Pith. sign in

REVIEW 6 minor 1 cited by

Probing the independence within the dark sector in the fluid approximation

T0 review · 0 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read Current cosmological data show no statistically significant interaction between dark matter and dark energy in the simplest fluid models.

desk verdict Solid, honest null result for a minimal interacting dark sector; the main caveat is a fixed H0 that should be checked by marginalization. read the letter →

arxiv 1908.01953 v2 pith:35XMKBOM submitted 2019-08-06 astro-ph.CO gr-qc

Lawrence Dam , Krzysztof Bolejko , Geraint F. Lewis This is my paper · ORCID
classification astro-ph.COgr-qc
keywords darkmatter–darkenergyinteractiongeodesicmodelinteractingprincipalcomponentanalysisKarhunen-Loèvemodesgrowthofstructureredshift-spacedistortionsLambdaCDM
topics Dark EnergyDark Matter
open problems Dark MatterDark Energy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether the two dominant dark components — cold dark matter and dark energy — are truly independent, testing the simplest fluid model in which they can exchange energy. The authors reconstruct the interaction history from low-redshift cosmological data without committing to a particular functional form, using a data-oriented principal-component basis. Every reconstructed mode is consistent with zero interaction: the best-constrained mode gives $\alpha_1 = 1.2$–$1.5$ with $\sigma\approx 1.0$, the one-parameter coupling estimates are $q = 0.039 \pm 0.031$ and $q = 0.041 \pm 0.027$, and model-comparison criteria favour $\Lambda$CDM. The result matters because it constrains a generic extension of the standard model: any deviation that changes the expansion history would leave imprints in the same data, yet none appear. The paper also forecasts that forthcoming LSST and DESI data would pin a modest coupling down to about 20% precision, enough to test the non-interacting assumption.

What carries the argument

The carrying object is the geodesic interaction model, the minimal fluid description in which dark matter and dark energy exchange energy only along the dark-matter four-velocity, so there is no momentum transfer and dark energy stays spatially homogeneous. The interaction is encoded in the dimensionless history $q(a)$ through $Q = q(a) H(a) \rho_X(a)$, with $q$ reconstructed as piecewise-constant bins over $a \in [0.4, 1]$. The analysis identifies which features of $q$ the data actually probe by solving the Karhunen-Loève eigenvalue problem $F_\pi v_i = \lambda_i F_p v_i$, using a CPZ smoothing prior (a $1/r^2$ correlation) and the posterior Fisher matrix; the resulting modes are ordered by signal-to-noise, and the Bayesian complexity sets how many modes are genuinely constrained. A modified growth equation, carrying the term $\Gamma = Q/(\rho_m H)$, ties the interaction to redshift-space-distortion measurements, which are needed to break the degeneracy between $q$ and $\Omega_{m0}$ that geometric probes cannot resolve.

What would settle it

Run the same reconstruction with a newer, larger supernova sample and with the full CMB likelihood in place of the compressed distance prior, and compare the best-constrained low-redshift mode with $\alpha_1 \approx 1.5 \pm 1.0$: if it moves above about $2\sigma$ from zero, the paper's null conclusion is falsified; if it stays near zero, the conclusion holds. An even more direct check is the forecast itself: LSST/DESI data returning $q \approx 0.04$ with 20% precision would falsify the non-interacting scenario.

Watch

Extended reading notes

Core claim

The paper's central claim is a null result: in the geodesic fluid model, where the interaction four-vector is $Q^\mu = Q u_c^\mu$ with no momentum transfer and dark energy has equation of state $w_X = -1$, current data do not reveal any statistically significant interaction between dark matter and dark energy. Reconstructing the dimensionless interaction history $q(a)$, defined by $Q = q H \rho_X$, over twenty bins spanning $z < 1.5$, the best-constrained Karhunen-Loève mode gives $\alpha_1 = 1.2$–$1.5$ with $\sigma \approx 1.0$, and the one-parameter models give $q = 0.039 \pm 0.031$ and $q = 0.041 \pm 0.027$, both consistent with no coupling at 95% confidence. AIC, BIC, and Bayes-factor comparisons all favour the non-interacting $\Lambda$CDM model. The paper additionally shows that a future one-year LSST supernova sample combined with DESI BAO and RSD data would constrain the coupling to about 20% of a modest fiducial value and could falsify the no-interaction scenario at roughly $3\sigma$ if such a coupling is present.

Load-bearing premise

The analysis presumes both that any dark-sector exchange follows the dark-matter flow with no momentum transfer and dark energy's equation of state is fixed at $-1$, and that the compressed CMB likelihood remains valid for late-time dark-energy modifications; if either premise fails, the null conclusion does not apply.

Editorial extensions

If this is right

  • If the central claim is right, the dark sector in the minimal geodesic fluid model is effectively non-interacting at $z < 1.5$, and any future detection must come from the low-redshift modes where the data have the most leverage.
  • The null conclusion rules out the earlier claimed 99% detection of a late-time interaction, since the same model class reanalysed with newer data gives no significant signal.
  • Geometric probes alone cannot settle the question; only the combination of expansion data with growth-rate data breaks the $q$–$\Omega_{m0}$ degeneracy.
  • Upcoming LSST and DESI data should improve the coupling constraint by a factor of about 3.5 over current data, reaching roughly 20% precision and about $3\sigma$ sensitivity to a coupling of $q \approx 0.04$.
  • Model-selection criteria will continue to prefer $\Lambda$CDM unless the interaction is strong enough to overcome the penalty for extra parameters.

Reading between the lines

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

  • The scope of the null result is narrower than it may appear: the geodesic assumption sets dark-energy density perturbations to zero, so an interaction that transfers momentum, or allows $w_X$ to vary, could evade every constraint reported here.
  • A testable extension would be to run the same reconstruction on mock catalogs built with a momentum-transfer interaction; if that interaction leaks into the geodesic $q$ reconstruction as a bias, the method's blindness to such models could be quantified.
  • The mild low-redshift hint, $\alpha_1 \approx 1.5 \pm 1.0$ at $z \lesssim 0.4$, is the place to look for a real signal; if future data harden it above $2\sigma$, it would indicate late-time transfer from dark matter to dark energy.
  • The reported 85% shift in $q$ when the baryon-density datum $\omega_b$ is removed suggests the central estimate leans heavily on that single compressed CMB number; a stability check with the full CMB likelihood would test whether the null result is an artifact of the compression.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 6 minor

Summary. The paper tests for a non-gravitational coupling between cold dark matter and dark energy within a minimal fluid model, assuming a geodesic interaction Q^mu = Q u_c^mu and a dark-energy equation of state w_X = -1. The interaction history q(a) is reconstructed non-parametrically in 20 bins over the redshift window z < 1.5 using a Gaussian smoothing prior and a Karhunen-Loeve decomposition, with data from BAO, RSD, SNe Ia, cosmic chronometers, and a compressed Planck 2015 CMB likelihood. The authors find no statistically significant deviation from LambdaCDM: the best-constrained KL mode has amplitude alpha1 = 1.2-1.5 with sigma about 1.0, the one-parameter extensions give q = 0.039 +/- 0.031 (q1XCDM) and q = 0.041 +/- 0.027 (qXCDM), and model comparison via AIC, BIC, and Bayes factors favors LambdaCDM. A Fisher forecast combining current data with projected LSST and DESI measurements suggests that a coupling of order q ~ 0.04 could be detected at about 20% precision with a ten-year LSST SN sample.

Significance. If the result holds, the paper provides a careful, transparent null test of dark-sector interactions in a minimal model class that is often invoked in the literature. The analysis is notable for its methodological care: it uses two fiducial priors (a running-average prior and a LambdaCDM-biased prior), performs a sensitivity analysis over the smoothing amplitude, checks robustness to the number of bins, and avoids using the data twice in model comparison by switching to one-parameter models for the information criteria and Bayes factors. The reconstruction correctly identifies that only a handful of modes are constrained and that the low-redshift features are robust to the prior choice. The main caveat is that the null conclusion applies only to the assumed geodesic, w_X = -1 model class; interactions with momentum transfer or a time-varying equation of state could evade these constraints, as the authors acknowledge.

minor comments (6)
  1. [Section 4, Eq. (4.1)] The Hubble constant is fixed to H0 = 67.3 km/s/Mpc without a sensitivity test; although the compressed CMB likelihood is nearly H0-independent and the conclusion of no detection is unlikely to change, a brief test marginalizing over H0 (or a justification for the fixed value) would make the quoted q constraints more robust.
  2. [Section 3.3.1] The normalization rescaling for Prior II is not correct as written: inserting q_fid = Rq into the Gaussian density and multiplying by det[(I - R)(I - R)^T] does not give the correct normalization; the prior precision should be (I - R)^T C_pi^{-1} (I - R), as correctly stated in Section 3.4, and the Jacobian factor is |det(I - R)|, not its square.
  3. [Section 4.1.1] The relationship between the Bayesian complexity values (C = 5.2 for Prior I and C = 3.2 for Prior II) and the number of modes shown in Figure 5 (m = 4 and 5 for Prior I, m = 2 and 3 for Prior II) is not explicitly resolved; the text should state which m is adopted and reconcile this with the MSE criterion that favors m = 1.
  4. [Section 4.2] The statement that leaving out omega_b produces 'a ~85% shift in the mean value' is misleading: the mean changes from q = 0.039 to q = 0.021, which is about a 46% change relative to 0.039; please rephrase.
  5. [Section 5 and Abstract] The Fisher forecast includes the current data as a prior through F_data, so the abstract's phrasing that LSST and DESI 'will be able to constrain a DM-DE coupling at 20% precision' could be misread as using only future data; please clarify that the forecast combines future surveys with the current data likelihood.
  6. [Abstract and Section 2] The statement that any significant deviation changing the expansion history 'should leave imprints detectable by our analysis' is too strong given that the reconstruction is confined to z < 1.5 and to the geodesic, w_X = -1 model class; a qualifying phrase would improve precision.

Circularity Check

0 steps flagged · score 1.0 of 10

No meaningful circularity: the null result is a data-driven fit, with only openly acknowledged statistical caveats (fixed H0, post-hoc best-mode comparison) that are not load-bearing.

full rationale

The paper's central claims are parameter constraints, not first-principles predictions. The 20-bin q(a) reconstruction and the one-parameter limits q = 0.039 +/- 0.031 (q1XCDM) and q = 0.041 +/- 0.027 (qXCDM) are obtained by MCMC sampling of the joint likelihood of BAO, RSD, SNe Ia, cosmic chronometers, and a compressed CMB likelihood, using the forward model in Eqs. (2.3)-(2.6) and (2.9). The data are external to the model assumptions, and the inversion is a standard fit rather than an identity. The Fisher forecast (Section 5) uses the maximum-likelihood q = 0.041 as a fiducial, but it explicitly forecasts future survey precision and does not present that fiducial as independent evidence. Prior II is LambdaCDM-biased, but Prior I is not, and Section 4.1.2 shows the low-redshift features survive marginalizing over the smoothing scale xi_0; the paper itself notes the prior-dependence caveat in Section 6. The only quasi-circular element is the post-hoc best-mode comparison in Section 4.2.1, where pi(alpha1) is assigned variance 1/lambda1 from the same posterior used to compute the Savage-Dickey Bayes factor; however, the paper explicitly labels this 'post-hoc tuning' and treats it as a favorable-case illustration, and the main no-deviation conclusion rests on the direct q constraints and AIC/BIC, so this is not load-bearing. Fixing H0 = 67.3 km/s/Mpc in Section 4 is a robustness assumption that could affect the quoted error bars but is not a circular reduction: q is not defined in terms of H0, and no result is presented as a prediction of H0. Appendix A independently checks the fitting-formula approximation against CAMB. No self-citation chain or uniqueness theorem is invoked to force the result.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The analysis rests on a specific minimal interacting-fluid model (geodesic interaction, w_X = -1), a Gaussian smoothing prior with chosen hyperparameters, and the compressed CMB likelihood. No new fundamental entities are introduced; the interaction is a phenomenological coupling from the literature.

free parameters (7)
  • bin interaction amplitudes q1..q20 = posterior means shown in Fig. 2, all consistent with zero at 68-95% CL
    The 20 piecewise-constant interaction amplitudes are the primary fitted parameters; the reconstruction produces weak constraints, with only the first few bins informative.
  • one-bin interaction parameter q (q1XCDM) = q = 0.039 ± 0.031
    Fitted to combined data; consistent with zero at 95% CL.
  • logistic interaction parameter q (qXCDM) = q = 0.041 ± 0.027
    Fitted to combined data; used as fiducial for the Fisher forecast.
  • smoothing prior scale ξ0 = 0.2 (fixed in main analysis; marginalized over [0.02, 2] in sensitivity)
    Sets the strength of the CPZ correlated prior on the reconstruction; the main results use ξ0 = 0.2, with robustness checks.
  • correlation length ac = 0.12
    Characteristic correlation length of the CPZ prior, spanning about 4 bins.
  • base cosmological parameters Omega_m0, Omega_b0, sigma_80 = fitted; not central to the null result
    Standard cosmological parameters varied in the MCMC, with flat priors as listed in Section 3.3.2.
  • SN nuisance parameters alpha, beta, M0, x*, c*, R_M, R_x, R_c = fitted, not central
    SN Ia standardization parameters in the hierarchical likelihood; standard practice.
assumptions (6)
  • domain assumption Spatial flatness (Omega_K0 = 0)
    Stated in Section 4; restricts to zero spatial curvature.
  • domain assumption DE equation of state w_X = -1
    Assumes dark energy is a cosmological constant aside from the coupling; stated in Section 2.
  • domain assumption Geodesic interaction with no momentum transfer (Q^mu = Q u_c^mu)
    Removes momentum transfer and sets delta_rho_X = 0; from [18], stated in Section 2.
  • domain assumption Fluid approximation and linear perturbation theory for growth
    The growth equation (2.9) assumes ideal fluids and linear perturbations; the title acknowledges this limitation.
  • domain assumption Compressed CMB likelihood (R, l_A, omega_b) is sufficient and model-independent for late-time DE
    Used in Section 3.1; justified by the interaction vanishing before a = 0.4, checked for z* and zd in Appendix A.
  • ad hoc to paper Interaction vanishes outside the binning window a < 0.4 (z > 1.5)
    The reconstruction is restricted to low redshifts, effectively imposing LambdaCDM evolution at early times (Sections 2.1 and 4).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Probing the independence within the dark sector in the fluid approximation." pith.science (2026). https://pith.science/paper/35XMKBOM

@misc{pith2026190801953,
  author       = {Pith},
  title        = {Pith review of: Probing the independence within the dark sector in the fluid approximation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/35XMKBOM}},
  note         = {Machine review of arXiv:1908.01953}
}
abstract

The standard model of cosmology is based on two unknown dark components that are uncoupled from each other. In this paper we investigate whether there is evidence for an interaction between these components of cold dark matter (CDM) and dark energy (DE). In particular, we focus on a minimal extension and reconstruct the interaction history at low-redshifts non-parametrically using a variation of the commonly used principal component analysis. Although we focus on the interaction in the dark sector, any significant deviation from the standard model that changes the expansion history of the Universe, should leave imprints detectable by our analysis. Thus, detecting signatures of interaction could also be indicative of other non-standard phenomena even if they are not the results of the interaction. It is thus interesting to note that the results presented in this paper do not provide support for the interaction in the dark sector, although the uncertainty is still quite large. In so far as interaction is present but undetectable using current data, we show from a Fisher forecast that forthcoming LSST and DESI surveys will be able to constrain a DM-DE coupling at $20\%$ precision --- enough to falsify the non-interacting scenario, assuming the presence of a modest amount of interaction.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Looking for interactions in the cosmological dark sector

    astro-ph.CO 2019-08 conditional novelty 4.0 of 10

    Across Planck 2015 CMB, JLA supernovae, H0 and deuterium abundance data, the dark sector interaction parameter alpha is consistent with zero at 1 sigma, and freeing Neff shifts the posterior mean toward negative alpha.

Reference graph

Works this paper leans on

106 extracted references · 7 canonical work pages · cited by 1 Pith paper

  1. [1]

    Planck Collaboration, Planck 2018 results. VI. Cosmological parameters [arxiv:1807.06209]

    arXiv 2018

  2. [2]

    A. G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009 [ astro-ph/9805201]

    arXiv 1998

  3. [3]

    Perlmutter et al., Measurements of Ω and Λ from 42 high-redshift supernovae, Astrophys

    S. Perlmutter et al., Measurements of Ω and Λ from 42 high-redshift supernovae, Astrophys. J. 517 (1999) 565 [ astro-ph/9812133]

    arXiv 1999

  4. [4]

    D. L. Wiltshire, What is dust? - Physical foundations of the averaging problem in cosmology , Class. Quant. Grav. 28 (2011) 164006 [ arXiv:1106.1693]

    arXiv 2011

  5. [5]

    Desjacques, D

    V. Desjacques, D. Jeong and F. Schmidt, Large-Scale Galaxy Bias, Phys. Rept. 733 (2018) 1 [arxiv:1611.09787]

    arXiv 2018

  6. [6]

    Y. L. Bolotin, A. Kostenko, O. A. Lemets and D. A. Yerokhin, Cosmological evolution with interaction between dark energy and dark matter , Int. J. Mod. Phys. D 24 (2015) 1530007 [arXiv:1310.0085]

    arXiv 2015

  7. [7]

    B. Wang, E. Abdalla, F. Atrio-Barandela and D. Pavon, Dark Matter and Dark Energy Interactions: Theoretical Challenges, Cosmological Implications and Observational Signatures , Rept. Prog. Phys. 79 (2016) 096901 [ arXiv:1603.08299]

    arXiv 2016

  8. [8]

    E. J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy , Int. J. Mod. Phys. D 15 (2006) 1753 [ hep-th/0603057]

    arXiv 2006

Show all 106 references
  1. [9]

    Amendola, Coupled quintessence, Phys

    L. Amendola, Coupled quintessence, Phys. Rev. D 62 (2000) 043511 [ astro-ph/9908023]

    2000 arXiv

  2. [10]

    L. P. Chimento, A. S. Jakubi, D. Pavon and W. Zimdahl, Interacting quintessence solution to the coincidence problem, Phys. Rev. D 67 (2003) 083513 [ astro-ph/0303145]

    2003 arXiv

  3. [11]

    Zimdahl and D

    W. Zimdahl and D. Pavon, Interacting quintessence, Phys. Lett. B 521 (2001) 133 [astro-ph/0105479]

    2001 arXiv

  4. [12]

    G. R. Farrar and P. J. E. Peebles, Interacting dark matter and dark energy , Astrophys. J. 604 (2004) 1 [ astro-ph/0307316]

    2004 arXiv

  5. [13]

    Amendola and C

    L. Amendola and C. Quercellini, Tracking and coupled dark energy as seen by WMAP , Phys. Rev. D 68 (2003) 023514 [ astro-ph/0303228]

    2003 arXiv

  6. [14]

    Sandvik, M

    H. Sandvik, M. Tegmark, M. Zaldarriaga and I. Waga, The end of unified dark matter? , Phys. Rev. D 69 (2004) 123524 [ astro-ph/0212114]

    2004 arXiv

  7. [15]

    M. C. Bento, O. Bertolami and A. A. Sen, Revival of the unified dark energy-dark matter model?, Phys. Rev. D 70 (2004) 083519 [ astro-ph/0407239]

    2004 arXiv

  8. [16]

    J. D. Barrow and T. Clifton, Cosmologies with energy exchange , Phys. Rev. D 73 (2006) 103520 [gr-qc/0604063]

    2006 arXiv

  9. [17]

    Z. K. Guo, N. Ohta and S. Tsujikawa, Probing the Coupling between Dark Components of the Universe, Phys. Rev. D 76 (2007) 023508 [ astro-ph/0702015]

    2007 arXiv

  10. [18]

    V¨ aliviita, E

    J. V¨ aliviita, E. Majerotto and R. Maartens, Instability in interacting dark energy and dark matter fluids, JCAP 0807 (2008) 020 [ arXiv:0804.0232]

    2008 arXiv

  11. [19]

    del Campo, R

    S. del Campo, R. Herrera and D. Pavon, Interacting models may be key to solve the cosmic coincidence problem, JCAP 0901 (2009) 020 [ arXiv:0812.2210]

    2009 arXiv

  12. [20]

    Caldera-Cabral, R

    G. Caldera-Cabral, R. Maartens and B. M. Schaefer, The Growth of Structure in Interacting Dark Energy Models, JCAP 0907 (2009) 027 [ arXiv:0905.0492]

    2009 arXiv

  13. [21]

    Majerotto, J

    E. Majerotto, J. V¨ aliviita and R. Maartens, Adiabatic initial conditions for perturbations in interacting dark energy models , Mon. Not. Roy. Astron. Soc. 402 (2010) 2344 [arXiv:0907.4981]. – 29 –

    2010 arXiv

  14. [22]

    V¨ aliviita, R

    J. V¨ aliviita, R. Maartens and E. Majerotto, Observational constraints on an interacting dark energy model, Mon. Not. Roy. Astron. Soc. 402 (2010) 2355 [ arXiv:0907.4987]

    2010 arXiv

  15. [23]

    C. G. Boehmer, G. Caldera-Cabral, R. Lazkoz and R. Maartens, Dynamics of dark energy with a coupling to dark matter , Phys. Rev. D 78 (2008) 023505 [ arXiv:0801.1565]

    2008 arXiv

  16. [24]

    Wands, J

    D. Wands, J. De-Santiago and Y. Wang, Inhomogeneous vacuum energy Class. Quant. Grav. 29 (2012) 145017 [ arxiv:1203.6776]

    2012 arXiv

  17. [25]

    Y. Wang, D. Wands, L. Xu, J. De-Santiago and A. Hojjati, Cosmological constraints on a decomposed Chaplygin gas, Phys. Rev. D 87 (2013) 083503 [ arXiv:1301.5315]

    2013 arXiv

  18. [26]

    Y. Wang, D. Wands, G. B. Zhao and L. Xu, Post-Planck constraints on interacting vacuum energy, Phys. Rev. D 90 (2014) 023502 [ arXiv:1404.5706]

    2014 arXiv

  19. [27]

    Salvatelli, N

    V. Salvatelli, N. Said, M. Bruni, A. Melchiorri and D. Wands, Indications of a late-time interaction in the dark sector , Phys. Rev. Lett. 113 (2014) 181301 [ arxiv:1406.7297]

    2014 arXiv

  20. [28]

    Y. Wang, G. B. Zhao, D. Wands, L. Pogosian and R. G. Crittenden, Reconstruction of the dark matter-vacuum energy interaction, Phys. Rev. D 92 (2015) 103005 [ arxiv:1505.01373]

    2015 arXiv

  21. [29]

    R. C. Nunes, S. Pan and E. N. Saridakis, New constraints on interacting dark energy from cosmic chronometers, Phys. Rev. D 94 (2016) 023508 [ arXiv:1605.01712]

    2016 arXiv

  22. [30]

    Kumar and R

    S. Kumar and R. C. Nunes, Echo of interactions in the dark sector , Phys. Rev. D 96 (2017) 103511 [arXiv:1702.02143]

    2017 arXiv

  23. [31]

    Di Valentino, A

    E. Di Valentino, A. Melchiorri and O. Mena, Can interacting dark energy solve the H0 tension?, Phys. Rev. D 96 (2017) 043503 [ arxiv:1704.08342]

    2017 arXiv

  24. [32]

    W. Yang, S. Pan, E. Di Valentino, R. C. Nunes, S. Vagnozzi and D. F. Mota, Tale of stable interacting dark energy, observational signatures, and the H0 tension, JCAP 1809 (2018) 019 [arXiv:1805.08252]

    2018 arXiv

  25. [33]

    W. Yang, O. Mena, S. Pan and E. Di Valentino, Dark sectors with dynamical coupling , Phys. Rev. D 100 (2019) 083509 [ arXiv:1906.11697]

    2019 arXiv

  26. [34]

    S. Pan, W. Yang, E. Di Valentino, E. N. Saridakis and S. Chakraborty, Interacting scenarios with dynamical dark energy: observational constraints and alleviation of the H0 tension, [arXiv:1907.07540]

    1907 arXiv

  27. [35]

    Zhang, R

    J. Zhang, R. An, S. Liao, W. Luo, Z. Li and B. Wang, Fully self-consistent cosmological simulation pipeline for interacting dark energy models , Phys. Rev. D 98 (2018) 103530 [arXiv:1811.01519]

    2018 arXiv

  28. [36]

    Zhang, R

    J. Zhang, R. An, W. Luo, Z. Li, S. Liao and B. Wang, The First Constraint from SDSS GalaxyGalaxy Weak Lensing Measurements on Interacting Dark Energy Models , Astrophys. J. 875 (2019) L11 [ arXiv:1807.05522]

    2019 arXiv

  29. [37]

    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. D 80 (2009) 123001 [ astro-ph/0702615]

    2009 arXiv

  30. [38]

    Vattis, S

    K. Vattis, S. M. Koushiappas and A. Loeb, Dark matter decaying in the late Universe can relieve the H0 tension , Phys. Rev. D 99 (2019) 121302 [ arXiv:1903.06220]

    2019 arXiv

  31. [39]

    A. G. Riess, S. Casertano, W. Yuan, L. M. Macri and D. Scolnic, Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM , Astrophys. J. 876 (2019) 85 [arxiv:1903.07603]

    2019 arXiv

  32. [40]

    L. Knox, Y. S. Song and J. A. Tyson, Distance-redshift and growth-redshift relations as two windows on acceleration and gravitation: Dark energy or new gravity? , Phys. Rev. D 74 (2006) 023512 [astro-ph/0503644]. – 30 –

    2006 arXiv

  33. [41]

    Ishak, A

    M. Ishak, A. Upadhye and D. N. Spergel, Probing cosmic acceleration beyond the equation of state: Distinguishing between dark energy and modified gravity models , Phys. Rev. D 74 (2006) 043513 [astro-ph/0507184]

    2006 arXiv

  34. [42]

    Chiba and R

    T. Chiba and R. Takahashi, A Consistency Relation in Cosmology , Phys. Rev. D 75 (2007) 101301 [astro-ph/0703347]

    2007 arXiv

  35. [43]

    Beutler et al., The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant, Mon

    F. Beutler et al., The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant, Mon. Not. Roy. Astron. Soc. 416 (2011) 3017 [ arxiv:1106.3366]

    2011 arXiv

  36. [44]

    A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. Burden and M. Manera, The clustering of the SDSS DR7 main Galaxy sample I. A 4 per cent distance measure at z = 0.15, Mon. Not. Roy. Astron. Soc. 449 (2015) 835 [ arxiv:1409.3242]

    2015 arXiv

  37. [45]

    A. J. Cuesta et al., The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the correlation function of LOWZ and CMASS galaxies in Data Release 12 , Mon. Not. Roy. Astron. Soc. 457 (2016) 1770 [arxiv:1509.06371]

    2016 arXiv

  38. [46]

    Padmanabhan, X

    N. Padmanabhan, X. Xu, D. J. Eisenstein, R. Scalzo, A. J. Cuesta, K. T. Mehta and E. Kazin, A 2 per cent distance to z=0.35 by reconstructing baryon acoustic oscillations - I. Methods and application to the Sloan Digital Sky Survey , Mon. Not. Roy. Astron. Soc. 427 (2012) 2132...

    2012 arXiv

  39. [47]

    Blake et al., The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations , Mon

    C. Blake et al., The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations , Mon. Not. Roy. Astron. Soc. 418 (2011) 1707 [ arxiv:1108.2635]

    2011 arXiv

  40. [48]

    Betoule et al

    M. Betoule et al. [SDSS Collaboration], Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples , Astron. Astrophys. 568 (2014) A22 [arxiv:1401.4064]

    2014 arXiv

  41. [49]

    D. M. Scolnic et al., The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample , Astrophys. J. 859 (2018) 101 [ arxiv:1710.00845]

    2018 arXiv

  42. [50]

    M. M. Phillips, The absolute magnitudes of Type IA supernovae , Astrophys. J. 413 (1993) L105

    1993

  43. [51]

    M. M. Phillips, P. Lira, N. B. a. Suntzeff, R. A. Schommer, M. Hamuy and J. Maza, The reddening-free decline rate versus luminosity relationship for type ia supernovae , Astron. J. 118 (1999) 1766 [ astro-ph/9907052]

    1999 arXiv

  44. [52]

    Guy et al

    J. Guy et al. [SNLS Collaboration], SALT2: Using distant supernovae to improve the use of Type Ia supernovae as distance indicators , Astron. Astrophys. 466 (2007) 11 [astro-ph/0701828]

    2007 arXiv

  45. [53]

    M. C. March, R. Trotta, P. Berkes, G. D. Starkman and P. M. Vaudrevange, Improved constraints on cosmological parameters from SNIa data , Mon. Not. Roy. Astron. Soc. 418 (2011) 2308 [ arxiv:1102.3237]

    2011 arXiv

  46. [54]

    Gelman, J

    A. Gelman, J. Carlin, H. Stern, D. Dunson, A. Vehtari and D. Rubin, Bayesian Data Analysis , CRC Press, Boca Raton, FL (2014)

    2014

  47. [55]

    Gull, in J

    S. Gull, in J. Skilling, ed., Maximum Entropy and Bayesian Methods , Kluwer Academic Publishers, Dordrecht (1989)

    1989

  48. [56]

    Vonlanthen, S

    M. Vonlanthen, S. R¨ as¨ anen and R. Durrer,Model-independent cosmological constraints from the CMB, JCAP 1008 (2010) 023 [ arxiv:1003.0810]

    2010 arXiv

  49. [57]

    Kosowsky, M

    A. Kosowsky, M. Milosavljevic and R. Jimenez, Efficient cosmological parameter estimation from microwave background anisotropies, Phys. Rev. D 66 (2002) 063007 [ astro-ph/0206014]

    2002 arXiv

  50. [58]

    Wang and P

    Y. Wang and P. Mukherjee, Observational Constraints on Dark Energy and Cosmic Curvature , Phys. Rev. D 76 (2007) 103533 [ astro-ph/0703780]. – 31 –

    2007 arXiv

  51. [59]

    Mukherjee, M

    P. Mukherjee, M. Kunz, D. Parkinson and Y. Wang, Planck priors for dark energy surveys , Phys. Rev. D 78 (2008) 083529 [ arxiv:0803.1616]

    2008 arXiv

  52. [60]

    Efstathiou and J

    G. Efstathiou and J. R. Bond, Cosmic confusion: Degeneracies among cosmological parameters derived from measurements of microwave background anisotropies , Mon. Not. Roy. Astron. Soc. 304 (1999) 75 [ astro-ph/9807103]

    1999 arXiv

  53. [61]

    Planck Collaboration, Planck 2015 results. XIV. Dark energy and modified gravity , Astron. Astrophys. 594 (2016) A14 [ arxiv:1502.01590]

    2016 arXiv

  54. [62]

    M. Moresco et al., Improved constraints on the expansion rate of the Universe up to z∼ 1.1 from the spectroscopic evolution of cosmic chronometers , JCAP 1208 (2012) 006 [arxiv:1201.3609]

    2012 arXiv

  55. [63]

    Moresco, L

    M. Moresco, L. Verde, L. Pozzetti, R. Jimenez and A. Cimatti, New constraints on cosmological parameters and neutrino properties using the expansion rate of the Universe to z∼ 1.75, JCAP 1207 (2012) 053 [ arxiv:1201.6658]

    2012 arXiv

  56. [64]

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

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

    2015 arXiv

  57. [65]

    Moresco et al., A 6% measurement of the Hubble parameter at z∼ 0.45: direct evidence of the epoch of cosmic re-acceleration, JCAP 1605 (2016) 014 [ arxiv:1601.01701]

    M. Moresco et al., A 6% measurement of the Hubble parameter at z∼ 0.45: direct evidence of the epoch of cosmic re-acceleration, JCAP 1605 (2016) 014 [ arxiv:1601.01701]

    2016 arXiv

  58. [66]

    R. G. Crittenden, L. Pogosian and G. B. Zhao, Investigating dark energy experiments with principal components, JCAP 0912 (2009) 025 [ astro-ph/0510293]

    2009 arXiv

  59. [67]

    R. G. Crittenden, G. B. Zhao, L. Pogosian, L. Samushia and X. Zhang, Fables of reconstruction: controlling bias in the dark energy equation of state , JCAP 1202 (2012) 048 [arxiv:1112.1693]

    2012 arXiv

  60. [68]

    G. B. Zhao, R. G. Crittenden, L. Pogosian and X. Zhang, Examining the evidence for dynamical dark energy, Phys. Rev. Lett. 109 (2012) 171301 [ arxiv:1207.3804]

    2012 arXiv

  61. [69]

    G. B. Zhao et al., Dynamical dark energy in light of the latest observations , Nat. Astron. 1 (2017) 627 [ arxiv:1701.08165]

    2017 arXiv

  62. [70]

    Huterer, D

    D. Huterer, D. Shafer, D. Scolnic and F. Schmidt, Testing ΛCDM at the lowest redshifts with SN Ia and galaxy velocities , JCAP 1705 (2017) 015 [ arxiv:1611.09862]

    2017 arXiv

  63. [71]

    Beutler et al., The 6dF Galaxy Survey: z≈ 0 measurement of the growth rate and σ8, Mon

    F. Beutler et al., The 6dF Galaxy Survey: z≈ 0 measurement of the growth rate and σ8, Mon. Not. Roy. Astron. Soc. 423 (2012) 3430 [ arxiv:1204.4725]

    2012 arXiv

  64. [72]

    Howlett, A

    C. Howlett, A. Ross, L. Samushia, W. Percival and M. Manera, The clustering of the SDSS main galaxy sample ? II. Mock galaxy catalogues and a measurement of the growth of structure from redshift space distortions at z = 0.15, Mon. Not. Roy. Astron. Soc. 449 (2015) 848 [arxiv:1...

    2015 arXiv

  65. [73]

    A. Oka, S. Saito, T. Nishimichi, A. Taruya and K. Yamamoto, Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample, Mon. Not. Roy. Astron. Soc. 439 (2014) 2515 [ arxiv:1310.2820]

    2014 arXiv

  66. [74]

    Blake et al., Galaxy And Mass Assembly (GAMA): improved cosmic growth measurements using multiple tracers of large-scale structure , Mon

    C. Blake et al., Galaxy And Mass Assembly (GAMA): improved cosmic growth measurements using multiple tracers of large-scale structure , Mon. Not. Roy. Astron. Soc. 436 (2013) 3089 [arxiv:1309.5556]

    2013 arXiv

  67. [75]

    Alam et al

    S. Alam et al. [BOSS Collaboration], The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample , Mon. Not. Roy. Astron. Soc. 470 (2017) 2617 [ arxiv:1607.03155]

    2017 arXiv

  68. [76]

    Blake et al., The WiggleZ Dark Energy Survey: Joint measurements of the expansion and growth history at z <1, Mon

    C. Blake et al., The WiggleZ Dark Energy Survey: Joint measurements of the expansion and growth history at z <1, Mon. Not. Roy. Astron. Soc. 425 (2012) 405 [ arxiv:1204.3674]. – 32 –

    2012 arXiv

  69. [77]

    A. Pezzotta et al., The VIMOS Public Extragalactic Redshift Survey (VIPERS): The growth of structure at 0.5<z < 1.2 from redshift-space distortions in the clustering of the PDR-2 final sample, Astron. Astrophys. 604 (2017) A33 [ arxiv:1612.05645]

    2017 arXiv

  70. [78]

    Okumura et al., The Subaru FMOS galaxy redshift survey (FastSound)

    T. Okumura et al., The Subaru FMOS galaxy redshift survey (FastSound). IV. New constraint on gravity theory from redshift space distortions at z∼ 1.4, Publ. Astron. Soc. Jap. 68 (2016) 38 [arxiv:1511.08083]

    2016 arXiv

  71. [79]

    P. Zarrouk et al., The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measurement of the growth rate of structure from the anisotropic correlation function between redshift 0.8 and 2.2 , Mon. Not. Roy. Astron. Soc. 477 (2018) 163...

    2018 arXiv

  72. [80]

    Huterer and G

    D. Huterer and G. Starkman, Parameterization of Dark-Energy Properties: A Principal-Component Approach, Phys. Rev. Lett. 90 (2003) 031301 [ astro-ph/0207517]

    2003 arXiv

  73. [81]

    Huterer and A

    D. Huterer and A. Cooray, Uncorrelated estimates of dark energy evolution , Phys. Rev. D 71 (2005) 023506 [ astro-ph/0404062]

    2005 arXiv

  74. [82]

    Sarkar, S

    D. Sarkar, S. Sullivan, S. Joudaki, A. Amblard, D. E. Holz and A. Cooray, Beyond two dark energy parameters, Phys. Rev. Lett. 100 (2008) 241302 [ arxiv:0709.1150]

    2008 arXiv

  75. [83]

    Clarkson and C

    C. Clarkson and C. Zunckel, Direct reconstruction of dark energy, Phys. Rev. Lett. 104 (2010) 211301 [arxiv:1002.5004]

    2010 arXiv

  76. [84]

    N. Said, C. Baccigalupi, M. Martinelli, A. Melchiorri and A. Silvestri, New Constraints On The Dark Energy Equation of State , Phys. Rev. D 88 (2013) 043515 [ arxiv:1303.4353]

    2013 arXiv

  77. [85]

    D. J. Spiegelhalter, N. G. Best, B. P. Carlin and A. van der Linde, Bayesian measures of model complexity and fit , J. R. Stat. Soc. B, 64 (2002) 583

    2002

  78. [86]

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

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

    2008 arXiv

  79. [87]

    Tegmark, A

    M. Tegmark, A. Taylor and A. Heavens, Karhunen-Lo` eve eigenvalue problems in cosmology: How should we tackle large data sets? , Astrophys. J. 480 (1997) 22 [ astro-ph/9603021]

    1997 arXiv

  80. [88]

    M. Kunz, R. Trotta and D. Parkinson, Measuring the effective complexity of cosmological models, Phys. Rev. D 74 (2006) 023503 [ astro-ph/0602378]

    2006 arXiv

  81. [89]

    Foreman-Mackey, D

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

    2013 arXiv

  82. [90]

    A. Y. Kamenshchik, U. Moschella and V. Pasquier, An Alternative to quintessence , Phys. Lett. B 511 (2001) 265 [ gr-qc/0103004]

    2001 arXiv

  83. [91]

    Gorini, A

    V. Gorini, A. Kamenshchik and U. Moschella, Can the Chaplygin gas be a plausible model for dark energy?, Phys. Rev. D 67 (2003) 063509 [ astro-ph/0209395]

    2003 arXiv

  84. [92]

    Makler, S

    M. Makler, S. Quinet de Oliveira and I. Waga, Constraints on the generalized Chaplygin gas from supernovae observations, Phys. Lett. B 555 (2003) 1 [ astro-ph/0209486]

    2003 arXiv

  85. [93]

    E. V. Linder and R. N. Cahn, Parameterized Beyond-Einstein Growth, Astropart. Phys. 28 (2007) 481 [ astro-ph/0701317]

    2007 arXiv

  86. [94]

    E. V. Linder, Cosmic growth history and expansion history , Phys. Rev. D 72 (2005) 043529 [astro-ph/0507263]

    2005 arXiv

  87. [95]

    A. R. Liddle, How many cosmological parameters?, Mon. Not. Roy. Astron. Soc. 351 (2004) L49 [astro-ph/0401198]

    2004 arXiv

  88. [96]

    LSST Science and LSST Project Collaborations, LSST Science Book, Version 2.0 [arxiv:0912.0201]. – 33 –

    arXiv

  89. [97]

    DESI Collaboration, The DESI Experiment Part I: Science, Targeting, and Survey Design [arxiv:1611.00036]

    arXiv

  90. [98]

    Chevallier and D

    M. Chevallier and D. Polarski, Accelerating universes with scaling dark matter , Int. J. Mod. Phys. D 10 (2001) 213 [ gr-qc/0009008]

    2001 arXiv

  91. [99]

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

    2003 arXiv

  92. [100]

    W. Yang, H. Li, Y. Wu and J. Lu, Cosmological constraints on coupled dark energy , JCAP 1610 (2016) 007 [ arXiv:1608.07039]

    2016 arXiv

  93. [101]

    A. G. Riess et al., A 2.4% Determination of the Local Value of the Hubble Constant , Astrophys. J. 826 (2016) 56 [ arXiv:1604.01424]

    2016 arXiv

  94. [102]

    R. An, A. A. Costa, L. Xiao, J. Zhang and B. Wang, Testing a quintessence model with Yukawa interaction from cosmological observations and N-body simulations , Mon. Not. Roy. Astron. Soc. 489 (2019) 297 [ arXiv:1809.03224]

    2019 arXiv

  95. [103]

    A. A. Costa, L. C. Olivari and E. Abdalla, Quintessence with Yukawa Interaction , Phys. Rev. D 92 (2015) 103501 [ arXiv:1411.3660]

    2015 arXiv

  96. [104]

    Martinelli, N

    M. Martinelli, N. B. Hogg, S. Peirone, M. Bruni and D. Wands, Constraints on the interacting vacuumgeodesic CDM scenario, Mon. Not. Roy. Astron. Soc. 488 (2019) 3423 [arXiv:1902.10694]

    2019 arXiv

  97. [105]

    Hu and N

    W. Hu and N. Sugiyama, Small scale cosmological perturbations: An Analytic approach , Astrophys. J. 471 (1996) 542 [ astro-ph/9510117]

    1996 arXiv

  98. [106]

    Lewis, A

    A. Lewis, A. Challinor and A. Lasenby, Efficient computation of CMB anisotropies in closed FRW models, Astrophys. J. 538 (2000) 473 [ astro-ph/9911177]. – 34 –

    2000 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.