Cuscuta-Galileon cosmology: Dynamics, gravitational "constant"s and the Hubble Constant

TL;DR

This paper explores a Cuscuta-Galileon gravity model with a scalar field affecting cosmological dynamics, including a time-dependent gravitational constant, and discusses implications for the Hubble tension problem.

Contribution

It introduces a scalar field potential within Cuscuta-Galileon gravity, analyzing its impact on cosmology and the effective gravitational constant, and connects these to observational constraints.

Findings

The gravitational constant becomes time-dependent in the model.

The model can reproduce $ m extLambda$CDM background evolution.

Constraints from big-bang nucleosynthesis limit model parameters.

Abstract

We discuss cosmology based on a Cuscuta-Galileon gravity theory, which preserves just two degrees of freedom. Although there exists no additional degrees of freedom, introduction of a potential of a scalar field changes the dynamics. The scalar field is completely determined by matter fields. Giving an exponential potential as an example, we discuss the cosmological dynamics. The gravitational "constant" $G_{\rm F}$ appeared in the effective Friedmann equation becomes time dependent. We also present how to construct a potential when we know the evolution of the Hubble parameter. When we assume the $\Lambda$CDM cosmology for the background evolution, we find the potential form. We then analyze the density perturbations, which equation is characterized only by a change of the gravitational "constant"$G_{\rm eff}$, which also becomes time dependent. From the observational constraints such as the constraint from the big-bang nucleosynthesis and the constraint on time-variation of gravitational constant, we restrict the parameters in our models. Taking into account the time dependence of the gravitational constant in the effective Friedmann equation, we may have a chance to explain the Hubble tension problem.