arxiv: 2604.21962 · v1 · submitted 2026-04-23 · 🌀 gr-qc

Recognition: unknown

Perturbation Dynamics and Structure Formation in Extended Proca-Nuevo Gravity

N. S. Kavya , Avik De , Tee-How Loo

Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:04 UTC · model grok-4.3

classification 🌀 gr-qc

keywords extended proca-nuevo gravitycosmological perturbationsstructure formationvector-tensor gravitymassive vector fieldanisotropic stressmodified gravity

0 comments

The pith

In Extended Proca-Nuevo gravity the vector field adds effective anisotropic stress to perturbations yet leaves the matter growth equation identical to general relativity.

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

The paper examines linear cosmological perturbations and the growth of cosmic structure inside the Extended Proca-Nuevo framework, a vector-tensor extension of general relativity that includes a massive spin-1 field. This field imposes an algebraic constraint on the background, producing a Hubble expansion rate that matches the Lambda-CDM model at early and late times while deviating at intermediate redshifts. Under the assumption of minimal matter coupling the authors derive gauge-invariant perturbation equations and show that the vector sector generates effective anisotropic stress while coupling one propagating scalar mode to the metric potentials. The resulting equation for the evolution of matter density contrasts therefore retains exactly the same form as in general relativity, only evaluated against the modified expansion history instead of the standard one. The full scalar system is written out explicitly and stability conditions are identified to prepare the model for confrontation with observations.

Core claim

In the Extended Proca-Nuevo framework the massive vector field modifies the cosmological background through an algebraic constraint, yielding a characteristic Hubble evolution that interpolates between Lambda-CDM limits. At the linear perturbation level this sector induces effective anisotropic stress and couples a single propagating scalar mode to the metric potentials. As a direct consequence the equation that governs the growth of matter inhomogeneities remains formally identical to the one in general relativity, but it now operates with the altered expansion history rather than the standard Lambda-CDM background.

What carries the argument

the massive vector field subject to an algebraic constraint on the background, which sources effective anisotropic stress and couples one scalar mode to the metric potentials in the linear equations

If this is right

The differential equation for the growth of matter density contrasts stays exactly the same as in general relativity.
Deviations from Lambda-CDM appear only through the background expansion history at intermediate redshifts.
The complete set of gauge-invariant scalar perturbation equations is available for numerical integration.
Stability conditions for the scalar modes can be read off directly from the derived system.
The framework supplies a concrete baseline for comparing future observations of structure growth against a modified background.

Where Pith is reading between the lines

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

Surveys that measure the growth rate at multiple redshifts could separate this model from modified-gravity theories that change the growth equation itself.
The primary observable signature would be a mismatch between the observed expansion history and the clustering amplitude predicted by the unchanged growth equation.
Nonlinear evolution or the inclusion of additional fields could generate further signatures not captured by the linear analysis presented here.

Load-bearing premise

The linear perturbation equations are derived under the assumption of minimal coupling between the vector field and ordinary matter.

What would settle it

A measurement showing that the growth rate of matter density contrasts deviates from the prediction obtained by inserting the modified expansion history into the standard general-relativity growth equation would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.21962 by Avik De, N. S. Kavya, Tee-How Loo.

**Figure 1.** Figure 1: FIG. 1: Posterior constraints on the EPN cosmological parameters from different dataset combinations. Contours [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2: (Top row) BAO measurements from DESI DR2: [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

read the original abstract

A comprehensive analysis of cosmological perturbations and structure formation is presented for the Extended Proca-Nuevo (EPN) framework, a vector-tensor extension of General Relativity with a massive spin-1 field. In this scenario, the vector field modifies the background expansion through an algebraic constraint, leading to a characteristic Hubble evolution that interpolates between $\Lambda$CDM limits while introducing deviations at intermediate redshifts. Assuming minimal matter coupling, the linear perturbation equations are derived in gauge-invariant form and the resulting growth of matter inhomogeneities is analyzed. The EPN sector induces effective anisotropic stress and couples a single propagating scalar mode to the metric potentials, leaving the matter growth equation in its GR form but with a modified expansion history. The full scalar perturbation system is presented, stability conditions are discussed, and the results provide a foundation for testing the EPN framework against current and future cosmological observations.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note private letter to a colleague

This paper gives the first gauge-invariant perturbation equations for Extended Proca-Nuevo gravity and claims the matter growth equation stays exactly GR form despite the induced anisotropic stress.

read the letter

The punchline is that this work moves the Extended Proca-Nuevo model from background-only studies to a usable linear perturbation framework. They start from the algebraic constraint on the vector field that sets the expansion history, then derive the gauge-invariant scalar perturbation equations and show how one extra propagating mode couples to the metric potentials while producing effective anisotropic stress. The central result is that the second-order equation for the matter density contrast reduces to the standard GR form, with all modifications absorbed into the background Hubble rate. That is the new piece: prior literature on this model stopped at the background, so the explicit scalar system and stability discussion fill a clear gap. They also lay out the full set of equations, which is useful for anyone who wants to confront the model with growth data. The derivation looks careful on the surface and the minimal-coupling assumption is stated plainly. The soft spot is the load-bearing claim about the growth equation. Anisotropic stress normally sources gravitational slip and alters the Poisson relation that drives delta growth, yet the paper asserts no extra friction, sound-speed, or effective-G terms appear after eliminating the auxiliary modes. The abstract states the outcome but the provided text does not walk through the algebra that confirms the cancellation, so it is impossible to judge whether the result is robust or follows by construction from the constraint. No numerical solutions, growth-rate plots, or comparison to current f sigma_8 data are given either. This paper is for cosmologists working on vector-tensor extensions or on model-independent tests of structure growth. A reader who already knows the background EPN solutions will find the perturbation setup directly usable. It deserves a serious referee because the derivation is new, the equations are presented, and the claim is falsifiable with existing and upcoming surveys, even if the referee will likely ask for the explicit elimination steps and at least one numerical check.

Referee Report

1 major / 1 minor

Summary. The paper analyzes cosmological perturbations and structure formation in the Extended Proca-Nuevo (EPN) vector-tensor extension of GR. The vector field imposes an algebraic constraint that sets a characteristic background Hubble evolution interpolating between ΛCDM limits. Assuming minimal matter coupling, gauge-invariant linear perturbation equations are derived; the EPN sector produces effective anisotropic stress and couples one propagating scalar mode to the metric potentials, yet the matter density contrast is asserted to obey the standard GR growth equation δ'' + 2Hδ' − (3/2)Ω_m H² δ = 0, with deviations entering only through the modified expansion history. The full scalar perturbation system, stability conditions, and observational implications are presented.

Significance. If the central claim that the growth equation remains exactly GR form is verified, the model supplies a clean observational signature—modified background expansion without altered structure growth—that distinguishes it from most modified-gravity scenarios. The gauge-invariant formulation and explicit stability discussion provide a concrete foundation for confronting the theory with current and future data.

major comments (1)

[Section presenting the full scalar perturbation system] In the section presenting the full scalar perturbation system, the elimination of the auxiliary scalar and vector modes must be shown explicitly to confirm that the second-order equation for the matter density contrast δ remains exactly δ'' + 2Hδ' − (3/2)Ω_m H² δ = 0. The presence of effective anisotropic stress generally sources gravitational slip (Φ − Ψ ≠ 0) and thereby modifies the Poisson-like relation that sources δ growth; without the explicit reduction it is impossible to verify that no extra friction, sound-speed, or effective-G terms appear.

minor comments (1)

[Abstract] The abstract states that equations were derived and stability discussed but supplies no explicit forms, key intermediate results, or error analysis, making the support for the central claim difficult to assess from the summary alone.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive major comment. We address the point below.

read point-by-point responses

Referee: In the section presenting the full scalar perturbation system, the elimination of the auxiliary scalar and vector modes must be shown explicitly to confirm that the second-order equation for the matter density contrast δ remains exactly δ'' + 2Hδ' − (3/2)Ω_m H² δ = 0. The presence of effective anisotropic stress generally sources gravitational slip (Φ − Ψ ≠ 0) and thereby modifies the Poisson-like relation that sources δ growth; without the explicit reduction it is impossible to verify that no extra friction, sound-speed, or effective-G terms appear.

Authors: We agree that an explicit step-by-step elimination of the auxiliary modes is required to rigorously confirm the reduction. In the revised manuscript we will expand the scalar perturbation section to include the full derivation: starting from the gauge-invariant equations for the metric potentials and the vector-field perturbations, we solve the algebraic constraints for the auxiliary scalar and vector modes, substitute into the Einstein equations to obtain the relation between Φ, Ψ and the matter density contrast δ, and finally insert into the continuity and Euler equations for matter. This will demonstrate that all contributions from the effective anisotropic stress and gravitational slip cancel or are absorbed into the background Hubble evolution, leaving precisely the GR growth equation δ'' + 2Hδ' − (3/2)Ω_m H² δ = 0 with no additional friction, sound-speed or effective-G terms. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained.

full rationale

The paper derives the linear perturbation equations in gauge-invariant form from the EPN action under minimal coupling, presents the full scalar perturbation system, and obtains the matter growth equation as a derived result after eliminating auxiliary modes. The claim that this equation retains its GR form (with only H(t) replaced by the EPN-modified expansion) follows from explicit elimination rather than being imposed by definition or by a self-citation chain. No fitted parameters are renamed as predictions, no ansatz is smuggled via prior self-work, and the background algebraic constraint on the vector field is an input that is then propagated through the perturbation analysis without tautological reduction. The analysis is therefore independent of its target claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption of minimal matter coupling and the algebraic constraint that defines the vector-field background; no free parameters or invented entities are explicitly listed in the abstract.

axioms (1)

domain assumption Minimal matter coupling
Stated as the basis for deriving the linear perturbation equations.

pith-pipeline@v0.9.0 · 5451 in / 1115 out tokens · 27941 ms · 2026-05-09T21:04:34.289090+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

65 extracted references · 56 canonical work pages · 4 internal anchors

[1]

Kinetic operator and sound speed of the propagating scalar mode The quadratic action for the surviving EPN scalar mode can be written in the schematic form S(2) EPN = 1 2 Z d3k dt a3 " KEPN(a) ˙ˆχ 2 − GEPN(a,k) k2 a2 ˆχ 2 − MEPN(a) ˆχ 2 # , (A1) whereK EPN >0 ensures the absence of ghosts, while the effective sound speed is defined as c2 s (a)≡ GEPN(a,k) ...
[2]

Coefficients in the dynamical perturbation equation The coefficients appearing in Eq. (40) may be written as D(a) =a 3KEPN(a), (A7) E(a) = d dt h a3KEPN(a) i , (A8) F(a) =a 3MEPN(a), (A9) while the source couplings to the metric potentials are given by SΦ(a) =a 3ϕH(α 1,X +d 1,X ),S Ψ(a) =−2a 3 H(α1,X +d 1,X ), (A10) and the scale-dependent contribution re...
[3]

Weinberg, The Cosmological Constant Problem, Rev

S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys.61, 1 (1989). 13

1989
[4]

Padmanabhan, Phys

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

work page arXiv 2003
[5]

Quintessence, Cosmic Coincidence, and the Cosmological Constant

I. Zlatev, L.-M. Wang, and P . J. Steinhardt, Quintessence, cosmic coincidence, and the cosmological constant, Phys. Rev. Lett. 82, 896 (1999), arXiv:astro-ph/9807002

work page Pith review arXiv 1999
[6]

S. G. Choudhury, P . Mukherjee, and A. A. Sen, Toward a composite framework for simultaneous exploration of new physics in the background dynamics and in the perturbed Universe, Phys. Rev. D111, 123529 (2025), arXiv:2502.18457 [astro-ph.CO]

work page arXiv 2025
[7]

Lesgourgues, G

J. Lesgourgues, G. Marques-Tavares, and M. Schmaltz, Evidence for dark matter interactions in cosmological precision data?, JCAP02, 037, arXiv:1507.04351 [astro-ph.CO]

work page arXiv
[8]

Beyond the Cosmological Standard Model

A. Joyce, B. Jain, J. Khoury, and M. Trodden, Beyond the Cosmological Standard Model, Phys. Rept.568, 1 (2015), arXiv:1407.0059 [astro-ph.CO]

work page Pith review arXiv 2015
[9]

Giovannini, Growth rate of matter perturbations as a probe of large-scale magnetism, Phys

M. Giovannini, Growth rate of matter perturbations as a probe of large-scale magnetism, Phys. Rev. D84, 063010 (2011), arXiv:1106.5043 [astro-ph.CO]

work page arXiv 2011
[10]

Pogosian and A

L. Pogosian and A. Silvestri, The pattern of growth in viable f(R) cosmologies, Phys. Rev. D77, 023503 (2008), [Erratum: Phys.Rev.D 81, 049901 (2010)], arXiv:0709.0296 [astro-ph]

work page arXiv 2008
[11]

Jain and P

B. Jain and P . Zhang, Observational Tests of Modified Gravity, Phys. Rev. D78, 063503 (2008), arXiv:0709.2375 [astro-ph]

work page arXiv 2008
[12]

Milgrom, Bimetric MOND gravity, Phys

M. Milgrom, Bimetric MOND gravity, Phys. Rev. D80, 123536 (2009), arXiv:0912.0790 [gr-qc]

work page arXiv 2009
[13]

de Rham, G

C. de Rham, G. Gabadadze, and A. J. Tolley, Resummation of Massive Gravity, Phys. Rev. Lett.106, 231101 (2011), arXiv:1011.1232 [hep-th]

work page arXiv 2011
[14]

Comelli, M

D. Comelli, M. Crisostomi, F. Nesti, and L. Pilo, FRW Cosmology in Ghost Free Massive Gravity, JHEP03, 067, [Erratum: JHEP 06, 020 (2012)], arXiv:1111.1983 [hep-th]

work page arXiv 2012
[15]

Einstein-aether theory,

C. Eling, T. Jacobson, and D. Mattingly, Einstein-Aether theory, inDeserfest: A Celebration of the Life and Works of Stanley Deser (2004) pp. 163–179, arXiv:gr-qc/0410001

work page internal anchor Pith review arXiv 2004
[16]

Cosmology in generalized Proca theories

A. De Felice, L. Heisenberg, R. Kase, S. Mukohyama, S. Tsujikawa, and Y.-l. Zhang, Cosmology in generalized Proca theories, JCAP06, 048, arXiv:1603.05806 [gr-qc]

work page Pith review arXiv
[17]

de Rham and V

C. de Rham and V . Pozsgay, New class of Proca interactions, Phys. Rev. D102, 083508 (2020), arXiv:2003.13773 [hep-th]

work page arXiv 2020
[18]

Errasti D´ıez, M

V . Errasti D´ıez, M. Maier, and J. A. M ´endez-Zavaleta, Constraint characterization and degree of freedom counting in La- grangian field theory, Phys. Rev. D109, 025010 (2024), arXiv:2310.12218 [hep-th]

work page arXiv 2024
[19]

E. N. Saridakis, Do we need soft cosmology?, Phys. Lett. B822, 136649 (2021), arXiv:2105.08646 [astro-ph.CO]

work page arXiv 2021
[20]

Sudharani, N

L. Sudharani, N. S. Kavya, and V . Venkatesha, Unveiling the effects of coupling extended Proca-Nuevo gravity on cosmic expansion with recent observations, Mon. Not. Roy. Astron. Soc.535, 1998 (2024), arXiv:2412.02707 [gr-qc]

work page arXiv 1998
[21]

A. M. Sultan, Gravitational Baryogenesis in Extended Proca-Nuevo Gravity, arXiv 2504.06133 (2025), arXiv:2504.06133 [gr- qc]

work page arXiv 2025
[22]

N. S. Kavya, L. Sudharani, and V . Venkatesha, Constraining extended Proca-Nuevo theory through big bang nucleosynthesis, Gen. Rel. Grav.57, 53 (2025)

2025
[23]

Chiang, C

H.-W. Chiang, C. de Rham, S. Garcia-Saenz, and X. Zhou, Cosmological tensions in Proca-Nuevo theory, arXiv 2511.21071 (2025), arXiv:2511.21071 [hep-th]

work page arXiv 2025
[24]

F. K. Anagnostopoulos and E. N. Saridakis, Observational constraints on extended Proca-Nuevo gravity and cosmology, JCAP04, 051, arXiv:2312.15483 [astro-ph.CO]

work page arXiv
[25]

Lagos, T

M. Lagos, T. Baker, P . G. Ferreira, and J. Noller, A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories, JCAP08, 007, arXiv:1604.01396 [gr-qc]

work page arXiv
[26]

Lagos, E

M. Lagos, E. Bellini, J. Noller, P . G. Ferreira, and T. Baker, A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics, JCAP03, 021, arXiv:1711.09893 [gr-qc]

work page arXiv
[27]

K. Aoki, M. A. Gorji, S. Mukohyama, and K. Takahashi, The effective field theory of vector-tensor theories, JCAP01(01), 059, arXiv:2111.08119 [hep-th]

work page arXiv
[28]

Scalar-Vector-Tensor Gravity Theories,

L. Heisenberg, Scalar-Vector-Tensor Gravity Theories, JCAP10, 054, arXiv:1801.01523 [gr-qc]

work page arXiv
[29]

Kase and S

R. Kase and S. Tsujikawa, Dark energy in scalar-vector-tensor theories, JCAP11, 024, arXiv:1805.11919 [gr-qc]

work page arXiv
[30]

de Rham, S

C. de Rham, S. Garcia-Saenz, L. Heisenberg, and V . Pozsgay, Cosmology of Extended Proca-Nuevo, JCAP03, 053, arXiv:2110.14327 [hep-th]

work page arXiv
[31]

de Rham, S

C. de Rham, S. Garcia-Saenz, L. Heisenberg, V . Pozsgay, and X. Wang, To Half-Be or Not To Be?, JHEP06, 088, arXiv:2303.05354 [hep-th]

work page arXiv
[32]

Ruiz-Zapatero, D

J. Ruiz-Zapatero, D. Alonso, P . G. Ferreira, and C. Garcia-Garcia, Impact of the Universe’s expansion rate on constraints on modified growth of structure, Phys. Rev. D106, 083523 (2022), arXiv:2207.09896 [astro-ph.CO]

work page arXiv 2022
[33]

Unveiling dark fifth forces with linear cosmology,

M. Archidiacono, E. Castorina, D. Redigolo, and E. Salvioni, Unveiling dark fifth forces with linear cosmology, JCAP10, 074, arXiv:2204.08484 [astro-ph.CO]

work page arXiv
[34]

A. Alho, C. Uggla, and J. Wainwright, Perturbations of the Lambda-CDM model in a dynamical systems perspective, JCAP 09, 045, arXiv:1904.02463 [gr-qc]

work page arXiv 1904
[35]

Rampf, S

C. Rampf, S. O. Schobesberger, and O. Hahn, Analytical growth functions for cosmic structures in aΛCDM Universe, Mon. Not. Roy. Astron. Soc.516, 2840 (2022), arXiv:2205.11347 [astro-ph.CO]. 14

work page arXiv 2022
[36]

N. S. Kavya, S. Swagat Mishra, and P . K. Sahoo, f(Q) gravity as a possible resolution of the H0 and S8 tensions with DESI DR2, Sci. Rep.15, 36504 (2025)

2025
[37]

S. S. Mishra and P . K. Sahoo, Hubble Constant,S8, and Sound Horizon Tensions: A Study Within the Teleparallel Framework, PTEP2025, 103E03 (2025)

2025
[38]

Sudharani, N

L. Sudharani, N. S. Kavya, and V . Venkatesha, Cosmic structure growth and perturbation analysis in logarithmicf(Q)grav- ity, Eur. Phys. J. C85, 997 (2025)

2025
[39]

S. S. Mishra, N. S. Kavya, P . K. Sahoo, and V . Venkatesha, Impact of Teleparallelism on Addressing Current Tensions and Exploring the GW Cosmology, Astrophys. J.981, 13 (2025)

2025
[40]

C. Li, X. Ren, Y. Yang, E. N. Saridakis, and Y.-F. Cai, Decoupling perturbations from background inf(Q)gravity: the square- root correction and the alleviation of theσ 8 tension, arXiv 2512.16551 (2025), arXiv:2512.16551 [astro-ph.CO]

work page arXiv 2025
[41]

Tzerefos and E

C. Tzerefos and E. Saridakis, Alleviating theσ8 tension via Soft Cosmology and Modified Gravity, PoSCORFU2022, 210 (2023)

2023
[42]

Subramaniam, A

G. Subramaniam, A. De, T.-H. Loo, and Y. K. Goh, Scalar perturbation and density contrast evolution in f(Q,C) gravity, JCAP 11, 058, arXiv:2412.05382 [gr-qc]

work page arXiv
[43]

A. E. Gumrukcuoglu, C. Lin, and S. Mukohyama, Cosmological perturbations of self-accelerating universe in nonlinear massive gravity, JCAP03, 006, arXiv:1111.4107 [hep-th]

work page arXiv
[44]

Thaalba, N

F. Thaalba, N. Franchini, M. Bezares, and T. P . Sotiriou, Hyperbolicity in scalar-Gauss-Bonnet gravity: A gauge invariant study for spherical evolution, Phys. Rev. D111, 024053 (2025), arXiv:2410.16264 [gr-qc]

work page arXiv 2025
[45]

Gao, Higher derivative scalar-tensor theory from the spatially covariant gravity: a linear algebraic analysis, JCAP11, 004, arXiv:2006.15633 [gr-qc]

X. Gao, Higher derivative scalar-tensor theory from the spatially covariant gravity: a linear algebraic analysis, JCAP11, 004, arXiv:2006.15633 [gr-qc]

work page arXiv 2006
[46]

Black hole perturbation in the most general scalar-tensor theory with second-order field equations I: The odd-parity sector

T. Kobayashi, H. Motohashi, and T. Suyama, Black hole perturbation in the most general scalar-tensor theory with second- order field equations I: the odd-parity sector, Phys. Rev. D85, 084025 (2012), [Erratum: Phys.Rev.D 96, 109903 (2017)], arXiv:1202.4893 [gr-qc]

work page Pith review arXiv 2012
[47]

Perenon, F

L. Perenon, F. Piazza, C. Marinoni, and L. Hui, Phenomenology of dark energy: general features of large-scale perturbations, JCAP11, 029, arXiv:1506.03047 [astro-ph.CO]

work page arXiv
[48]

E. N. Saridakis, From Cosmology to Cosmonomy, arXiv 2512.20416 (2025), arXiv:2512.20416 [astro-ph.CO]

work page arXiv 2025
[49]

emcee: The MCMC Hammer

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

work page internal anchor Pith review arXiv 2013
[50]

Hahn, M.J

C. Hahnet al., The DESI Bright Galaxy Survey: Final Target Selection, Design, and Validation, Astron. J.165, 253 (2023), arXiv:2208.08512 [astro-ph.CO]

work page arXiv 2023
[51]

Raichoor, J

A. Raichooret al., Target Selection and Validation of DESI Emission Line Galaxies, Astron. J.165, 126 (2023), arXiv:2208.08513 [astro-ph.CO]

work page arXiv 2023
[52]

Zhouet al.(DESI), Astron

R. Zhouet al.(DESI), Target Selection and Validation of DESI Luminous Red Galaxies, Astron. J.165, 58 (2023), arXiv:2208.08515 [astro-ph.CO]

work page arXiv 2023
[53]

Chaussidon, C

E. Chaussidonet al., Target Selection and Validation of DESI Quasars, Astrophys. J.944, 107 (2023), arXiv:2208.08511 [astro- ph.CO]

work page arXiv 2023
[54]

DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

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

work page internal anchor Pith review arXiv 2025
[55]

Perivolaropoulos and F

L. Perivolaropoulos and F. Skara, On the homogeneity of SnIa absolute magnitude in the Pantheon+ sample, Mon. Not. Roy. Astron. Soc.520, 5110 (2023), arXiv:2301.01024 [astro-ph.CO]

work page arXiv 2023
[56]

The Pantheon+ Analysis: Cosmological Constraints

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

work page internal anchor Pith review arXiv 2022
[57]

M. Morescoet al., Improved constraints on the expansion rate of the Universe up to z˜1.1 from the spectroscopic evolution of cosmic chronometers, JCAP08, 006, arXiv:1201.3609 [astro-ph.CO]

work page Pith review arXiv
[58]

Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2

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]

work page Pith review arXiv 2015
[59]

A 6% measurement of the Hubble parameter at $z\sim0.45$: direct evidence of the epoch of cosmic re-acceleration

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

work page Pith review arXiv
[60]

Constraints on the equation of state of dark energy and the Hubble constant from stellar ages and the CMB

R. Jimenez, L. Verde, T. Treu, and D. Stern, Constraints 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

work page Pith review arXiv 2003
[61]

Moresco, R

M. Moresco, R. Jimenez, L. Verde, A. Cimatti, and L. Pozzetti, Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix, Astrophys. J.898, 82 (2020), arXiv:2003.07362 [astro-ph.GA]

work page arXiv 2020
[62]

Alestas, L

G. Alestas, L. Kazantzidis, and S. Nesseris, Machine learning constraints on deviations from general relativity from the large scale structure of the Universe, Phys. Rev. D106, 103519 (2022), arXiv:2209.12799 [astro-ph.CO]

work page arXiv 2022
[63]

I. D. Saltas, I. Sawicki, L. Amendola, and M. Kunz, Anisotropic Stress as a Signature of Nonstandard Propagation of Gravi- 15 tational Waves, Phys. Rev. Lett.113, 191101 (2014), arXiv:1406.7139 [astro-ph.CO]

work page Pith review arXiv 2014
[64]

Tutusaus, D

I. Tutusaus, D. Sobral-Blanco, and C. Bonvin, Combining gravitational lensing and gravitational redshift to measure the anisotropic stress with future galaxy surveys, Phys. Rev. D107, 083526 (2023), arXiv:2209.08987 [astro-ph.CO]

work page arXiv 2023
[65]

Sobral-Blanco and C

D. Sobral-Blanco and C. Bonvin, Measuring anisotropic stress with relativistic effects, Phys. Rev. D104, 063516 (2021), arXiv:2102.05086 [astro-ph.CO]

work page arXiv 2021