Dark Energy Versus Modified Gravity
Open accessAbstract
Understanding the reason for the observed accelerated expansion of the Universe represents one of the fundamental open questions in physics. In cosmology, a classification has emerged among physical models for this acceleration, distinguishing between dark energy and modified gravity. In this review, we provide a brief overview of models in both categories as well as their phenomenology and characteristic observable signatures in cosmology. We also introduce a rigorous distinction between dark energy and modified gravity based on the strong and weak equivalence principles.
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Joyce et al. (2016) state that using SEP can be motivated by the conjecture that GR is the only metric theory that satisfies the SEP.
“They state that using the SEP to make this distinction can be motivated further by the conjecture that GR is the only metric theory that satisfy the SEP, see Will (2014).”
From Testing general relativity in cosmology (2019) · cites this paper as Joyce et al. (2016)
Joyce et al. (2016) propose to use the strong equivalence principle to distinguish GR dark energy models from MG models: any model satisfying SEP is dark energy, any violating SEP is MG.
“Joyce et al. (2016) and possibly others, propose to use the strong equivalence principle (SEP) (see Sect. 2.1) to draw a distinction between GR dark energy models versus MG models. They suggest to call any model that satisfies the SEP as a dark energy model and any model that violates SEP to be an MG model.”
From Testing general relativity in cosmology (2019) · cites this paper as Joyce et al. (2016)
Joyce et al. (2016) state that the SEP forbids the presence of a fifth force.
“They state that, heuristically, the SEP forbids the presence of a fifth force which motivates the use of such a discriminant.”
From Testing general relativity in cosmology (2019) · cites this paper as Joyce et al. (2016)
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Erickcek, A., Smith, T. L., & Kamionkowski, M. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.74.121501 · Cited by 184 · see citing works
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Quintessence cosmologies with a growing matter component
Amendola, L., Baldi, M., & WETTERICH, C. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.023015 · Cited by 181 · see citing works
Nonlinear evolution of f(R) cosmologies. I. Methodology
Oyaizu, H. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.123523 · Cited by 176 · see citing works
On the Growth of Perturbations as a Test of Dark Energy and Gravity
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Non-Local Modification of Gravity and the Cosmological Constant ProblemPreprint
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Practical approach to cosmological perturbations in modified gravity
Silvestri, A., Pogosian, L., & Buniy, R. V. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.104015 · Cited by 153 · see citing works
No-Go Theorems for Generalized Chameleon Field Theories
Wang, J., Hui, L., & Khoury, J. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.241301 · Cited by 149 · see citing works
Constraints on f(R) gravity from probing the large-scale structure
Lombriser, L., Slosar, A., Seljak, U., & Hu, W. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.124038 · Cited by 149 · see citing works
Self-citationPietroni, M. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.72.043535 · Cited by 145 · see citing works
New constraints on f(R) gravity from clusters of galaxies
Cataneo, M., Rapetti, D., Schmidt, F., Mantz, A. B., Allen, S. W., Applegate, D., Kelly, P. L., von der Linden, A., & Morris, R. G. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.92.044009 · Cited by 142 · see citing works
Self-citationDynamical masses in modified gravity
Schmidt, F. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.103002 · Cited by 140 · see citing works
Self-citationSpherical collapse in quintessence models with zero speed of sound
Creminelli, P., D’Amico, G., Noreña, J., Senatore, L., & Vernizzi, F. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/03/027 · Cited by 137 · see citing works
Constraining dark energy anisotropic stress
Mota, D. F., Kristiansen, J. R., Koivisto, T., & Groeneboom, N. E. (2007) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2007.12413.x · Cited by 132 · see citing works
Cosmic degeneracies – I. Joint N-body simulations of modified gravity and massive neutrinos
Baldi, M., Villaescusa-Navarro, F., Viel, M., Puchwein, E., Springel, V., & Moscardini, L. (2014) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stu259 · Cited by 130 · see citing works
Interacting vectorlike dark energy, the first and second cosmological coincidence problems
Wei, H., & Cai, R.-G. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.083002 · Cited by 130 · see citing works
Beltrán Jiménez, J., Piazza, F., & Velten, H. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.061101 · Cited by 129 · see citing works
The observational status of Galileon gravity after Planck
Barreira, A., Li, B., Baugh, C. M., & Pascoli, S. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/08/059 · Cited by 128 · see citing works
Cosmological simulations of normal-branch braneworld gravity
Schmidt, F. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.123003 · Cited by 124 · see citing works
Self-citationImproving relativistic modified Newtonian dynamics with Galileon k -mouflage
Babichev, E., Deffayet, C., & Esposito-Farèse, G. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.061502 · Cited by 117 · see citing works
Effective theory of interacting dark energy
Gleyzes, J., Langlois, D., Mancarella, M., & Vernizzi, F. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/08/054 · Cited by 117 · see citing works
Testing chameleon gravity with the Coma cluster
Terukina, A., Lombriser, L., Yamamoto, K., Bacon, D., Koyama, K., & Nichol, R. C. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/04/013 · Cited by 115 · see citing works
Self-citationCluster density profiles as a test of modified gravity
Lombriser, L., Schmidt, F., Baldauf, T., Mandelbaum, R., Seljak, U., & Smith, R. C. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.102001 · Cited by 114 · see citing works
Self-citationWeak lensing by voids in modified lensing potentials
Barreira, A., Cautun, M., Li, B., Baugh, C. M., & Pascoli, S. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/08/028 · Cited by 111 · see citing works
Cosmological constraints on DGP braneworld gravity with brane tension
Lombriser, L., Hu, W., Fang, W., & Seljak, U. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.063536 · Cited by 110 · see citing works
Self-citationAstrophysical Tests of Modified Gravity: Constraints from Distance Indicators in the Nearby UniversePreprint
Jain, B., Vikram, V., & Sakstein, J. (2016) · Cited by 109 · see citing works
Measuring the speed of dark: Detecting dark energy perturbations
de Putter, R., Dragan Huterer, A., & Linder, E. V. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.103513 · Cited by 107 · see citing works
Cosmological Tests of General Relativity with Future Tomographic Surveys
Zhao, G., Pogosian, L., Silvestri, A., & Zylberberg, J. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.241301 · Cited by 105 · see citing works
de Rham, C. (2012) · Comptes Rendus Physique · doi:10.1016/j.crhy.2012.04.006 · Cited by 105 · see citing works
Vainshtein mechanism in binary pulsars
de Rham, C., Tolley, A. J., & Wesley, D. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.044025 · Cited by 104 · see citing works
Alternative to particle dark matter
Khoury, J. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.024022 · Cited by 95 · see citing works
Riding on irrelevant operators
de Rham, C., & Ribeiro, R. H. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/11/016 · Cited by 89 · see citing works
The Theorem of OstrogradskyPreprint
Woodard, R. P. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1506.02210 · Cited by 80 · see citing works
Falsifying paradigms for cosmic acceleration
Mortonson, M. J., Hu, W., & Dragan Huterer, A. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.79.023004 · Cited by 74 · see citing works
Testing Gravity with the Stacked Phase Space around Galaxy Clusters
Lam, T. Y., Nishimichi, T., Schmidt, F., & Takada, M. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.051301 · Cited by 67 · see citing works
Self-citationGalaxy infall kinematics as a test of modified gravity
Zu, Y., Weinberg, D. H., Jennings, E., Li, B., & Wyman, M. (2014) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stu1739 · Cited by 66 · see citing works
Testing gravity using large-scale redshift-space distortions
Raccanelli, A., Bertacca, D., Pietrobon, D., Schmidt, F., Samushia, L., Bartolo, N., Doré, O., Matarrese, S., & Percival, W. J. (2013) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stt1517 · Cited by 61 · see citing works
Self-citationTesting the dark energy consistency with geometry and growth
Ruiz, E. J., & Dragan Huterer, A. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.063009 · Cited by 59 · see citing works
Equivalence principle violation in Vainshtein screened two-body systems
Hiramatsu, T., Hu, W., Koyama, K., & Schmidt, F. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.063525 · Cited by 56 · see citing works
Self-citationRetarded Green’s function of a Vainshtein system and Galileon waves
Chu, Y.-Z., & Trodden, M. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.024011 · Cited by 52 · see citing works
Unscreening Modified Gravity in the Matter Power Spectrum
Lombriser, L., Simpson, F., & Mead, A. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.251101 · Cited by 45 · see citing works
Self-citationParametrized modified gravity constraints after Planck
Hu, B., Liguori, M., Bartolo, N., & Matarrese, S. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.123514 · Cited by 38 · see citing works
Motion of small bodies in classical field theory
Gralla, S. E. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.084060 · Cited by 37 · see citing works
Searching for scalar gravitational interactions in current and future cosmological data
Hojjati, A., Plahn, A. S., Zucca, A., Pogosian, L., Brax, P., Davis, A.-C., & Zhao, G. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.043531 · Cited by 33 · see citing works
Enhanced peculiar velocities in brane-induced gravity
Wyman, M., & Khoury, J. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.044032 · Cited by 31 · see citing works
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Alam, S., Ata, M., Bailey, S., Beutler, F., Bizyaev, D., Blazek, J. A., Bolton, A. S., Brownstein, J. R., Burden, A., Chuang, C.-H., et al. (2017) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stx721 · Cited by 3,056 · see citing works
Aghanim, N., Akrami, Y., Arroja, F. M. A., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., et al. (2019) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201833880 · Cited by 2,002 · see citing works
DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations
Adame, A. G., Aguilar, J., Ahlen, S. P., Alam, S., Alexander, D. M., Alvarez, M. A., Alves, O., Anand, A., Andrade, U., Armengaud, E., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/02/021 · Cited by 1,156 · see citing works
Desjacques, V., Jeong, D., & Schmidt, F. (2018) · Physics Reports · doi:10.1016/j.physrep.2017.12.002 · Cited by 836 · see citing works
Self-citationBlack holes, gravitational waves and fundamental physics: a roadmap
Askar, A., Belczynski, C., Bertone, G., Bon, E., Blas, D., Brito, R., Bulik, T., Burrage, C., Byrnes, C. T., Caprini, C., et al. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab0587 · Cited by 803 · see citing works
Testing general relativity in cosmology
Ishak, M. (2019) · Living Reviews in Relativity · doi:10.1007/s41114-018-0017-4 · Cited by 449 · see citing works
“For our review, we focus on the notions of universality of free fall and the matter coupling in the context of GR+dark energy versus modified gravity (MG) models following for example Joyce et al (2016).”
MethodProspects for fundamental physics with LISA
Barausse, E., Berti, E., Hertog, T., Hughes, S. A., Jetzer, P., Pani, P., Sotiriou, T. P., Tamanini, N., Witek, H., Yagi, K., et al. (2020) · General Relativity and Gravitation · doi:10.1007/s10714-020-02691-1 · Cited by 404 · see citing works
Farooq, O., Madiyar, F. R., Crandall, S., & Ratra, B. (2017) · The Astrophysical Journal · doi:10.3847/1538-4357/835/1/26 · Cited by 365 · see citing works
“In addition, the binned H(z) 1 For reviews of this picture, as well as of the alternate modified gravity scenario, see Ratra & Vogeley (2008), Weinberg et al. (2013), Martin (2012), Joyce et al. (2016), and references therein.”
BackgroundDark energy two decades after: observables, probes, consistency tests
Dragan Huterer, A., & Shafer, D. L. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa997e · Cited by 328 · see citing works
New horizons for fundamental physics with LISA
Arun, K. G., Belgacem, E., Benkel, R., Bernard, L., Berti, E., Bertone, G., Besançon, M., Blas, D., Böhmer, C. G., Brito, R., et al. (2022) · Living Reviews in Relativity · doi:10.1007/s41114-022-00036-9 · Cited by 315 · see citing works
Self-citationFarooq, O., Madiyar, F. R., Crandall, S., & Ratra, B. (2017) · K-State Research Exchange (Kansas State University) · Cited by 287 · see citing works
Planck 2018 results. I. Overview and the cosmological legacy of Planck
Collaboration, P., Akrami, Y., Arroja, F. M. A., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., et al. (2020) · Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU) · doi:10.17863/cam.33674 · Cited by 374 · see citing works
Mimetic Gravity: A Review of Recent Developments and Applications to Cosmology and Astrophysics
Sebastiani, L., Vagnozzi, S., & Myrzakulov, R. (2017) · Advances in High Energy Physics · doi:10.1155/2017/3156915 · Cited by 251 · see citing works
Lombriser, L., & Lima, N. A. (2017) · Physics Letters B · doi:10.1016/j.physletb.2016.12.048 · Cited by 261 · see citing works
Self-citationBlack holes, gravitational waves and fundamental physics: a roadmap
Barack, L., Cardoso, V., Nissanke, S., Sotiriou, T. P., Askar, A., Belczynski, C., Bertone, G., Bon, E., Blas, D., Brito, R., et al. (2019) · Zurich Open Repository and Archive (University of Zurich) · doi:10.5167/uzh-172594 · Cited by 233 · see citing works
Modified theories of gravity: Why, how and what?
Shankaranarayanan, S., & Johnson, J. P. (2022) · General Relativity and Gravitation · doi:10.1007/s10714-022-02927-2 · Cited by 222 · see citing works
Paschalidis, V., & Stergioulas, N. (2017) · Living Reviews in Relativity · doi:10.1007/s41114-017-0008-x · Cited by 221 · see citing works
Dark energy in Horndeski theories after GW170817: A review
Kase, R., & Tsujikawa, S. (2018) · International Journal of Modern Physics D · doi:10.1142/s0218271819420057 · Cited by 172 · see citing works
DESI 2024 VII: cosmological constraints from the full-shape modeling of clustering measurements
Adame, A. G., Aguilar, J., Ahlen, S. P., Alam, S., Alexander, D. M., Prieto, C. A., Alvarez, M. A., Alves, O., Anand, A., Andrade, U., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/07/028 · Cited by 217 · see citing works
Lensing is low: cosmology, galaxy formation or new physics?
Leauthaud, A., Saito, S., Hilbert, S., Barreira, A., More, S., White, M. J., Alam, S., Behroozi, P., Bundy, K. A., Coupon, J., et al. (2017) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stx258 · Cited by 212 · see citing works
Self-citationEffective field theory of dark energy: A review
Frusciante, N., & Perenon, L. (2020) · Physics Reports · doi:10.1016/j.physrep.2020.02.004 · Cited by 215 · see citing works
Cosmography in f ( Q ) gravity
Mandal, S., Wang, D., & Sahoo, P. K. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.124029 · Cited by 210 · see citing works
Galileon gravity in light of ISW, CMB, BAO and H 0 data
Renk, J. J., Zumalacárregui, M., Montanari, F., & Barreira, A. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/10/020 · Cited by 192 · see citing works
Simulations of the WFIRST Supernova Survey and Forecasts of Cosmological Constraints
Hounsell, R., Scolnic, D. M., Foley, R. J., Kessler, R., Miranda, V., Avelino, A., Bohlin, R. C., Filippenko, A. V., Frieman, J. A., Jha, S. W., et al. (2018) · The Astrophysical Journal · doi:10.3847/1538-4357/aac08b · Cited by 190 · see citing works
“…energy equation of state can be used to distinguish between many alternative explanations for the accelerated expansion of the Universe (e.g., see Joyce et al. 2016, for a review of dark energy and modified gravity), and it is parameterised as, P = wρc2, (1) where P and ρ are the dark energy…”
BackgroundCosmology in symmetric teleparallel gravity and its dynamical system
Lu, J., Zhao, X., & Chee, G. (2019) · The European Physical Journal C · doi:10.1140/epjc/s10052-019-7038-3 · Cited by 160 · see citing works
Khyllep, W., Dutta, J., Saridakis, E., & Yesmakhanova, K. (2022) · Physical Review D · doi:10.1103/physrevd.107.044022 · Cited by 32 · see citing works
“[13] Austin Joyce, Lucas Lombriser, and Fabian Schmidt, “Dark Energy Versus Modified Gravity,” Ann.”
Cosmology at high redshift — a probe of fundamental physics
Sailer, N., Castorina, E., Ferraro, S., & White, M. J. (2021) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2021/12/049 · Cited by 120 · see citing works
Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity
Haghani, Z., & Harko, T. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-021-09359-3 · Cited by 104 · see citing works
Underdetermination of dark energy
Wolf, W. J., & Ferreira, P. G. (2023) · Physical Review D · doi:10.1103/physrevd.108.103519 · Cited by 77 · see citing works
“…shear volume of dark energy models that have been explored is extensive: a by no means exhaustive list includes canonical quintessence, k-essence, α -attractors, f(R) gravity, Horndeski scalar-tensor gravity, DHOST theories, Einstein-Aether theories, bi-metric theories, and many more [8, 9, 26–34].”
BackgroundPlanck 2015 Constraints on the Non-flat ΛCDM Inflation Model
Ooba, J., Ratra, B., & Sugiyama, N. (2018) · The Astrophysical Journal · doi:10.3847/1538-4357/aad633 · Cited by 93 · see citing works
Brief review of recent advances in understanding dark matter and dark energy
Oks, E. (2021) · New Astronomy Reviews · doi:10.1016/j.newar.2021.101632 · Cited by 93 · see citing works
Symmetries of Differential Equations in Cosmology
Tsamparlis, M., & Paliathanasis, A. (2018) · Symmetry · doi:10.3390/sym10070233 · Cited by 90 · see citing works
Novel Probes Project: Tests of gravity on astrophysical scales
Baker, T., Barreira, A., Desmond, H., Ferreira, P. G., Jain, B., Koyama, K., Li, B., Lombriser, L., Nicola, A., Sakstein, J., et al. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.015003 · Cited by 90 · see citing works
Self-citationA designer approach to f ( Q ) gravity and cosmological implications
Albuquerque, I. S., & Frusciante, N. (2022) · Physics of the Dark Universe · doi:10.1016/j.dark.2022.100980 · Cited by 88 · see citing works
Evidence for Suppression of Structure Growth in the Concordance Cosmological Model
Nguyen, N.-M., Dragan Huterer, A., & Wen, Y. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.111001 · Cited by 86 · see citing works
An overview of what current data can (and cannot yet) say about evolving dark energy
Giarè, W., Mahassen, T., Valentino, E. D., & Pan, S. (2025) · Physics of the Dark Universe · doi:10.1016/j.dark.2025.101906 · Cited by 86 · see citing works
Cosmological discordances. II. Hubble constant, Planck and large-scale-structure data sets
Lin, W., & Ishak, M. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.083532 · Cited by 79 · see citing works
Robustness of dark energy phenomenology across different parameterizations
Wolf, W. J., García-García, C., & Ferreira, P. G. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/05/034 · Cited by 79 · see citing works
Chen, S.-F., White, M. J., DeRose, J., & Kokron, N. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/07/041 · Cited by 77 · see citing works
On the road to per cent accuracy IV: ReACT – computing the non-linear power spectrum beyond ΛCDM
Bose, B., Cataneo, M., Tröster, T., Xia, Q., Heymans, C., & Lombriser, L. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa2696 · Cited by 75 · see citing works
Self-citationProspects for fundamental physics with LISA
Barausse, E., Berti, E., Hertog, T., Hughes, S. A., Jetzer, P., & Pani, P. (2020) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · doi:10.5167/uzh-191485 · Cited by 74 · see citing works
Omnipotent dark energy: A phenomenological answer to the Hubble tension
Adil, S. A., Akarsu, Ö., Valentino, E. D., Nunes, R. C., Özülker, E., Sen, A. A., & Specogna, E. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.023527 · Cited by 71 · see citing works
“with sufficiently precise tests beyond the background level [114].”
BackgroundLate-time cosmology with phantom dark-energy in f(Q) gravity
Lymperis, A. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/11/018 · Cited by 73 · see citing works
Gravitational waves in theories with a non-minimal curvature-matter coupling
Orfeu Bertolami, A., Gomes, C., & Lobo, F. S. N. (2018) · The European Physical Journal C · doi:10.1140/epjc/s10052-018-5781-5 · Cited by 72 · see citing works
Rational approximations of f(R) cosmography through Pad'e polynomials
Capozziello, S., D'Agostino, R., & Luongo, O. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/05/008 · Cited by 58 · see citing works
Lin, W., & Ishak, M. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.023532 · Cited by 70 · see citing works
Uddin, S. A., Burns, C. R., Phillips, M. M., Suntzeff, N. B., Contreras, C., Hsiao, E. Y., Morrell, N., Galbany, L., Stritzinger, M., Hoeflich, P., et al. (2020) · The Astrophysical Journal · doi:10.3847/1538-4357/abafb7 · Cited by 67 · see citing works
“Although recent results tend to point towards a value consistent with the cosmological constant, other explanations are also possible (see Joyce et al. 2016).”
ResultModel-independent reconstruction of f(T) teleparallel cosmology
Capozzıello, S., D’Agostino, R., & Luongo, O. (2017) · General Relativity and Gravitation · doi:10.1007/s10714-017-2304-x · Cited by 66 · see citing works
Validating estimates of the growth rate of structure with modified gravity simulations
Barreira, A., Sánchez, A. G., & Schmidt, F. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.084022 · Cited by 65 · see citing works
Self-citationGravitational decoupling in cosmology
Cedeño, F. X. L., & Contreras, E. (2020) · Physics of the Dark Universe · doi:10.1016/j.dark.2020.100543 · Cited by 63 · see citing works
Tsallis agegraphic dark energy model
Zadeh, M. A., Sheykhi, A., & Moradpour, H. (2019) · Modern Physics Letters A · doi:10.1142/s021773231950086x · Cited by 62 · see citing works
Ajani, V., Baldi, M., Barthelemy, A., Boyle, A., Burger, P., Cardone, V. F., Cheng, S., Codis, S., Giocoli, C., Harnois-Déraps, J., et al. (2023) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202346017 · Cited by 61 · see citing works
Kinematic model-independent reconstruction of Palatini f(R) cosmology
Capozziello, S., D'Agostino, R., & Luongo, O. (2018) · General Relativity and Gravitation · doi:10.1007/s10714-018-2483-0 · Cited by 55 · see citing works
Inflation and Early Dark Energy with a Stage II Hydrogen Intensity Mapping ExperimentPreprint
Cosmic Visions 21 Cm Collaboration, Ansari, R., Arena, E. J., Bandura, K., Bull, P., Castorina, E., Chang, T., Chen, S.-F., Connor, L., Foreman, S., et al. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1810.09572 · Cited by 56 · see citing works
The Taipan Galaxy Survey: scientific goals and observing strategy
da Cunha, E., Hopkins, A., Colless, M., Taylor, E., Blake, C., Howlett, C., Magoulas, C., Lucey, J. R., Lagos, C. D. P., Kuehn, K. (., et al. (2017) · Figshare · Cited by 57 · see citing works
Giblin, B., Cataneo, M., Moews, B., & Heymans, C. (2019) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stz2659 · Cited by 55 · see citing works
Planck 2015 Constraints on the Non-flat XCDM Inflation Model
Ooba, J., Ratra, B., & Sugiyama, N. (2018) · The Astrophysical Journal · doi:10.3847/1538-4357/aaec6f · Cited by 55 · see citing works
Cosmological Constraints from the BOSS DR12 Void Size Function
Contarini, S., Pisani, A., Hamaus, N., Marulli, F., Moscardini, L., & Baldi, M. (2023) · The Astrophysical Journal · doi:10.3847/1538-4357/acde54 · Cited by 54 · see citing works
“Using real data catalogs to obtain effective cosmological constraints on the ΛCDM parameters, or to examine its main alternatives (see, e.g., Yoo & Watanabe 2012; Joyce et al. 2016; Amendola et al. 2018, for a review), requires complete and statistically relevant void samples.”
MethodGeneralized framework for testing gravity with gravitational-wave propagation. III. Future prospect
Nishizawa, A., & Arai, S. (2017) · Physical Review D · doi:10.1103/physrevd.99.104038 · Cited by 130 · see citing works
Adams, C., & Blake, C. (2017) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stx1529 · Cited by 53 · see citing works
“See Joyce et al. (2016) for an excellent review of both.”
BackgroundLimit on graviton mass from galaxy cluster Abell 1689
Desai, S. (2018) · Physics Letters B · doi:10.1016/j.physletb.2018.01.052 · Cited by 53 · see citing works
Challenges in connecting modified gravity theory and observations
Linder, E. V. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.023518 · Cited by 52 · see citing works
Speeding upN-body simulations of modified gravity: chameleon screening models
Bose, S., Li, B., Barreira, A., He, J.-H., Hellwing, W. A., Koyama, K., Llinares, C., & Zhao, G. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/02/050 · Cited by 51 · see citing works
“Modified gravity theories [1, 2] are popular alternatives to the cosmological constant and dark energy models [3] to explain the observed accelerating expansion of our Universe [4–9].”
BackgroundInflation in a closed universe
Ratra, B. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.103534 · Cited by 51 · see citing works
Statefinder diagnosis for interacting Tsallis holographic dark energy models with ω−ω′ pair
Varshney, G., Sharma, U. K., & Pradhan, A. (2019) · New Astronomy · doi:10.1016/j.newast.2019.02.004 · Cited by 51 · see citing works
Testing (modified) gravity with 3D and tomographic cosmic shear
Mancini, A. S., Reischke, R., Pettorino, V., Schäfer, B. M., & Zumalacárregui, M. (2018) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/sty2092 · Cited by 49 · see citing works
“The distinction between these two classes can at times be feeble (see Joyce et al. 2016, for a recent discussion) and the vast amount of proposed theories (see Clifton et al. 2012, for a review) urgently calls for methods to be developed, aiming at distinguishing among the large number of…”
MethodModified gravity constraints from the full shape modeling of clustering measurements from DESI 2024
Ishak, M., Pan, J., Calderón, R., Lodha, K., Valogiannis, G., Avilés, A., Niz, G., Yi, L., Zheng, C., García-Quintero, C., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/09/053 · Cited by 49 · see citing works
An effective description of dark matter and dark energy in the mildly non-linear regime
Lewandowski, M., Maleknejad, A., & Senatore, L. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/05/038 · Cited by 48 · see citing works
Lagrangian perturbation theory for modified gravity
Avilés, A., & Cervantes–Cota, J. L. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.123526 · Cited by 47 · see citing works
The well-tempered cosmological constant
Appleby, S. A., & Linder, E. V. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/07/034 · Cited by 47 · see citing works
Cosmological evolution and dark energy in osculating Barthel–Randers geometry
Hama, R., Harko, T., Sabău, S. V., & Shahidi, S. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-021-09517-7 · Cited by 44 · see citing works
Cosmology with dropout selection: straw-man surveys & CMB lensing
Wilson, M. J., & White, M. J. (2019) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2019/10/015 · Cited by 46 · see citing works
Dark matter as a Weyl geometric effect
Burikham, P., Harko, T., Pimsamarn, K., & Shahidi, S. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.064008 · Cited by 45 · see citing works
Kennedy, J., Lombriser, L., & Taylor, A. N. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.044051 · Cited by 45 · see citing works
Self-citationPrabhu, K., & Stein, L. C. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.021503 · Cited by 45 · see citing works
“These range from attempts at quantum theories of gravity [2, 3], to trying to explain some phenomenon or fix some problem (inflation [4, 5], dark matter [6, 7], dark energy [7, 8], black hole information [9, 10]) by changing the gravity theory, or exploring the theory space to better understand gravity theories.”
BackgroundCorrea, C. M., Paz, D. J., Sánchez, A. G., Ruiz, A. N., Padilla, N. D., & Angulo, R. E. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa3252 · Cited by 45 · see citing works
“…Li et al. (2012),Clampitt et al. (2013),Clifton et al. (2012),Barreira et al. (2015),Cai et al. (2015),Lam et al. (2015),Zivick et al. (2015),Achitouv (2016),Joyce et al. (2016),Koyama (2016), Cautun et al. (2018),Falck et al. (2018),Paillas et al. (2018),Sahlén & Silk (2018),Davies et al. (2019).”
Falsifying cosmological models based on a non-linear electrodynamics
Övgün, A., Leon, G., Magaña, J. A., & Jusufi, K. (2018) · The European Physical Journal C · doi:10.1140/epjc/s10052-018-5936-4 · Cited by 44 · see citing works
On the implementation of the spherical collapse model for dark energy models
Pace, F., Meyer, S., & Bartelmann, M. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/10/040 · Cited by 42 · see citing works
Bose, B., Wright, B. S., Cataneo, M., Pourtsidou, A., Giocoli, C., Lombriser, L., McCarthy, I. G., Baldi, M., Pfeifer, S., & Xia, Q. (2021) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab2731 · Cited by 40 · see citing works
Self-citationRevisiting cosmological diffusion models in Unimodular Gravity and the H 0 tension
Cedeño, F. X. L., & Nucamendi, U. (2021) · Physics of the Dark Universe · doi:10.1016/j.dark.2021.100807 · Cited by 42 · see citing works
Standard Sirens as a Novel Probe of Dark Energy
Wolf, W. J., & Lagos, M. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.061101 · Cited by 38 · see citing works
N-body simulations for parametrized modified gravity
Hassani, F., & Lombriser, L. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa2083 · Cited by 38 · see citing works
Self-citationNon-minimal geometry–matter couplings in Weyl–Cartan space–times: f ( R , T , Q , T m ) gravity
Harko, T., Myrzakulov, N., Myrzakulov, R., & Shahidi, S. (2021) · Physics of the Dark Universe · doi:10.1016/j.dark.2021.100886 · Cited by 38 · see citing works
Cosmological tests of the osculating Barthel–Kropina dark energy model
Bouali, A., Chaudhary, H., Hama, R., Harko, T., Sabău, S. V., & Martín, M. S. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11265-9 · Cited by 37 · see citing works
Reconstructing Horndeski models from the effective field theory of dark energy
Kennedy, J., Lombriser, L., & Taylor, A. N. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.084051 · Cited by 36 · see citing works
Self-citationThe Well-Tempered Cosmological Constant
Appleby, S. A., & Linder, E. V. (2018) · Nazarbayev University Repository (Nazarbayev University) · Cited by 36 · see citing works
Dark energy and accelerating cosmological evolution from osculating Barthel–Kropina geometry
Hama, R., Harko, T., & Sabău, S. V. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10318-9 · Cited by 35 · see citing works
Gravity beyond general relativity
Koyama, K. (2018) · International Journal of Modern Physics D · doi:10.1142/s0218271818480012 · Cited by 33 · see citing works
A comprehensive numerical study on four categories of holographic dark energy models
Li, J.-X., & Wang, S. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/07/047 · Cited by 33 · see citing works
Stochastic dark energy from inflationary quantum fluctuations
Glavan, D., Prokopec, T., & Starobinsky, A. A. (2018) · The European Physical Journal C · doi:10.1140/epjc/s10052-018-5862-5 · Cited by 33 · see citing works
Bayesian evidence for α-attractor dark energy models
Cedeño, F. X. L., Montiel, A., Hidalgo, J. C., & Germán, G. (2019) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2019/08/002 · Cited by 33 · see citing works
“An alternative approach is the extension of the gravity theory beyond GR, in a strategy generically dubbed Modified Gravity [21–28].”
MethodLatest evidence for a late time vacuum–geodesic CDM interaction
Hogg, N. B., Bruni, M., Crittenden, R., Martinelli, M., & Peirone, S. (2020) · Physics of the Dark Universe · doi:10.1016/j.dark.2020.100583 · Cited by 33 · see citing works
Neural network reconstructions for the Hubble parameter, growth rate and distance modulus
Gómez-Vargas, I., Esquivel, R. M., García‐Salcedo, R., & Vazquez, J. A. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11435-9 · Cited by 33 · see citing works
“The presence of these issues opens the possibility to extensions beyond the standard cosmological model by considering, for instance, a dynamical DE, modifications to the general theory of relativity [11] or other approaches.”
BackgroundObservational constraints on dark energy models with Λ as an equilibrium point
Paliathanasis, A. (2025) · Physics of the Dark Universe · doi:10.1016/j.dark.2025.101956 · Cited by 32 · see citing works
Narrowing down the possible explanations of cosmic acceleration with geometric probes
Dhawan, S., Goobar, A., Mörtsell, E., Amanullah, R., & Feindt, U. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/07/040 · Cited by 31 · see citing works
Limitations on Standard Sirens tests of gravity from screening
Dalang, C., & Lombriser, L. (2019) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2019/10/013 · Cited by 32 · see citing works
Self-citationTesting gravitational wave propagation with multiband detections
Baker, T., Barausse, E., Chen, A., de Rham, C., Pieroni, M., & Gianmassimo Tasinato, C. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/03/044 · Cited by 30 · see citing works
Cosmological constraints on dark energy models using DESI BAO 2024
Zheng, J., Qiang, D.-C., & You, Z.-Q. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/08/056 · Cited by 30 · see citing works
Investigating scalar-tensor-gravity with statistics of the cosmic large-scale structure
Reischke, R., Mancini, A. S., Schäfer, B. M., & Merkel, P. M. (2018) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/sty2919 · Cited by 31 · see citing works
“From this discussion it should be clear that general relativity needs to be tested on cosmological scales (Lue et al. 2004; Laszlo & Bean 2007; Kunz & Sapone 2007; Koyama 2016; Joyce et al. 2016; White 2016).”
BackgroundScalar modes in extended hybrid metric-Palatini gravity: Weak field phenomenology
Bombacigno, F., Moretti, F., & Montani, G. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.124036 · Cited by 30 · see citing works
- Authors
- Joyce, A., Lombriser, L., & Schmidt, F.
- Affiliations
- University of Chicago (US)
- Royal Observatory (GB)
- Max Planck Institute for Astrophysics (DE)
- Corresponding author
- Schmidt, Fabian
- Venue
- Annual Review of Nuclear and Particle Science
- Publisher
- Annual Reviews
- Published
- 2016-10-19
- Volume
- 66
- Issue
- 1
- Pages
- 95-122
- ISSN
- 0163-8998 (ISSN-L)
- 1545-4134
- OpenAlex
- W2253235198
- Cited by
- 463
- References
- 158
- Citations by year
- 2026: 30 · 2025: 56 · 2024: 57 · 2023: 46 · 2022: 37 · 2021: 42 · 2020: 52 · 2019: 46 · 2018: 43 · 2017: 46 · 2016: 8
- FWCI
- 3.45
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Annual Review of Nuclear and Particle Science (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
- Keywords
- dark energy, modified gravity, cosmic acceleration, equivalence principle, strong equivalence principle, weak equivalence principle, cosmological models, observational signatures
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