smooth sign-switching profile class. Since result (iv) is advertised as a main result, I recommend adding a sentence (or footnote) that explicitly emphasizes that without the stationary-point bound, more than three sign-changing zeros are not excluded by the local crossing theorems, and noting whether the three worked examples have been checked to satisfy the bound. This is a clarity issue rather than a mathematical error, because the paper already presents the count as conditional.

Circularity Check

0 steps flagged

No circular derivation: the crossing theorems follow algebraically from definitions; self-citations are contextual, and the one-or-three q=0 count is an explicitly conditional scope result.

full rationale

The central results in Sec. IIIB are derived from the definitions I_de = ρ_de + p_de and M_de = ρ_de + 3p_de together with separate conservation, which gives p_de = (1+z)ρ'_de/3 − ρ_de, I_de = (1+z)ρ'_de/3, and M_de = (1+z)ρ'_de − 2ρ_de. Substituting the Taylor expansion ρ_de = A(z−z†)^n + ... with odd n and A<0 then yields the negativity of I_de and M_de near z† and the w-de pole residue n(1+z†)/3 by direct algebra. The input is the assumed smooth sign-switching density profile; the conclusions are consequences, not restatements of the input. The z_rep > z† statement is an intermediate-value theorem argument from M_de < 0 near the crossing and the assumed M_de(z_hi) > 0, not a fitted or definitional result. The one-or-three q=0 counting in Sec. IVB is explicitly conditional on the stated single-impulse and at-most-two-stationary-point assumptions; the paper identifies these as assumptions and derives the Rolle bound from them, so this is a disclosed scope limitation rather than a circular reduction. The ΛsCDM, f(T), and braneworld examples are illustrative: parameters are chosen to fix z† and the diagnostics are then computed from the model equations, so no fitted quantity is relabeled as a prediction. The many self-citations (ΛsCDM/VCDM, DESI-related analyses, sign-switching reconstructions) motivate the framework and supply worked realizations, but the theorems do not depend on their validity; the paper explicitly separates kinematic regularity from microphysical stability. No uniqueness theorem or ansatz is imported from the authors' prior work as the justification for the central derivation. A minor algebraic typo appears in the printed Eq. (74) factor ΩΛs0/η, which is inconsistent with the quoted 3.9 ≲ η ≲ 11.6 window; this is a numerical-illustration error, not circularity.

Axiom & Free-Parameter Ledger

6 free parameters · 7 axioms · 0 invented entities

The theorems are computed from definitions and standard equations, but the sector-level interpretation rests on the assumed GR-like split, separate conservation, smoothness of the crossing, and the high-redshift condition. The q-zero counting adds an unproved bound on stationary points. Illustrative parameters are chosen by hand, not fitted, and do not enter the proofs.

free parameters (6)
  • Ωm0 = 0.3
    Present-day matter density parameter chosen by hand for all illustrative backgrounds; shifts inferred z† and zrep through the split-dependence formula Eq. (94).
  • z† = 2
    Density sign-switch redshift chosen for the illustrative sign-switching histories; the theorems are independent of its value.
  • η = 2 and 5
    Transition rapidity in the smooth-ΛsCDM tanh profile; chosen to show a case without (η=2) and with (η=5) intermediate acceleration.
  • β = ≈ -0.977
    Parameter of the exponential infrared f(T) model, fixed by requiring z†=2 with Ωm0=0.3; illustrative, and the minimal branch is noted as disfavored by Ref. [100].
  • Ωℓ0 = 0.036
    Brane parameter for the minimal phantom brane, chosen to place the density sign switch at z†=2; illustrative.
  • CPL (w0, wa) = (-0.42, -1.75)
    Reference CPL history using DESI DR2 joint BAO+CMB central values from Ref. [32]; not fitted in this paper.
axioms (7)
  • standard math Standard GR field equations, FLRW equations, and the Raychaudhuri equation with u^μ = δ^μ_0.
    Used throughout Sec. II to define I=ρ+p and M=ρ+3p as the combinations selected by the field equations.
  • domain assumption The effective DE sector is separately conserved, so pde is fixed by Eq. (28) from ρde(z).
    Assumed in Sec. IIIB and used for Eqs. (30)–(31); without it the crossing-side signs and pole residue change.
  • domain assumption The density crossing is smooth, of finite odd order n, with C^{n+1} regularity and negative-to-positive orientation.
    Invoked in Sec. IIIB Eq. (36); jump-like, cusp-like, and fractional-order crossings are explicitly excluded from the main results.
  • domain assumption Mde > 0 at some sufficiently high redshift z_hi > z† for the z_rep existence argument.
    Used after Eq. (46) to obtain at least one repulsion boundary by continuity; stated as a mild high-redshift condition.
  • ad hoc to paper The single-impulse class: each sign switch generates at most one non-positive excursion in Mde, and Mtot has at most two stationary points in the post-recombination interval.
    Assumed in Sec. IVB to obtain the one-or-three q=0 counting via Rolle's theorem; not derived from the profile class.
  • domain assumption Spatial flatness and, for the deceleration counting and the simpler windows, neglect of radiation.
    Used in Sec. IV for Eqs. (49)–(57); the radiation generalization is given in Eq. (58).
  • domain assumption The GR-like split into separately conserved matter, radiation, and an inferred effective DE sector (dark degeneracy).
    Adopted in Secs. I and IIIA; the sector-level statements are split-dependent, as the paper explicitly acknowledges.

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read the original abstract

In general relativity, cosmic acceleration is timelike defocusing of the comoving congruence and requires a negative total active gravitational mass density, $\mathcal{M}_{\rm tot}=\rho_{\rm tot}+3p_{\rm tot}<0$. The criterion $w\equiv p/\rho<-1/3$ diagnoses sector repulsion only for $\rho>0$: the inequality reverses for $\rho<0$, and ratio variables are ill-defined at $\rho=0$ even when the stress-energy tensor is finite. For sign-changing effective dark energy (DE), as in $\Lambda_{\rm s}$CDM-type histories, we instead use the signed density $\rho_{\rm de}$ and two branch-independent combinations. The regular null energy condition (NEC) boundary $\mathcal{I}_{\rm de}=\rho_{\rm de}+p_{\rm de}=0$ replaces the phantom divide $w_{\rm de}=-1$, while $\mathcal{M}_{\rm de}=\rho_{\rm de}+3p_{\rm de}<0$ governs sector-level Raychaudhuri repulsion. For a separately conserved DE sector with a smooth negative-to-positive density crossing of finite odd order $n$ at $z_\dagger$, we prove that $\mathcal{I}_{\rm de}$ and $\mathcal{M}_{\rm de}$ are negative in a punctured neighborhood and non-positive at the crossing, while $w_{\rm de}$ develops a kinematic pole with universal residue $n(1+z_\dagger)/3$. If $\mathcal{M}_{\rm de}>0$ at some sufficiently high redshift, continuity requires at least one repulsion boundary $z_{\rm rep}>z_\dagger$: the sector is already repulsive while $\rho_{\rm de}<0$. We derive the exact range of $\rho_{\rm de}'(z_\dagger)$ for acceleration at the crossing with the total NEC satisfied. Under the stated single-impulse and stationary-point assumptions, the deceleration parameter has one or three sign-changing zeros. A smooth $\Lambda_{\rm s}$CDM profile, an exponential infrared $f(T)$ model, and the minimal phantom brane illustrate the results. These results motivate organizing late-time inference around $(\rho,p,\mathcal{I},\mathcal{M})$ rather than around $w$ alone.

Figures

Figures reproduced from arXiv: 2607.18008 by Antonio De Felice, N. Merve Uzun, \"Ozg\"ur Akarsu.

Figure 1
Figure 1. Figure 1: FIG. 1. Evolution of separately conserved sign-switching DE sectors on a spatially flat matter plus DE background, with [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Inertial and active gravitational mass densities, defined in Eq. [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

129 extracted references · 103 linked inside Pith

  1. [1]

    Addressing observational tensions in cosmology with sys- tematics and fundamental physics

    For the tanh profile (66) this gives |∆z†| ≃ (1 + z†)3 tanh(ηz†) ∆Ωm0/(ΩΛs0 η), i.e.,|∆z†| ≃0.19for η = 2 and ≃ 0.08for η = 5per∆Ω m0 = 0.01; the repulsion- onset redshift zrep is likewise split dependent. Reported values of z† and zrep should therefore be quoted jointly with the matter-density posterior of the analysis that produced them. Second, by cont...

  2. [2]

    A. G. Riesset al.(Supernova Search Team), Obser- vational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J.116, 1009 (1998), astro-ph/9805201

    Pith/arXiv arXiv 1998

  3. [3]

    Perlmutteret al.(Supernova Cosmology Project), Measurements ofΩandΛfrom 42 high redshift super- novae, Astrophys

    S. Perlmutteret al.(Supernova Cosmology Project), Measurements ofΩandΛfrom 42 high redshift super- novae, Astrophys. J.517, 565 (1999), astro-ph/9812133

    Pith/arXiv arXiv 1999

  4. [4]

    Ratra and P

    B. Ratra and P. J. E. Peebles, Cosmological Conse- quences of a Rolling Homogeneous Scalar Field, Phys. Rev. D37, 3406 (1988)

    1988

  5. [5]

    R. R. Caldwell, R. Dave, and P. J. Steinhardt, Cosmo- logical imprint of an energy component with general equation of state, Phys. Rev. Lett.80, 1582 (1998), astro-ph/9708069

    Pith/arXiv arXiv 1998

  6. [6]

    R. R. Caldwell, A Phantom menace? Cosmological conse- quences of a dark energy component with super-negative 25 equation of state, Phys. Lett. B545, 23 (2002), astro- ph/9908168

    arXiv 2002

  7. [7]

    Weinberg, The Cosmological Constant Problem, Rev

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

    1989

  8. [8]

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

    Pith/arXiv arXiv 2003

  9. [9]

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

    Pith/arXiv arXiv 2006

  10. [10]

    Frieman, M

    J. Frieman, M. Turner, and D. Huterer, Dark Energy and the Accelerating Universe, Ann. Rev. Astron. Astrophys. 46, 385 (2008), 0803.0982

    Pith/arXiv arXiv 2008

  11. [11]

    Chevallier and D

    M. Chevallier and D. Polarski, Accelerating universes with scaling dark matter, Int. J. Mod. Phys. D10, 213 (2001), gr-qc/0009008

    Pith/arXiv arXiv 2001

  12. [12]

    E. V. Linder, Exploring the expansion history of the universe, Phys. Rev. Lett.90, 091301 (2003), astro- ph/0208512

    arXiv 2003

  13. [13]

    E. V. Linder, Mapping the Cosmological Expansion, Rept. Prog. Phys.71, 056901 (2008), 0801.2968

    Pith/arXiv arXiv 2008

  14. [14]

    Visinelli, S

    L. Visinelli, S. Vagnozzi, and U. Danielsson, Revisiting a negative cosmological constant from low-redshift data, Symmetry11, 1035 (2019), 1907.07953

    Pith/arXiv arXiv 2019

  15. [15]

    Akarsu, J

    Ö. Akarsu, J. D. Barrow, L. A. Escamilla, and J. A. Vazquez, Graduated dark energy: Observational hints of a spontaneous sign switch in the cosmological constant, Phys. Rev. D101, 063528 (2020), 1912.08751

    Pith/arXiv arXiv 2020

  16. [16]

    Calderón, R

    R. Calderón, R. Gannouji, B. L’Huillier, and D. Polarski, Negative cosmological constant in the dark sector?, Phys. Rev. D103, 023526 (2021), 2008.10237

    Pith/arXiv arXiv 2021

  17. [17]

    A. A. Sen, S. A. Adil, and S. Sen, Do cosmological observations allow a negativeΛ?, Mon. Not. Roy. Astron. Soc.518, 1098 (2022), 2112.10641

    Pith/arXiv arXiv 2022

  18. [18]

    Malekjani, R

    M. Malekjani, R. M. Conville, E. Ó. Colgáin, S. Pouro- jaghi, and M. M. Sheikh-Jabbari, On redshift evolution and negative dark energy density in Pantheon + Super- novae, Eur. Phys. J. C84, 317 (2024), 2301.12725

    Pith/arXiv arXiv 2024

  19. [19]

    Alam and V

    U. Alam and V. Sahni, Confronting braneworld cosmol- ogy with supernova data and baryon oscillations, Phys. Rev. D73, 084024 (2006), astro-ph/0511473

    Pith/arXiv arXiv 2006

  20. [20]

    U. Alam, S. Bag, and V. Sahni, Constraining the Cos- mology of the Phantom Brane using Distance Measures, Phys. Rev. D95, 023524 (2017), 1605.04707

    Pith/arXiv arXiv 2017

  21. [21]

    Özülker, Is the dark energy equation of state pa- rameter singular?, Phys

    E. Özülker, Is the dark energy equation of state pa- rameter singular?, Phys. Rev. D106, 063509 (2022), 2203.04167

    Pith/arXiv arXiv 2022

  22. [22]

    Raychaudhuri, Relativistic cosmology

    A. Raychaudhuri, Relativistic cosmology. I, Phys. Rev. 98, 1123 (1955)

    1955

  23. [23]

    R. M. Wald,General Relativity(Chicago Univ. Pr., Chicago, USA, 1984)

    1984

  24. [24]

    S. W. Hawking and G. F. R. Ellis,The Large Scale Struc- ture of Space-Time, Cambridge Monographs on Mathe- matical Physics (Cambridge University Press, 1973)

    1973

  25. [25]

    Akarsu, M

    Ö. Akarsu, M. Caruana, K. F. Dialektopoulos, L. A. Escamilla, E. O. Kahya, and J. Levi Said, Do equation of state parametrizations of dark energy faithfully capture the dynamics of the late universe? (2026), 2604.12987

    Pith/arXiv arXiv 2026

  26. [26]

    Akarsu, M

    Ö. Akarsu, M. Caruana, K. F. Dialektopoulos, L. A. Escamilla, E. O. Kahya, and J. Levi Said, Hints of sign-changing scalar field energy density and a tran- sient acceleration phase atz∼ 2from model-agnostic reconstructions (2026), 2602.08928

    arXiv 2026

  27. [27]

    Gupta Choudhury, P

    S. Gupta Choudhury, P. Mukherjee, E. Di Valentino, and A. A. Sen, Model-Independent Indication for a Localized Anomaly in the Late-Time Expansion History (2026), 2607.13009

    Pith/arXiv arXiv 2026

  28. [28]

    S. A. Adil, M. A. Zapata, Ö. Akarsu, and J. A. Vazquez, Background-level reconstruction of scalar-field potentials from dark-energy histories and comparison with analytic potential families, Phys. Dark Univ.53, 102387 (2026), 2603.14693

    Pith/arXiv arXiv 2026

  29. [29]

    Kunz, The dark degeneracy: On the number and nature of dark components, Phys

    M. Kunz, The dark degeneracy: On the number and nature of dark components, Phys. Rev. D80, 123001 (2009), astro-ph/0702615

    Pith/arXiv arXiv 2009

  30. [30]

    R. R. Caldwell and E. V. Linder, Null impact of the null energy condition in current cosmology, J. Cosmol. Astropart. Phys.05, 008 (2026), 2511.07526

    arXiv 2026

  31. [31]

    S. S. Mishra, Effective Phantom Dark Energy: What Cosmological Reconstruction Does and Does Not Imply (2026), 2605.27301

    Pith/arXiv arXiv 2026

  32. [32]

    A. G. Adameet al.(DESI), DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations, J. Cosmol. Astropart. Phys.2025(02), 021 (2025), 2404.03002

    Pith/arXiv arXiv 2024

  33. [33]

    Abdul Karimet al.(DESI), DESI DR2 results

    M. Abdul Karimet al.(DESI), DESI DR2 results. II. Measurements of baryon acoustic oscillations and cos- mological constraints, Phys. Rev. D112, 083515 (2025), 2503.14738

    Pith/arXiv arXiv 2025

  34. [34]

    T. Xu, S. Kumar, Y. Chen, A. J. S. Capistrano, and Ö. Akarsu, Probing Dynamical Dark Energy with Late- Time Data: Evidence, Tensions, and the Limits of the w0waCDM Framework (2026), 2602.11936

    Pith/arXiv arXiv 2026

  35. [35]

    Özülker, E

    E. Özülker, E. Di Valentino, and W. Giarè, Dark Energy Crosses the Line: Quantifying and Testing the Evidence for Phantom Crossing (2025), 2506.19053

    Pith/arXiv arXiv 2025

  36. [36]

    Gökçen, Ö

    M. Gökçen, Ö. Akarsu, and E. Di Valentino, Revisiting CPL with sign-switching density: To cross or not to cross the NECB, Phys. Dark Univ.52, 102273 (2026), 2602.21169

    arXiv 2026

  37. [37]

    H. K. Jassal, J. S. Bagla, and T. Padmanabhan, WMAP constraints on low redshift evolution of dark energy, Mon. Not. Roy. Astron. Soc.356, L11 (2005), astro- ph/0404378

    arXiv 2005

  38. [38]

    H. K. Jassal, J. S. Bagla, and T. Padmanabhan, Ob- servational constraints on low redshift evolution of dark energy: How consistent are different observations?, Phys. Rev. D72, 103503 (2005), astro-ph/0506748

    Pith/arXiv arXiv 2005

  39. [39]

    E. M. Barboza, Jr. and J. S. Alcaniz, A parametric model for dark energy, Phys. Lett. B666, 415 (2008), 0805.1713

    Pith/arXiv arXiv 2008

  40. [40]

    S. Pan, W. Yang, and A. Paliathanasis, Imprints of an extended Chevallier–Polarski–Linder parametrization on the large scale of our universe, Eur. Phys. J. C80, 274 (2020), 1902.07108

    Pith/arXiv arXiv 2020

  41. [41]

    Najafi, S

    M. Najafi, S. Pan, E. Di Valentino, and J. T. Firouz- jaee, Dynamical dark energy confronted with multiple CMB missions, Phys. Dark Univ.45, 101539 (2024), 2407.14939

    Pith/arXiv arXiv 2024

  42. [42]

    Tripathi, A

    A. Tripathi, A. Sangwan, and H. K. Jassal, Dark energy equation of state parameter and its evolution at low redshift, J. Cosmol. Astropart. Phys.06, 012 (2017), 1611.01899

    Pith/arXiv arXiv 2017

  43. [43]

    Di Valentino, A

    E. Di Valentino, A. Mukherjee, and A. A. Sen, Dark Energy with Phantom Crossing and the H0 Tension, Entropy23, 404 (2021), 2005.12587

    Pith/arXiv arXiv 2021

  44. [44]

    S. A. Adil, Ö. Akarsu, E. Di Valentino, R. C. Nunes, E. Özülker, A. A. Sen, and E. Specogna, Omnipotent 26 dark energy: A phenomenological answer to the Hubble tension, Phys. Rev. D109, 023527 (2024), 2306.08046

    Pith/arXiv arXiv 2024

  45. [45]

    Montefalcone and R

    G. Montefalcone and R. Stiskalek, Parameterizing Dark Energy at the density level: A two-parameter alternative to CPL (2026), 2603.25735

    arXiv 2026

  46. [46]

    A. A. Sen, Deviation From LambdaCDM: Pressure Parametrization, Phys. Rev. D77, 043508 (2008), 0708.1072

    Pith/arXiv arXiv 2008

  47. [47]

    Cheng, E

    H. Cheng, E. Di Valentino, L. A. Escamilla, A. A. Sen, and L. Visinelli, Pressure parametrization of dark energy: first and second-order constraints with latest cosmolog- ical data, J. Cosmol. Astropart. Phys.09, 031 (2025), 2505.02932

    arXiv 2025

  48. [48]

    Acquaviva, Ö

    G. Acquaviva, Ö. Akarsu, N. Katirci, and J. A. Vazquez, Simple-graduated dark energy and spatial curvature, Phys. Rev. D104, 023505 (2021), 2104.02623

    Pith/arXiv arXiv 2021

  49. [49]

    L. A. Escamilla, B. Karadavut, and N. Katırcı, Dark Energy with Constant Inertial Mass Density: Updated Constraints and Curvature-Induced Sign Transitions in ρDE andρ DE +p DE (2026), 2603.15868

    arXiv 2026

  50. [50]

    L. A. Escamilla, O. Akarsu, E. Di Valentino, and J. A. Vazquez, Model-independent reconstruction of the inter- acting dark energy kernel: Binned and Gaussian process, JCAP11, 051 (2023), 2305.16290

    Pith/arXiv arXiv 2023

  51. [51]

    M. A. Sabogal, Ö. Akarsu, A. Bonilla, E. Di Valentino, and R. C. Nunes, Exploring new physics in the late Universe’s expansion through non-parametric inference, Eur. Phys. J. C84, 703 (2024), 2407.04223

    Pith/arXiv arXiv 2024

  52. [52]

    Verde, T

    L. Verde, T. Treu, and A. G. Riess, Tensions between the Early and the Late Universe, Nature Astron.3, 891 (2019), 1907.10625

    Pith/arXiv arXiv 2019

  53. [53]

    Di Valentinoet al., Snowmass2021 - Letter of interest cosmology intertwined II: The hubble constant tension, Astropart

    E. Di Valentinoet al., Snowmass2021 - Letter of interest cosmology intertwined II: The hubble constant tension, Astropart. Phys.131, 102605 (2021), 2008.11284

    Pith/arXiv arXiv 2021

  54. [54]

    A. G. Riesset 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, L7 (2022), 2112.04510

    Pith/arXiv arXiv 2022

  55. [55]

    S. Alamet al.(eBOSS Collaboration), Completed SDSS- IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectro- scopic surveys at the Apache Point Observatory, Phys. Rev. D103, 083533 (2021), 2007.08991

    Pith/arXiv arXiv 2021

  56. [56]

    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), 2103.01183

    Pith/arXiv arXiv 2021

  57. [57]

    Perivolaropoulos and F

    L. Perivolaropoulos and F. Skara, Challenges forΛCDM: An update, New Astron. Rev.95, 101659 (2022), 2105.05208

    Pith/arXiv arXiv 2022

  58. [58]

    High Energy Astrophys.34, 49 (2022), 2203.06142

    E.Abdallaet al.,Cosmologyintertwined: Areviewofthe particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies, J. High Energy Astrophys.34, 49 (2022), 2203.06142

    Pith/arXiv arXiv 2022

  59. [59]

    Akarsu, E

    Ö. Akarsu, E. Ó. Colgáin, A. A. Sen, and M. M. Sheikh- Jabbari,ΛCDM Tensions: Localising Missing Physics through Consistency Checks, Universe10, 305 (2024), 2402.04767

    Pith/arXiv arXiv 2024

  60. [60]

    Di Valentinoet al.(CosmoVerse Network), The Cos- moVerseWhitePaper: Addressingobservationaltensions in cosmology with systematics and fundamental physics, Phys

    E. Di Valentinoet al.(CosmoVerse Network), The Cos- moVerseWhitePaper: Addressingobservationaltensions in cosmology with systematics and fundamental physics, Phys. Dark Univ.49, 101965 (2025), 2504.01669

    Pith/arXiv arXiv 2025

  61. [61]

    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)], 1807.06209

    Pith/arXiv arXiv 2018

  62. [62]

    Akarsu, A

    Ö. Akarsu, A. Çam, E. A. Paraskevas, and L. Perivolaropoulos, Linear matter density perturbations in theΛ sCDM model: Examining growth dynamics and addressing the S8 tension, J. Cosmol. Astropart. Phys. 2025(08), 089 (2025), 2502.20384

    Pith/arXiv arXiv 2025

  63. [63]

    Akarsu, S

    Ö. Akarsu, S. Kumar, E. Özülker, and J. A. Vazquez, Relaxing cosmological tensions with a sign switching cosmological constant, Phys. Rev. D104, 123512 (2021), 2108.09239

    Pith/arXiv arXiv 2021

  64. [64]

    Akarsu, S

    Ö. Akarsu, S. Kumar, E. Özülker, J. A. Vazquez, and A. Yadav, Relaxing cosmological tensions with a sign switching cosmological constant: Improved results with Planck, BAO, and Pantheon data, Phys. Rev. D108, 023513 (2023), 2211.05742

    Pith/arXiv arXiv 2023

  65. [65]

    Akarsu, E

    Ö. Akarsu, E. Di Valentino, S. Kumar, R. C. Nunes, J. A. Vazquez, and A. Yadav,ΛsCDM model: A promising scenario for alleviation of cosmological tensions (2023), 2307.10899

    Pith/arXiv arXiv 2023

  66. [66]

    Akarsu, A

    Ö. Akarsu, A. De Felice, E. Di Valentino, S. Kumar, R. C. Nunes, E. Özülker, J. A. Vazquez, and A. Ya- dav,Λ sCDM cosmology from a type-II minimally modi- fied gravity, Mon. Not. Roy. Astron. Soc.546, staf2276 (2026), 2402.07716

    Pith/arXiv arXiv 2026

  67. [67]

    Akarsu, A

    Ö. Akarsu, A. De Felice, E. Di Valentino, S. Kumar, R. C. Nunes, E. Özülker, J. A. Vazquez, and A. Yadav, Cosmological constraints onΛsCDM scenario in a type II minimally modified gravity, Phys. Rev. D110, 103527 (2024), 2406.07526

    Pith/arXiv arXiv 2024

  68. [68]

    L. A. Escamilla, Ö. Akarsu, E. Di Valentino, E. Özülker, and J. A. Vazquez, Exploring the Growth-Index (γ) Tension withΛ sCDM (2025), 2503.12945

    Pith/arXiv arXiv 2025

  69. [69]

    E. A. Paraskevas, A. Çam, L. Perivolaropoulos, and Ö. Akarsu, Transition dynamics in theΛsCDM model: Implications for bound cosmic structures, Phys. Rev. D 109, 103522 (2024), 2402.05908

    Pith/arXiv arXiv 2024

  70. [70]

    Akarsu, E

    Ö. Akarsu, E. Di Valentino, J. Vyskočil, E. Yılmaz, A. E. Yükselci, and A. Zhuk, Nonlinear matter power spectrum from relativistic N-body simulations:ΛsCDM versus ΛCDM, Phys. Rev. D113, 083508 (2026), 2510.18741

    Pith/arXiv arXiv 2026

  71. [71]

    Yadav, S

    A. Yadav, S. Kumar, C. Kıbrıs, and Ö. Akarsu,ΛsCDM cosmology: alleviating major cosmological tensions by predicting standard neutrino properties, J. Cosmol. As- tropart. Phys.2025(01), 042 (2025), 2406.18496

    Pith/arXiv arXiv 2025

  72. [72]

    Kıbrıs, W

    C. Kıbrıs, W. Elbers, Ö. Akarsu, and E. Di Valentino, Negative neutrino mass or negative dark energy? (2026), 2605.21456

    Pith/arXiv arXiv 2026

  73. [73]

    M. S. Souza, A. M. Barcelos, R. C. Nunes, Ö. Akarsu, and S. Kumar, Mapping theΛsCDM Scenario to f(T) Modified Gravity: Effects on Structure Growth Rate, Universe11, 2 (2025), 2501.18031

    Pith/arXiv arXiv 2025

  74. [74]

    A. Awad, W. El Hanafy, G. G. L. Nashed, and E. N. Saridakis, Phase Portraits of general f(T) Cosmology, J. Cosmol. Astropart. Phys.02, 052 (2018), 1710.10194

    Pith/arXiv arXiv 2018

  75. [75]

    Hashim, W

    M. Hashim, W. El Hanafy, A. Golovnev, and A. A. El- Zant, Toward a concordance teleparallel cosmology. Part I. Background dynamics, J. Cosmol. Astropart. Phys. 07, 052 (2021), 2010.14964

    Pith/arXiv arXiv 2021

  76. [76]

    Hashim, A

    M. Hashim, A. A. El-Zant, W. El Hanafy, and A. Golovnev, Toward a concordance teleparallel cosmol- ogy. Part II. Linear perturbation, J. Cosmol. Astropart. Phys.07, 053 (2021), 2104.08311. 27

    Pith/arXiv arXiv 2021

  77. [77]

    Akarsu, B

    Ö. Akarsu, B. Bulduk, A. De Felice, N. Katırcı, and N. M. Uzun, Unexplored regions in teleparallel f(T) gravity: Sign-changing dark energy density, Phys. Rev. D112, 083532 (2025), 2410.23068

    arXiv 2025

  78. [78]

    Sahni and Y

    V. Sahni and Y. Shtanov, Brane world models of dark energy, J. Cosmol. Astropart. Phys.2003(11), 014 (2003), astro-ph/0202346

    Pith/arXiv arXiv 2003

  79. [79]

    Sahni and Y

    V. Sahni and Y. Shtanov, New vistas in brane world cosmology, Int. J. Mod. Phys. D11, 1515 (2002), gr- qc/0205111

    arXiv 2002

  80. [80]

    S. Bag, V. Sahni, A. Shafieloo, and Y. Shtanov, Phantom Braneworld and the Hubble Tension, Astrophys. J.923, 212 (2021), 2107.03271

    Pith/arXiv arXiv 2021

Showing first 80 references.