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Register a new userThe effective field theory of dark energy diagnostic of linear Horndeski theories after GW170817 and GRB170817A
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We summarise the effective field theory of dark energy construction to explore observable predictions of linear Horndeski theories. Based on cite{Perenon:2016blf}, we review the diagnostic of these theories on the correlation of the large-scale structure phenomenological functions: the effective Newton constant, the light deflection parameter and the growth function of matter perturbations. We take this opportunity to discuss the evolution of the bounds the propagation speed of gravitational waves has undergone and use the most restrictive one to update the diagnostic.
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The gravitational-wave event GW170817 from a binary neutron star merger together with the electromagnetic counterpart showed that the speed of gravitational waves $c_t$ is very close to that of light for the redshift $z<0.009$. This places tight constraints on dark energy models constructed in the framework of modified gravitational theories. We review models of the late-time cosmic acceleration in scalar-tensor theories with second-order equations of motion (dubbed Horndeski theories) by paying particular attention to the evolution of dark energy equation of state and observables relevant to the cosmic growth history. We provide a gauge-ready formulation of scalar perturbations in full Horndeski theories and estimate observables associated with the evolution of large-scale structures, cosmic microwave background, and weak lensing by employing a so-called quasi-static approximation for the modes deep inside the sound horizon. In light of the recent observational bound of $c_t$, we also classify surviving dark energy models into four classes depending on different structure-formation patterns and discuss how they can be observationally distinguished from each other. In particular, the nonminimally coupled theories in which the scalar field $phi$ has a coupling with the Ricci scalar $R$ of the form $G_4(phi) R$, including $f(R)$ gravity, can be tightly constrained not only from the cosmic expansion and growth histories but also from the variation of screened gravitational couplings. The cross correlation of integrated Sachs-Wolfe signal with galaxy distributions can be a key observable for placing bounds on the relative ratio of cubic Galileon density to total dark energy density. The dawn of gravitational-wave astronomy will open up a new window to constrain nonminimally coupled theories further by the modified luminosity distance of tensor perturbations.
The effective field theory (EFT) of cosmological perturbations is a useful framework to deal with the low-energy degrees of freedom present for inflation and dark energy. We review the EFT for modified gravitational theories by starting from the most general action in unitary gauge that involves the lapse function and the three-dimensional geometric scalar quantities appearing in the Arnowitt-Deser-Misner (ADM) formalism. Expanding the action up to quadratic order in the perturbations and imposing conditions for the elimination of spatial derivatives higher than second order, we obtain the Lagrangian of curvature perturbations and gravitational waves with a single scalar degree of freedom. The resulting second-order Lagrangian is exploited for computing the scalar and tensor power spectra generated during inflation. We also show that the most general scalar-tensor theory with second-order equations of motion-Horndeski theory-belongs to the action of our general EFT framework and that the background equations of motion in Horndeski theory can be conveniently expressed in terms of three EFT parameters. Finally we study the equations of matter density perturbations and the effective gravitational coupling for dark energy models based on Horndeski theory, to confront the models with the observations of large-scale structures and weak lensing.
Studying the effects of dark energy and modified gravity on cosmological scales has led to a great number of physical models being developed. The effective field theory (EFT) of cosmic acceleration allows an efficient exploration of this large model space, usually carried out on a phenomenological basis. However, constraints on such parametrized EFT coefficients cannot be trivially connected to fundamental covariant theories. In this paper we reconstruct the class of covariant Horndeski scalar-tensor theories that reproduce the same background dynamics and linear perturbations as a given EFT action. One can use this reconstruction to interpret constraints on parametrized EFT coefficients in terms of viable covariant Horndeski theories. We demonstrate this method with a number of well-known models and discuss a range of future applications.
The combined observation of GW170817 and its electromagnetic counterpart GRB170817A reveals that gravitational waves propagate at the speed of light in high precision. We apply the effective field theory approach to investigate the experimental consequences for the theory of $f(T)$ gravity. We find that the speed of gravitational waves within $f(T)$ gravity is exactly equal to the light speed, and hence the constraints from GW170817 and GRB170817A are trivially satisfied. The results are verified through the standard analysis of cosmological perturbations. Nevertheless, by examining the dispersion relation and the frequency of cosmological gravitational waves, we observe a deviation from the results of General Relativity, quantified by a new parameter. Although its value is relatively small in viable $f(T)$ models, its possible future measurement in advancing gravitational-wave astronomy would be the smoking gun of testing this type of modified gravity.
We revisit the status of scalar-tensor theories with applications to dark energy in the aftermath of the gravitational wave signal GW170817 and its optical counterpart GRB170817A. At the level of the cosmological background, we identify a class of theories, previously declared unviable in this context, whose anomalous gravitational wave speed is proportional to the scalar equation of motion. As long as the scalar field is assumed not to couple directly to matter, this raises the possibility of compatibility with the gravitational wave data, for any cosmological sources, thanks to the scalar dynamics. This newly rescued class of theories includes examples of generalised quintic galileons from Horndeski theories. Despite the promise of this leading order result, we show that the loophole ultimately fails when we include the effect of large scale inhomogeneities.
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