Scalar-field dark energy nonminimally and kinetically coupled to dark matter

TL;DR

This paper develops a comprehensive framework for scalar-field dark energy models with nonminimal and kinetic couplings to dark matter, analyzing stability and effective gravitational interactions relevant for cosmic structure growth.

Contribution

It introduces a general approach to scalar-field dark energy coupled to dark matter within Horndeski theories, deriving perturbation equations and stability conditions without gauge fixing.

Findings

Conditions for absence of ghosts and Laplacian instabilities derived.

Effective gravitational couplings for dark matter and baryons obtained.

Potential for weaker gravitational interaction with dark matter explored.

Abstract

We provide a general framework for studying the dark energy cosmology in which a scalar field $\phi$ is nonminimally and kinetically coupled to Cold Dark Matter (CDM). The scalar-graviton sector is described by the action of Horndeski theories with the speed of gravitational waves equivalent to that of light, whereas CDM is treated as a perfect fluid given by a Schutz-Sorkin action. We consider two interacting Lagrangians of the forms $f_1(\phi,X)\rho_c (n_c)$ and $f_2 (n_c, \phi,X) J_c^{\mu} \partial_{\mu}\phi$, where $X=-\partial^{\mu} \phi \partial_{\mu} \phi/2$, $\rho_c$ and $n_c$ are the energy density and number density of CDM respectively, and $J_c^{\mu}$ is a vector field related to the CDM four velocity. We derive the scalar perturbation equations of motion without choosing any special gauges and identify conditions for the absence of ghosts and Laplacian instabilities on scales deep inside the sound horizon. Applying a quasi-static approximation in a gauge-invariant manner, we also obtain the effective gravitational couplings felt by CDM and baryons for the modes relevant to the linear growth of large-scale structures. In particular, the $n_c$ dependence in the coupling $f_2$ gives rise to an interesting possibility for realizing the gravitational coupling with CDM weaker than the Newton gravitational constant $G$.