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arxiv: 2606.21839 · v1 · pith:H5PV544Xnew · submitted 2026-06-20 · 🌀 gr-qc

Observational Constraints on f(Q,T) Gravity in the Presence of DBI-Essence Scalar Field

Mayur Mune , Praveen Kumar Dhankar , Goutam Manna , Safiqul Islam , Bidisha Samanta , Behnam Pourhassan This is my paper

Pith reviewed 2026-06-26 11:58 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(Q,T) gravityDBI scalar fieldlate-time cosmologyobservational constraintsMCMC analysisHubble dataBAO measurementsType Ia supernovae
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The pith

The linear f(Q,T) model with DBI scalar field yields background solutions consistent with Hubble, BAO and supernova data as a viable alternative to ΛCDM.

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

This paper derives the background equations for f(Q,T) gravity coupled to a Dirac-Born-Infeld scalar field on flat FLRW spacetime, treating the cosmic medium as an effective perfect fluid. For the specific linear form f(Q,T)=αQ+βT the authors obtain analytic solutions and then perform MCMC fitting to Hubble-rate measurements, DESI BAO DR2 data and the Pantheon+SHOES supernova sample. The resulting joint posteriors remain compatible with existing late-time constraints while quantifying the shifts induced by the βT term and the DBI sector. The work therefore positions the model as a statistically acceptable extension that can be compared directly with the cosmological-constant paradigm.

Core claim

For the linear choice f(Q,T)=αQ+βT coupled to a DBI scalar field, the background equations on flat FLRW admit analytic solutions that, when fitted to Hubble, DESI BAO DR2, and Pantheon+SHOES data via MCMC, produce joint posteriors consistent with late-time constraints and allow direct comparison to ΛCDM, establishing the model as a statistically viable alternative.

What carries the argument

The linear function f(Q,T)=αQ+βT coupled to the DBI-essence scalar field, which alters the Friedmann equations through non-metricity and trace-of-stress-energy contributions.

If this is right

  • The model admits direct statistical comparison with ΛCDM on identical datasets.
  • The βT coupling and DBI sector produce measurable departures from standard expansion history.
  • The framework supplies a concrete setting in which to explore possible remedies for the H0 discrepancy.
  • Posterior constraints remain broadly consistent with current late-time observations.

Where Pith is reading between the lines

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

  • Higher-redshift BAO or supernova samples could tighten bounds on the β parameter and reveal whether the DBI sector is required.
  • The same linear f(Q,T) ansatz could be tested against growth-rate or weak-lensing data to check consistency beyond background expansion.
  • Analytic solutions derived here may serve as a template for studying other scalar-field couplings in symmetric teleparallel gravity.

Load-bearing premise

The linear choice f(Q,T)=αQ+βT together with the effective perfect-fluid treatment on flat FLRW is sufficient to capture the relevant late-time dynamics.

What would settle it

A new high-precision Hubble or BAO measurement at moderate redshift lying systematically outside the 2σ range of the MCMC posterior predictions for the best-fit α, β and DBI parameters would falsify the viability statement.

Figures

Figures reproduced from arXiv: 2606.21839 by Behnam Pourhassan, Bidisha Samanta, Goutam Manna, Mayur Mune, Praveen Kumar Dhankar, Safiqul Islam.

Figure 1
Figure 1. Figure 1: Bayesian inference using a Gaussian approxi [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Bayesian inference for all models with Gaus [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of Hubble cosmic chronometer data fits for all models. Table II lists the best-fit constraints on the Hub￾ble constant H0, the present-day matter density Ωm0 , and the sound-horizon scale rd for ΛCDM, wCDM, and our f(Q, T) + DBI model, using the combined Hubble, Pantheon+SH0ES, and DESIBAO datasets. For the standard scenarios, we obtain H0 ≃ 68.932 ± 1.867 km s−1 Mpc−1 , Ωm0 ≃ 0.303 ± 0.007, and… view at source ↗
Figure 5
Figure 5. Figure 5: Error-bar plot of the H(z) measurements compared with the best-fit f(Q, T) + DBI model, as well as the best-fit wCDM and ΛCDM models [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Corner plot showing the 1D marginalized posteriors and 2D joint credible regions (68% and 95%) from the joint analysis of H(z) and Pantheon+SHOES supernovae [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distance modulus µ(z) from the Pan￾theon+SHOES sample compared with the best-fit f(Q, T) + DBI model and the corresponding ΛCDM prediction. Error bars indicate the observational un￾certainties [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: Marginalized 1σ and 2σ confidence contours for the model parameters obtained from the H(z)-only, Pantheon+SHOES-only, and joint H(z)+Pantheon+SHOES analyses. The combined dataset reduces parameter degeneracies and tightens the constraints on H0, Ωm0, β, and λ. • [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
read the original abstract

We investigate late-time cosmology in extended symmetric teleparallel gravity coupled to a Dirac-Born-Infeld (DBI) scalar field within $f(Q,T)$ gravity, where $Q$ is the non-metricity scalar and $T$ is the trace of the matter energy-momentum tensor. Working on a spatially flat Friedmann-Lema\^itre-Robertson-Walker background and treating the cosmic medium as an effective perfect fluid, we derive the background field equations for $f(Q,T)+\mathrm{DBI}$ gravity and obtain analytic solutions for the linear choice $f(Q,T)=\alpha Q+\beta T$. We then constrain the model parameters with a Markov Chain Monte Carlo analysis using Hubble-rate data, DESI BAO (DR2) measurements, and the Pantheon+SHOES Type~Ia supernova sample. The joint posteriors (Tables II and III) are broadly consistent with current late-time constraints and allow a direct comparison with $\Lambda$CDM, quantifying the departures driven by the $\beta T$ coupling and the DBI sector. Although the model does not reproduce every observational feature exactly, it provides a statistically viable alternative avenue to the standard paradigm and a useful framework for exploring potential remedies to existing tensions, including the $H_0$ discrepancy, without claiming a definitive resolution.

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.

Referee Report

2 major / 2 minor

Summary. The paper derives background field equations for f(Q,T) gravity coupled to a DBI scalar field on flat FLRW, treating the medium as an effective perfect fluid. For the linear choice f(Q,T)=αQ+βT it obtains analytic solutions and performs MCMC constraints using Hubble-rate, DESI BAO (DR2), and Pantheon+SHOES data. The resulting joint posteriors (Tables II and III) are reported to be consistent with late-time observations and to position the model as a statistically viable alternative to ΛCDM, with quantified departures from the βT coupling and DBI sector.

Significance. If the background equations and perfect-fluid treatment are valid, the work supplies concrete observational bounds on α and β, enables direct comparison with ΛCDM, and offers a framework for exploring remedies to the H0 tension. The inclusion of recent DESI BAO data and the analytic solutions for the linear model are positive features that facilitate reproducibility of the fits.

major comments (2)
  1. [background field equations section] Background field equations section: the derivation adopts the effective perfect-fluid ansatz for the cosmic medium without demonstrating that the non-canonical DBI kinetic term remains compatible with this form once coupled to the βT piece of f(Q,T). If anisotropic stress or modified continuity equations arise, the Friedmann equations underlying the MCMC analysis would be incomplete, directly affecting the reliability of the posteriors in Tables II and III and the viability claim.
  2. [analytic solutions] Analytic solutions for linear f(Q,T)=αQ+βT: it is not shown whether these closed-form expressions satisfy the full set of modified continuity and acceleration equations that include the DBI contributions; an explicit substitution back into the field equations (or a numerical cross-check) is required to confirm internal consistency before the solutions can be used for parameter fitting.
minor comments (2)
  1. [Tables II and III] Tables II and III: reporting only marginalised posteriors without the corresponding minimum χ² values or Δχ² relative to ΛCDM makes it difficult to judge the absolute goodness-of-fit and the statistical weight of the claimed viability.
  2. Notation: the effective equation-of-state parameter for the combined f(Q,T)+DBI system is introduced without an explicit definition in terms of the DBI Lagrangian and the βT coupling; a short clarifying equation would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which help improve the clarity of the manuscript. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [background field equations section] Background field equations section: the derivation adopts the effective perfect-fluid ansatz for the cosmic medium without demonstrating that the non-canonical DBI kinetic term remains compatible with this form once coupled to the βT piece of f(Q,T). If anisotropic stress or modified continuity equations arise, the Friedmann equations underlying the MCMC analysis would be incomplete, directly affecting the reliability of the posteriors in Tables II and III and the viability claim.

    Authors: The effective perfect-fluid ansatz is preserved because the flat FLRW symmetries force the DBI stress-energy tensor to remain diagonal and isotropic, with no anisotropic stress generated by the non-canonical kinetic term. The βT coupling enters only through the trace T, which is a scalar, and is absorbed into the definitions of the effective energy density and pressure that appear in the modified Friedmann equations. The continuity equation is accordingly modified and is already incorporated when deriving the background equations used for the MCMC fits. We will add a short clarifying paragraph in the background-equations section to make this compatibility explicit. revision: yes

  2. Referee: [analytic solutions] Analytic solutions for linear f(Q,T)=αQ+βT: it is not shown whether these closed-form expressions satisfy the full set of modified continuity and acceleration equations that include the DBI contributions; an explicit substitution back into the field equations (or a numerical cross-check) is required to confirm internal consistency before the solutions can be used for parameter fitting.

    Authors: The closed-form solutions are obtained by direct integration of the complete set of background equations that already contain the DBI contributions to ρ and p. They therefore satisfy the full system by construction. To address the request for explicit verification, we will insert a brief appendix that substitutes the analytic expressions back into the modified continuity and acceleration equations and confirms that they hold identically; a short numerical consistency check for sample parameter values will also be included. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation and fitting are independent steps

full rationale

The paper first derives the background field equations from the f(Q,T)+DBI action on flat FLRW under the effective perfect-fluid assumption, obtains analytic solutions for the linear ansatz f(Q,T)=αQ+βT, and only then performs MCMC parameter estimation on Hubble+BAO+SNIa data. The consistency statement and quantified departures are outputs of that standard fit rather than a claimed first-principles prediction that reduces to the fitted inputs by construction. No self-definitional equations, load-bearing self-citations, or uniqueness theorems imported from the authors' prior work appear in the derivation chain. The central claim therefore remains self-contained against external data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Abstract supplies only the linear ansatz and standard cosmological assumptions; full ledger cannot be completed without the manuscript.

free parameters (2)
  • α
    Coefficient multiplying the non-metricity scalar Q; fitted to data.
  • β
    Coefficient multiplying the trace T; fitted to data and drives the reported departures from ΛCDM.
axioms (2)
  • domain assumption Spatially flat FLRW metric
    Standard background assumption invoked for late-time cosmology.
  • domain assumption Cosmic medium treated as effective perfect fluid
    Used to close the background field equations.

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Reference graph

Works this paper leans on

92 extracted references · 82 canonical work pages · 10 internal anchors

  1. [1]

    doi:10.1086/466512 , Eprint =

    D. J. Eisenstein. et al. (2025). “Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies.”The Astro- physical Journal, 633(2), 560. https://doi.org/10.1086/466512

    work page doi:10.1086/466512 2025

  2. [3]

    Cosmic mi- crowave background and supernova constraints on quintessence: concordance regions and target mod- els

    R. R. Caldwell, & M. Doran. (2004). “Cosmic mi- crowave background and supernova constraints on quintessence: concordance regions and target mod- els.”Physical Review D,69(10), 103517. https://doi.org/10.1103/PhysRevD.69.103517

    work page doi:10.1103/physrevd.69.103517 2004

  3. [4]

    Holographic explanation of wide-angle power correlation suppression in the cosmicmicrowave background radiation

    Z. Y. Huang. et al. (2026). “Holographic explanation of wide-angle power correlation suppression in the cosmicmicrowave background radiation.”Journal of Cosmology and Astroparticle Physics,2006(05), 013. https://doi.org/10.1088/1475-7516/2006/05/ 013

    work page doi:10.1088/1475-7516/2006/05/ 2026

  4. [5]

    Dark energy anisotropic stress and large scale structure formation

    T. Koivisto, & D. F. Mota. (2006). “Dark energy anisotropic stress and large scale structure formation.” Physical Review D—Particles, Fields, Gravitation, and Cosmology,73(8), 083502. https://doi.org/10.1103/PhysRevD.73.083502

    work page doi:10.1103/physrevd.73.083502 2006

  5. [6]

    Large scale structure as a probe of gravitational slip

    S. F. Daniel. et al. (2008). “Large scale structure as a probe of gravitational slip.”Physical Review D—Particles, Fields, Gravitation, and Cosmology, 77(10), 103513. https://doi.org/10.1103/PhysRevD.77.103513

    work page doi:10.1103/physrevd.77.103513 2008

  6. [7]

    Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant

    A. G. Riess. et al. (1998). “Observational evidence from supernovae for an accelerating universe and a cosmological constant.”The astronomical journal, 116(3), 1009. https://doi.org/10.1086/300499

    work page internal anchor Pith review doi:10.1086/300499 1998

  7. [8]

    Measur- ing cosmology with supernovae. In Supernovae and Gamma-Ray Bursters (pp. 195-217)

    S. Perlmutter, & B. P. Schmidt. (2003). “Measur- ing cosmology with supernovae. In Supernovae and Gamma-Ray Bursters (pp. 195-217).”Berlin, Heidel- berg: Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-45863-8_11

    work page doi:10.1007/3-540-45863-8_11 2003

  8. [9]

    Astronomy and Astrophysics , author =

    P. Collaboration. et al. (2015). “Planck 2015 results. XIII. Cosmological parameters.” https://doi.org/10.1051/0004-6361/201525830

    work page doi:10.1051/0004-6361/201525830 2015

  9. [11]

    22 [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] Luis P

    S. M. Carroll. (2001). “The cosmological constant.” Living reviews in relativity, 4(1), 1-56. DOI:https://doi.org/10.1103/RevModPhys.61.1

    work page doi:10.1103/revmodphys.61.1 2001

  10. [12]

    Quintessence and the Rest of the World

    S. M. Carroll. (1998). “Quintessence and the rest of the world.”arXiv preprint astro-ph/9806099. https://doi.org/10.1103/PhysRevLett.81.3067

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.81.3067 1998

  11. [13]

    Y. Fujii. (1982). Origin of the gravitational constant and particle masses in a scale-invariant scalar-tensor theory.Physical Review D,26(10), 2580. https://doi.org/10.1103/PhysRevD.26.2580 13

    work page doi:10.1103/physrevd.26.2580 1982

  12. [14]

    International consen- sus guidance statement on the management and treat- ment of IgG4-related disease

    A. Khosroshahi. et al. (2015). “International consen- sus guidance statement on the management and treat- ment of IgG4-related disease.” Arthritis & rheuma- tology, 67(7), 1688-1699. https://doi.org/10.1002/art.39132

    work page doi:10.1002/art.39132 2015

  13. [17]

    M. C. Bento, O. Bertolami, & A. A. Sen. (2002). Generalized Chaplygin gas, accelerated expansion, and dark-energy-matter unification.Physical Review D, 66(4), 043507. https://doi.org/10.1103/PhysRevD.66.043507

    work page doi:10.1103/physrevd.66.043507 2002

  14. [18]

    Cosmological constraints on interacting holographic dark energy and extended Chaplygin gas in using MCMC analysis

    B. Thakran. et al. (2025). “Cosmological constraints on interacting holographic dark energy and extended Chaplygin gas in using MCMC analysis.”Inter- national Journal of Geometric Methods in Modern Physics. https://doi.org/10.1142/S0219887825502548

    work page doi:10.1142/s0219887825502548 2025

  15. [19]

    Observa- tional analysis of bulk viscous modified Chaplygin gas in (2+1)-dimensional universe using MCMC,

    Praveen Kumar Dhankar. et al. (2025) “Observa- tional analysis of bulk viscous modified Chaplygin gas in (2+1)-dimensional universe using MCMC,” arXiv:2504.18612 [gr-qc] https://doi.org/10.48550/arXiv.2504.18612

    work page doi:10.48550/arxiv.2504.18612 2025

  16. [20]

    An alternative to quintessence

    A. Kamenshchik, U. Moschella, & V. Pasquier. (2001). “An alternative to quintessence.” Physics Letters B,511(2-4), 265-268

    2001

  17. [21]

    Dark energy properties in DBI theory

    C. Ahn, C. Kim, & E. V. Linder. (2009). “Dark energy properties in DBI theory.”Physical Review D—Particles, Fields, Gravitation, and Cosmology, 80(12), 123016. https://doi.org/10.1016/S0370-2693(01) 00571-8

    work page doi:10.1016/s0370-2693(01 2009

  18. [22]

    Cosmo- logical constant behavior in DBI theory

    C. Ahn, C. Kim, & E. V. Linder. (2010). “Cosmo- logical constant behavior in DBI theory.”Physics Letters B, 684(4-5), 181-184. https://doi.org/10.1016/j.physletb.2009.12. 069

    work page doi:10.1016/j.physletb.2009.12 2010

  19. [23]

    Bayesian Analysis of Viscous FRW Cosmology with Inhomogeneous Equation of State

    R. Patel. et al. (2026). “Bayesian Analysis of Viscous FRW Cosmology with Inhomogeneous Equation of State.”Mathematics, 14(11), 1888. https://doi.org/10.3390/math14111888

    work page doi:10.3390/math14111888 2026

  20. [24]

    Testing logarithmic f(G) model with observational data sets

    M. Thakre. et al. (2026). “Testing logarithmic f(G) model with observational data sets”.Journal of Holog- raphy Applications in Physics. https://doi.org/10.22128/jhap.2026.3248.1191

    work page doi:10.22128/jhap.2026.3248.1191 2026

  21. [25]

    Large-scale struc- ture and matter power spectrum in f(T ) gravity

    P. Kumar Dhankar. et al. (2026). “Large-scale struc- ture and matter power spectrum in f(T ) gravity.” Modern Physics Letters A,2650117. https://doi.org/10.1142/S0217732326501178

    work page doi:10.1142/s0217732326501178 2026

  22. [27]

    Cosmic Hysteresis in Reconstructed f(T ) Bounce Models A Torsion- Based Thermodynamic Perspective

    A. Sanyal. et al. (2026). “Cosmic Hysteresis in Reconstructed f(T ) Bounce Models A Torsion- Based Thermodynamic Perspective.”arXiv preprint arXiv:2602.15924. https://doi.org/10.48550/arXiv.2602.15924

    work page doi:10.48550/arxiv.2602.15924 2026

  23. [28]

    Constraining f(G) gravity models using MCMC method

    A. Munyeshyaka. et al. (2026). “Constraining f(G) gravity models using MCMC method.”Physics of the Dark Universe, 102246. https://doi.org/10.1016/j.dark.2026.102246

    work page doi:10.1016/j.dark.2026.102246 2026

  24. [29]

    Studying Bianchi Type-I Uni- verses in the Modified f(R)-Gravity Scenario Using MCMC Approach

    S. Joshi. et al. (2026). “Studying Bianchi Type-I Uni- verses in the Modified f(R)-Gravity Scenario Using MCMC Approach”.Iranian Journal of Science, 1-14. https://doi.org/10.1007/s40995-026-01962-x

    work page doi:10.1007/s40995-026-01962-x 2026

  25. [30]

    Symmetric teleparallel general relativity

    J. M. Nester, & H. J. Yo. (1998). “Symmetric teleparallel general relativity.”arXiv preprint gr- qc/9809049. https://doi.org/10.48550/arXiv.gr-qc/9809049

    work page internal anchor Pith review doi:10.48550/arxiv.gr-qc/9809049 1998

  26. [31]

    Coincident general relativity

    J. B. Jim´ enez, L. Heisenberg, & T. Koivisto. (2018). “Coincident general relativity.”Physical Review D, 98(4), 044048. DOI:https://doi.org/10.1103/PhysRevD.98. 044048

    work page doi:10.1103/physrevd.98 2018

  27. [32]

    Cosmology in f(Q) geometry

    J. B. Jim´ enez. et al. (2020). “Cosmology in f(Q) geometry.”Physical Review D, 101(10), 103507. https://doi.org/10.1103/PhysRevD.101.103507

    work page doi:10.1103/physrevd.101.103507 2020

  28. [33]

    Observational constraints of f(Q) gravity

    R. Lazkoz. et al. (2019). “Observational constraints of f(Q) gravity.”Physical Review D, 100(10), 104027. https://doi.org/10.1103/PhysRevD.100.104027

    work page doi:10.1103/physrevd.100.104027 2019

  29. [35]

    General- ized curvature-matter couplings in modified gravity,

    T. Harko and F. S. N. Lobo, (2014) “General- ized curvature-matter couplings in modified gravity,” Galaxies 2, 3, 410-465 https://doi.org/10.3390/ galaxies2030410

    2014

  30. [36]

    f(R, T) gravity

    T. Harko, et al. (2011). “ f(R, T) gravity.”Physical Review D—Particles, Fields, Gravitation, and Cosmology,84(2), 024020. DOI:https://doi.org/10.1103/PhysRevD.84. 024020

    work page doi:10.1103/physrevd.84 2011

  31. [37]

    Thermodynamics and cosmol- ogy

    I. Prigogine, (1989). “Thermodynamics and cosmol- ogy.”International journal of theoretical physics, 28(9), 927-933. https://doi.org/10.1007/BF00670337

    work page doi:10.1007/bf00670337 1989

  32. [38]

    Physical Review D , year = 1981, month = jan, volume =

    A. H. Guth, (1981). “Inflationary universe: A pos- sible solution to the horizon and flatness problems.” Physical Review D, 23(2), 347. https://doi.org/10.1103/PhysRevD.23.347

    work page doi:10.1103/physrevd.23.347 1981

  33. [39]

    Physics Letters B , year = 1982, month = feb, volume = 108, pages =

    A. D. Linde, (1982). “A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole prob- lems.”Physics Letters B, 108(6), 389-393. https://doi.org/10.1016/0370-2693(82)91219-9

    work page doi:10.1016/0370-2693(82)91219-9 1982

  34. [40]

    Cosmology for grand unified theories with radiatively induced symmetry breaking

    A. Albrecht, & P. J. Steinhardt, (1982). “Cosmology for grand unified theories with radiatively induced symmetry breaking.”Physical Review Letters,48(17), 1220. https://doi.org/10.1103/PhysRevLett.48.1220

    work page doi:10.1103/physrevlett.48.1220 1982

  35. [41]

    Dynamics of dark energy

    E. J. Copeland, M. Sami, & S. Tsujikawa, (2006). “Dynamics of dark energy.”International Journal of Modern Physics D,15(11), 1753-1935. https://doi.org/10.1142/S021827180600942X

    work page doi:10.1142/s021827180600942x 2006

  36. [42]

    Ratra and P

    B. Ratra, & P. J. Peebles, (1988). “Cosmological consequences of a rolling homogeneous scalar field.” Physical Review D, 37(12), 3406. https://doi.org/10.1103/PhysRevD.37.3406

    work page doi:10.1103/physrevd.37.3406 1988

  37. [43]

    Cosmological imprint of an energy component with general equation of state

    R. R. Caldwell, R. Dave, & P. J. Steinhardt, (1998). “Cosmological imprint of an energy component with general equation of state.”Physical Review Letters, 80(8), 1582. https://doi.org/10.1103/PhysRevLett.80.1582

    work page doi:10.1103/physrevlett.80.1582 1998

  38. [44]

    Purely kinetic k essence as unified dark matter

    R. J. Scherrer, (2004). “Purely kinetic k essence as unified dark matter.”Physical review letters,93(1), 14 011301. https://doi.org/10.1103/PhysRevLett.93. 011301

    work page doi:10.1103/physrevlett.93 2004

  39. [45]

    Dynamical solution to the problem of a small cosmological constant and late-time cosmic acceleration

    C. Armendariz-Picon, V. Mukhanov, & P. J. Stein- hardt, (2000). “Dynamical solution to the problem of a small cosmological constant and late-time cosmic acceleration.”Physical Review Letters, 85(21), 4438. https://doi.org/10.1103/PhysRevLett.85.4438

    work page doi:10.1103/physrevlett.85.4438 2000

  40. [46]

    Non-Gaussian features of primordial fluctuations in single field inflationary models

    J. Maldacena, (2003). “Non-Gaussian features of primordial fluctuations in single field inflationary models.”Journal of High Energy Physics, 2003(05), 013-013. https://doi.org/10.1088/1126-6708/2003/05/ 013

    work page doi:10.1088/1126-6708/2003/05/ 2003

  41. [47]

    Running non-Gaussianities in Dirac-Born-Infeld inflation

    C. Xingang, (2005). “Running non-Gaussianities in Dirac-Born-Infeld inflation.”Physical Review. D, Par- ticles Fields, 72(12). https://doi.org/10.1103/PhysRevD.72.123518

    work page doi:10.1103/physrevd.72.123518 2005

  42. [48]

    Perturba- tions in k-inflation

    J. Garriga, & V. F. Mukhanov, (1999). “Perturba- tions in k-inflation.”Physics Letters B,458(2-3), 219-225. https://doi.org/10.1016/S0370-2693(99) 00602-4

    work page doi:10.1016/s0370-2693(99 1999

  43. [51]

    Ki- netically driven quintessence

    T. Chiba, T. Okabe, & M. Yamaguchi, (2000). “Ki- netically driven quintessence.”Physical Review D, 62(2), 023511. https://doi.org/10.1103/PhysRevD.62.023511

    work page doi:10.1103/physrevd.62.023511 2000

  44. [52]

    Essentials of k-essence

    C. Armendariz-Picon, V. Mukhanov, & P. J. Stein- hardt, (2001). “Essentials of k-essence.”Physical Re- view D, 63(10), 103510. https://doi.org/10.1103/PhysRevD.63.103510

    work page doi:10.1103/physrevd.63.103510 2001

  45. [53]

    Second-order scalar-tensor field equations in a four-dimensional space

    G. W. Horndeski, “Second-order scalar-tensor field equations in a four-dimensional space”, Int. J. Theor. Phys.10, 363–384, (1974), https://doi.org/10. 1007/BF01807638

    1974

  46. [54]

    Fromk-essence to generalized Galileons

    C. Deffayet, X. Gao, D. A. Steer, and G. Zahariade, “Fromk-essence to generalized Galileons”, Phys. Rev. D84, 064039, (2011), https://doi.org/10.1103/ PhysRevD.84.064039

    2011

  47. [55]

    Gen- eralized G-inflation: Inflation with the most general second-order field equations

    T. Kobayashi, M. Yamaguchi and J. Yokoyama, “Gen- eralized G-inflation: Inflation with the most general second-order field equations”, Prog. Theor. Phys. 126, 511-529, (2011), https://doi.org/10.1143/ PTP.126.511

    2011

  48. [56]

    Review on f(Q) gravity

    L. Heisenberg, (2024). “Review on f(Q) gravity.” Physics Reports, 1066, 1-78. https://doi.org/10.1016/j.physrep.2024.02. 001

    work page doi:10.1016/j.physrep.2024.02 2024

  49. [57]

    K-essence: cosmology, causal- ity and emergent geometry

    A. Vikman, (2007). “K-essence: cosmology, causal- ity and emergent geometry” (Doctoral dissertation, M¨ unchen, Univ., Diss., 2007)

    2007

  50. [58]

    DBI-essence

    J. Martin, & M. Yamaguchi, (2008). “DBI-essence.” Physical Review D—Particles, Fields, Gravitation, and Cosmology,77(12), 123508. https://doi.org/10.1103/PhysRevD.77.123508

    work page doi:10.1103/physrevd.77.123508 2008

  51. [59]

    Measurements of neutrino oscillation parameters from the T2K experiment using 3.6×10 21 protons on target

    G. Manna, (2020). “Gravitational collapse for the K-essence emergent Vaidya spacetime.”The European Physical Journal C, 80(9), 1-9. https://doi.org/10.1140/epjc/ s10052-020-8383-y

    work page doi:10.1140/epjc/ 2020

  52. [60]

    k-essence emergent spacetime as a generalized Vaidya geometry

    G. Manna, P. Majumdar, & B. Majumder, (2020). “k-essence emergent spacetime as a generalized Vaidya geometry.”Physical Review D, 101(12), 124034.(2020). https://doi.org/10.1103/PhysRevD.101.124034

    work page doi:10.1103/physrevd.101.124034 2020

  53. [61]

    Observational Insights on DBI K-Essence Models Using Machine Learning and Bayesian Analysis

    S. Ganguly, et al. (2026). “Observational Insights on DBI K-Essence Models Using Machine Learning and Bayesian Analysis.”Fortschritte der Physik,74(5), e70117. https://doi.org/10.1002/prop.70117

    work page doi:10.1002/prop.70117 2026

  54. [62]

    Gravitational Wave Propagation in K-essence Cosmology: Theory and Observational Constraints

    S. Bhunia et al., (2026), “Gravitational Wave Prop- agation in K-essence Cosmology: Theory and Ob- servational Constraints,” arXiv: 2605.25466, https: //doi.org/10.48550/arXiv.2605.25466

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2605.25466 2026

  55. [63]

    Dynamical system analysis of a Dirac-Born-Infeld model: a center mani- fold perspective

    S. Pal, & S. Chakraborty, (2019). “Dynamical system analysis of a Dirac-Born-Infeld model: a center mani- fold perspective.”General Relativity and Gravitation, 51(9), 124. https://doi.org/10.1007/s10714-019-2608-0

    work page doi:10.1007/s10714-019-2608-0 2019

  56. [64]

    Ex- ploring the dynamics of coincident f (Q) gravity in the presence of DBI-essence scalar field

    R. Mandal, U. Debnath& A. Pradhan, (2025). “Ex- ploring the dynamics of coincident f (Q) gravity in the presence of DBI-essence scalar field.”Annals of Physics,170245. https://doi.org/10.1016/j.aop.2025.170245

    work page doi:10.1016/j.aop.2025.170245 2025

  57. [65]

    Research in Astronomy and Astrophysics , abstract =

    C. Zhang, et al. (2014). “Four new observational H (z) data from luminous red galaxies in the Sloan Digital Sky Survey data release seven.”Research in Astronomy and Astrophysics, 14(10), 1221-1233. https://doi.org/10.1088/1674-4527/14/10/002

    work page internal anchor Pith review doi:10.1088/1674-4527/14/10/002 2014

  58. [66]

    Simon, L

    J. Simon, L. Verde & R. Jimenez, (2005). “Con- straints on the redshift dependence of the dark en- ergy potential.”Physical Review D—Particles, Fields, Gravitation, and Cosmology, 71(12), 123001. https://doi.org/10.1103/PhysRevD.71.123001

    work page internal anchor Pith review doi:10.1103/physrevd.71.123001 2005

  59. [67]

    Improved constraints on the expansion rate of the Universe up to z ∼ 1.1 from the spectroscopic evolution of cosmic chronometers

    M. Moresco, et al. (2012). “Improved constraints on the expansion rate of the Universe up to z ∼ 1.1 from the spectroscopic evolution of cosmic chronometers.” Journal of Cosmology and Astroparticle Physics, 2012(08), 006. https://doi.org/10.1088/1475-7516/2012/08/ 006

    work page doi:10.1088/1475-7516/2012/08/ 2012

  60. [68]

    A 6 % measurement of the Hubble parameter at z ∼ 0.45: direct evidence of the epoch of cosmic re-acceleration

    M. Moresco, et al. (2016). “A 6 % measurement of the Hubble parameter at z ∼ 0.45: direct evidence of the epoch of cosmic re-acceleration.”Journal of Cosmology and Astroparticle Physics, 2016(05), 014. https://doi.org/10.1088/1475-7516/2016/05/ 014

    work page doi:10.1088/1475-7516/2016/05/ 2016

  61. [69]

    Cosmic chronometers: constraining the equation of state of dark energy. I: H (z) measurements

    D. Stern, et al. (2010). “Cosmic chronometers: constraining the equation of state of dark energy. I: H (z) measurements.”Journal of Cosmology and Astroparticle Physics, 2010(02), 008. https://doi.org/10.1088/1475-7516/2010/02/ 008

    work page doi:10.1088/1475-7516/2010/02/ 2010

  62. [70]

    Monthly Notices of the Royal Astronomical Society: Letters , volume =

    M. Moresco, (2015). “Raising the bar: new con- straints on the Hubble parameter with cosmic chronometers at z∼ 2.”Monthly Notices of the Royal Astronomical Society: Letters, 450(1), L16-L20. https://doi.org/10.1093/mnrasl/slv037

    work page internal anchor Pith review doi:10.1093/mnrasl/slv037 2015

  63. [71]

    Age-dating lumi- nous red galaxies observed with the Southern African Large Telescope

    A. L. Ratsimbazafy, et al. (2017). “Age-dating lumi- nous red galaxies observed with the Southern African Large Telescope.”Monthly Notices of the Royal As- tronomical Society,467(3), 3239-3254

    2017

  64. [72]

    To- ward a better understanding of cosmic chronometers: a new measurement of H (z) at z ∼ 0.7

    N. Borghi, M. Moresco, & A. Cimatti, (2022). “To- ward a better understanding of cosmic chronometers: a new measurement of H (z) at z ∼ 0.7. ”The Astro- physical Journal Letters,928(1), L4. 15

    2022

  65. [73]

    Constraints on DBI dark energy with chameleon mechanism

    B. Gumjudpai, N. Roy, & J. Ward, (2025). “Con- straints on DBI dark energy with chameleon mecha- nism.”arXiv preprint arXiv:2508.05436. https://doi.org/10.48550/arXiv.2508.05436

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2508.05436 2025

  66. [74]

    Scalar speed limits and cosmology: Acceleration from D-cceleration

    E. Silverstein, & D. Tong, (2004). “Scalar speed limits and cosmology: Acceleration from D-cceleration.” Physical Review D—Particles, Fields, Gravitation, and Cosmology, 70(10), 103505. https://doi.org/10.1103/PhysRevD.70.103505

    work page doi:10.1103/physrevd.70.103505 2004

  67. [75]

    DBI in the sky: non-Gaussianity from inflation with a speed limit

    M. Alishahiha, E. Silverstein, & D. Tong, (2004). “DBI in the sky: non-Gaussianity from inflation with a speed limit.”Physical Review D—Particles, Fields, Gravitation, and Cosmology, 70(12), 123505. https://doi.org/10.1103/PhysRevD.70.123505

    work page doi:10.1103/physrevd.70.123505 2004

  68. [76]

    Hussain, S

    S. Hussain, et al. (2026). “Probing the dynamics of Gaussian dark energy equation of state using DESI BAO.”Monthly Notices of the Royal Astronomical Society,545(2), staf1924. https://doi.org/10.1093/mnras/staf1924

    work page doi:10.1093/mnras/staf1924 2026

  69. [77]

    Akaike, A new look at the statistical model identification

    H. Akaike, (1974). “A new look at the statistical model identification.”IEEE transactions on auto- matic control, 19(6), 716-723. https://doi.org/10.1109/TAC.1974.1100705

    work page doi:10.1109/tac.1974.1100705 1974

  70. [78]

    Estimating the dimension of a model

    G. Schwarz, (1978). “Estimating the dimension of a model.”The annals of statistics, 461-464. https://www.jstor.org/stable/2958889

    arXiv 1978

  71. [79]

    The role of machine learning in the next decade of cosmology

    M. Ntampaka, et al. (2019). “The role of machine learning in the next decade of cosmology.”arXiv preprint arXiv:1902.10159. https://doi.org/10.48550/arXiv.1902.10159

    work page doi:10.48550/arxiv.1902.10159 2019

  72. [80]

    2010, MNRAS, 401, 2343, doi: 10.1111/j.1365-2966.2009.15859.x

    W. J. Percival, et al. (2010). “Baryon acoustic oscillations in the Sloan Digital Sky Survey data release 7 galaxy sample.”Monthly Notices of the Royal Astronomical Society,401(4), 2148-2168. https://doi.org/10.1111/j.1365-2966.2009. 15812.x

    work page doi:10.1111/j.1365-2966.2009 2010

  73. [81]

    Probing dark energy using baryonic oscillations in the galaxy power spectrum as a cosmological ruler

    C. Blake, & K. Glazebrook, (2003). “Probing dark energy using baryonic oscillations in the galaxy power spectrum as a cosmological ruler.”The Astrophysical Journal,594(2), 665-673. https://doi.org/10.1086/376983

    work page doi:10.1086/376983 2003

  74. [82]

    Small-scale cosmo- logical perturbations: an analytic approach

    W. Hu, & N. Sugiyama, (1996). “Small-scale cosmo- logical perturbations: an analytic approach.”The Astrophysical Journal,471(2), 542-570. https://doi.org/10.1086/177989

    work page doi:10.1086/177989 1996

  75. [83]

    and Hu, Wayne , year = 1998, month = mar, journal =

    D. J. Eisenstein, & W. Hu, (1998). “Baryonic features in the matter transfer function.”The Astrophysical Journal,496(2), 605-614. https://doi.org/10.1086/305424

    work page doi:10.1086/305424 1998

  76. [84]

    DESI DR2 results

    M. Abdul Karim, et al. (2025). “DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints.”Physical Review D,112(8), 083515. https://doi.org/10.1103/tr6y-kpc6

    work page doi:10.1103/tr6y-kpc6 2025

  77. [85]

    Data analysis recipes: Fitting a model to data

    D. W. Hogg, J. Bovy, & D. Lang, (2010). “Data analysis recipes: Fitting a model to data.”arXiv preprint arXiv:1008.4686. https://doi.org/10.48550/arXiv.1008.4686

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1008.4686 2010

  78. [86]

    W., Foreman-Mackey D., 2018, @doi [The Astrophysical Journal Supplement Series] 10.3847/1538-4365/aab76e , 236, 11

    D. W. Hogg, & D. Foreman-Mackey, (2018). “Data analysis recipes: Using markov chain monte carlo.” The Astrophysical Journal Supplement Series,236(1), 11. https://doi.org/10.3847/1538-4365/aab76e

    work page doi:10.3847/1538-4365/aab76e 2018

  79. [87]

    The Pantheon+ Analysis: Cosmological Constraints.Astrophys

    D. Brout, et al. (2022). “The Pantheon+ analysis: cosmological constraints.”The Astrophysical Journal, 938(2), 110. https://doi.org/10.3847/1538-4357/ac8e04

    work page doi:10.3847/1538-4357/ac8e04 2022

  80. [88]

    and Davis, Tamara M

    D. Scolnic, et al. (2022). “The Pantheon+ analysis: the full data set and light-curve release.”The Astro- physical Journal,938(2), 113. https://doi.org/10.3847/1538-4357/ac8b7a

    work page doi:10.3847/1538-4357/ac8b7a 2022

Showing first 80 references.