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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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“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)
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“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)
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“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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DESI 2024 VII: cosmological constraints from the full-shape modeling of clustering measurements
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“…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…”
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“[13] Austin Joyce, Lucas Lombriser, and Fabian Schmidt, “Dark Energy Versus Modified Gravity,” Ann.”
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“…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].”
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Ooba, J., Ratra, B., & Sugiyama, N. (2018) · The Astrophysical Journal · doi:10.3847/1538-4357/aad633 · Cited by 93
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“with sufficiently precise tests beyond the background level [114].”
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“Although recent results tend to point towards a value consistent with the cosmological constant, other explanations are also possible (see Joyce et al. 2016).”
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Tsallis agegraphic dark energy model
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“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.”
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“See Joyce et al. (2016) for an excellent review of both.”
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“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].”
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“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…”
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Cosmological evolution and dark energy in osculating Barthel–Randers geometry
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Cosmology with dropout selection: straw-man surveys & CMB lensing
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Dark matter as a Weyl geometric effect
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“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.”
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Falsifying cosmological models based on a non-linear electrodynamics
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On the implementation of the spherical collapse model for dark energy models
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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
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
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 42
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
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 44
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 39
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
Self-citationThe Well-Tempered Cosmological Constant
Appleby, S. A., & Linder, E. V. (2018) · Nazarbayev University Repository (Nazarbayev University) · Cited by 36
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
Gravity beyond general relativity
Koyama, K. (2018) · International Journal of Modern Physics D · doi:10.1142/s0218271818480012 · Cited by 33
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
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 37
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
“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
Neural Network Reconstructions for the Hubble Parameter, Growth Rate and Distance Modulus
Gómez-Vargas, I., Esquivel, R. M., García‐Salcedo, R., & Vazquez, J. A. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11435-9 · Cited by 42
“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
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
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
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
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
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
“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 31
Metadata
- 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 › Nuclear and High Energy 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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