# Coupled vector dark energy

## TL;DR

This paper develops a framework for analyzing vector field interactions with dark matter, showing how such couplings influence cosmological perturbations and can produce dark energy behavior close to a cosmological constant.

## Contribution

It introduces a general coupled vector dark energy model, analyzing its effects on perturbations and demonstrating how coupling can make dark energy resemble a cosmological constant.

## Key findings

- Coupling affects scalar perturbation stability and sound speed.
- Interaction can produce a dark energy equation of state close to -1.
- Tensor and vector perturbations remain unaffected by the coupling.

## Abstract

We provide a general framework for studying the evolution of background and cosmological perturbations in the presence of a vector field $A_{\mu}$ coupled to cold dark matter (CDM). We consider an interacting Lagrangian of the form $Q f(X) T_c$, where $Q$ is a coupling constant, $f$ is an arbitrary function of $X=-A_{\mu}A^{\mu}/2$, and $T_c$ is a trace of the CDM energy-momentum tensor. The matter coupling affects the no-ghost condition and sound speed of linear scalar perturbations deep inside the sound horizon, while those of tensor and vector perturbations are not subject to modifications. The existence of interactions also modifies the no-ghost condition of CDM density perturbations. We propose a concrete model of coupled vector dark energy with the tensor propagation speed equivalent to that of light. In comparison to the $Q=0$ case, we show that the decay of CDM to the vector field leads to the phantom dark energy equation of state $w_{\rm DE}$ closer to $-1$. This alleviates the problem of observational incompatibility of uncoupled models in which $w_{\rm DE}$ significantly deviates from $-1$. The maximum values of $w_{\rm DE}$ reached during the matter era are bounded from the CDM no-ghost condition of future de Sitter solutions.