Cuscuta-Galileon cosmology: Dynamics, gravitational constants, and the Hubble constant
Kei‐ichi Maeda, Sirachak Panpanich
Abstract
We discuss cosmology based on a Cuscuta-Galileon gravity theory, which preserves just two degrees of freedom. Although there exist 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'' ${G}_{\mathrm{F}}$ 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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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'' ${G}_{\mathrm{eff}}$, 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. The time dependence of the gravitational constant in the effective Friedmann equation, we may have a chance to explain the Hubble tension problem.