Weak cosmic growth in coupled dark energy with a Lagrangian formulation

TL;DR

This paper explores a coupled dark energy model with a scalar field interacting with cold dark matter, deriving stability conditions and showing that such coupling can weaken gravity on large scales, potentially addressing cosmological tensions.

Contribution

It introduces a Lagrangian formulation for coupled dark energy with derivative interactions, deriving stability conditions and analyzing its effects on cosmic structure growth.

Findings

Effective CDM sound speed remains close to zero.

Scalar field propagation speed is influenced by the interaction.

Weaker gravitational coupling can naturally occur for certain coupling parameters.

Abstract

We investigate a dark energy scenario in which a canonical scalar field $\phi$ is coupled to the four velocity $u_{c}^{\mu}$ of cold dark matter (CDM) through a derivative interaction $u_{c}^{\mu} \partial_{\mu} \phi$. The coupling is described by an interacting Lagrangian $f(X, Z)$, where $f$ depends on $X=-\partial^{\mu} \phi \partial_{\mu} \phi/2$ and $Z=u_{c}^{\mu} \partial_{\mu} \phi$. We derive stability conditions of linear scalar perturbations for the wavelength deep inside the Hubble radius and show that the effective CDM sound speed is close to 0 as in the standard uncoupled case, while the scalar-field propagation speed is affected by the interacting term $f$. Under a quasi-static approximation, we also obtain a general expression of the effective gravitational coupling felt by the CDM perturbation. We study the late-time cosmological dynamics for the coupling $f \propto X^{(2-m)/2}Z^m$ and show that the gravitational coupling weaker than the Newton constant can be naturally realized for $m>0$ on scales relevant to the growth of large-scale structures. This allows the possibility for alleviating the tension of $\sigma_8$ between low- and high-redshift measurements.