A new covariant foliation-based construction of scalar-tensor theories up to four derivatives of the scalar field that extends DHOST and U-DHOST without unitary gauge and propagates three degrees of freedom.
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The Effective Field Theory of Dark Energy
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abstract
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.
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representative citing papers
A minimal open EFT for late-time acceleration fits BAO observations without NEC violations and predicts dissipative suppression of GW luminosity distance, modified Bardeen potentials with gravitational slip, and enhanced low-z structure formation.
Eckart heat flux holds for all timelike scalar configurations in F(Φ,X)R + G theories if and only if F_X ≡ 0, reducing the theory to a Jordan-like subclass of Horndeski.
Non-parametric reconstruction of non-minimally coupled gravity with a smoothness prior on CMB, DESI BAO, supernovae, and DES data yields a 2.8σ hint for coupling and a preference for phantom divide crossing stabilized by the coupling.
A master screening equation is derived for luminal Horndeski gravity that recovers Vainshtein and Chameleon mechanisms and introduces Phaedrus screening with screening radius scaling linearly with source mass.
Higher-curvature terms deform the near-horizon potential of spherically symmetric black holes, producing progressively larger shifts in overtone quasinormal frequencies that remain detectable in ringdown waveforms when the fundamental mode stays close to its GR value.
In Hu-Sawicki f(R) gravity the redshift-space bispectrum monopole and quadrupole show 2-8% deviations from GR at z=0.7 and k~0.3 h/Mpc with forecasted SNR of 30 and 15 for Euclid.
Tests EFT-derived consistency relations between LSS and GW constraints on the effective gravitational coupling, finding agreement at current precision with GW170817 matching LSS accuracy.
An EFT consistency map transports cosmology-conditioned posteriors from scalar-tensor FLRW backgrounds to black-hole quasinormal-mode kernels, showing tensor-speed effects fall below ringdown detectability while other operators remain potentially active near black holes.
Dark energy perturbations induce a scale-dependent effective matter-gravity coupling that can become locally negative, potentially explaining low-redshift structure suppression for phantom models.
Five explicit polynomial spatially covariant gravity Lagrangians up to total derivative order three are identified that propagate only two degrees of freedom up to cubic order in perturbations around a cosmological background.
Early dark energy resolves CMB-BAO tension and, combined with thawing quintessence, reduces overall cosmological tensions without phantom crossing.
Final Planck CMB data confirms the flat 6-parameter ΛCDM model with Ω_c h² = 0.120 ± 0.001, Ω_b h² = 0.0224 ± 0.0001, n_s = 0.965 ± 0.004, τ = 0.054 ± 0.007, H_0 = 67.4 ± 0.5 km/s/Mpc, and no strong evidence for extensions.
Reconstruction of EFT background functions from cosmic chronometer Hubble data allows model-independent tests of dark energy evolution in scalar-tensor theories.
This review traces the history of dynamical dark energy, presents the no-go theorem against single-field crossing of w = -1, and surveys viable Quintom constructions including multi-field models and modified gravity in light of DESI DR2 hints.
Modified gravity theories supply viable mathematical frameworks for inflation, bounces, and dark energy eras that match observational data.
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A minimal open EFT for late-time acceleration fits BAO observations without NEC violations and predicts dissipative suppression of GW luminosity distance, modified Bardeen potentials with gravitational slip, and enhanced low-z structure formation.
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Eckart heat-flux applicability in $F(\Phi,X)R$ theories and the existence of temperature gradients
Eckart heat flux holds for all timelike scalar configurations in F(Φ,X)R + G theories if and only if F_X ≡ 0, reducing the theory to a Jordan-like subclass of Horndeski.
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Late-time reconstruction of non-minimally coupled gravity with a smoothness prior
Non-parametric reconstruction of non-minimally coupled gravity with a smoothness prior on CMB, DESI BAO, supernovae, and DES data yields a 2.8σ hint for coupling and a preference for phantom divide crossing stabilized by the coupling.
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A Master Equation for Screening in Luminal Horndeski Gravity
A master screening equation is derived for luminal Horndeski gravity that recovers Vainshtein and Chameleon mechanisms and introduces Phaedrus screening with screening radius scaling linearly with source mass.
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Probing higher curvature gravity via ringdown with overtones
Higher-curvature terms deform the near-horizon potential of spherically symmetric black holes, producing progressively larger shifts in overtone quasinormal frequencies that remain detectable in ringdown waveforms when the fundamental mode stays close to its GR value.
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Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid
In Hu-Sawicki f(R) gravity the redshift-space bispectrum monopole and quadrupole show 2-8% deviations from GR at z=0.7 and k~0.3 h/Mpc with forecasted SNR of 30 and 15 for Euclid.
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Testing the consistency of gravitational waves and large scale structure constraints on dark energy
Tests EFT-derived consistency relations between LSS and GW constraints on the effective gravitational coupling, finding agreement at current precision with GW170817 matching LSS accuracy.
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A cosmology-to-ringdown EFT consistency map for scalar-tensor gravity
An EFT consistency map transports cosmology-conditioned posteriors from scalar-tensor FLRW backgrounds to black-hole quasinormal-mode kernels, showing tensor-speed effects fall below ringdown detectability while other operators remain potentially active near black holes.
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The effects of dark energy on the matter-gravity coupling
Dark energy perturbations induce a scale-dependent effective matter-gravity coupling that can become locally negative, potentially explaining low-redshift structure suppression for phantom models.
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Spatially covariant gravity with two degrees of freedom: A perturbative analysis up to cubic order
Five explicit polynomial spatially covariant gravity Lagrangians up to total derivative order three are identified that propagate only two degrees of freedom up to cubic order in perturbations around a cosmological background.
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Disentangling cosmic distance tensions with early and late dark energy
Early dark energy resolves CMB-BAO tension and, combined with thawing quintessence, reduces overall cosmological tensions without phantom crossing.
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Planck 2018 results. VI. Cosmological parameters
Final Planck CMB data confirms the flat 6-parameter ΛCDM model with Ω_c h² = 0.120 ± 0.001, Ω_b h² = 0.0224 ± 0.0001, n_s = 0.965 ± 0.004, τ = 0.054 ± 0.007, H_0 = 67.4 ± 0.5 km/s/Mpc, and no strong evidence for extensions.
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EFT of Dark Energy with Cosmic Chronometers: Reconstructing Background EFT Functions
Reconstruction of EFT background functions from cosmic chronometer Hubble data allows model-independent tests of dark energy evolution in scalar-tensor theories.
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The Quintom theory of dark energy after DESI DR2
This review traces the history of dynamical dark energy, presents the no-go theorem against single-field crossing of w = -1, and surveys viable Quintom constructions including multi-field models and modified gravity in light of DESI DR2 hints.
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Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
Modified gravity theories supply viable mathematical frameworks for inflation, bounces, and dark energy eras that match observational data.