Varying constants entropic--$\Lambda$CDM cosmology

TL;DR

This paper develops a thermodynamical entropic force cosmology framework allowing for varying $G$ and $c$, tests it against observational data, and finds constraints on their evolution and the Hawking temperature coefficient.

Contribution

It introduces three approaches to formulate entropic cosmology with varying constants and tests their compatibility with observational data.

Findings

The Hawking temperature coefficient $\gamma$ is much smaller than the theoretical value.

Observational data allow for increasing $c$ and decreasing $G$ over cosmic time.

The variation of $c$ is constrained to be $\Delta c/c o 10^{-5}$, weaker than quasar bounds.

Abstract

We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant $G$ and the speed of light $c$. Three different approaches to the formulation of the field equations are presented. Some cosmological solutions for each framework are given and one of them is tested against combined observational data (supernovae, BAO, and CMB). From the fit of the data it is found that the Hawking temperature numerical coefficient $\gamma$ is two to four orders of magnitude less than usually assumed on the geometrical ground theoretical value of $O(1)$ and that it is also compatible with zero. Besides, in the entropic scenario we observationally test that the fit of the data is allowed for the speed of light $c$ growing and the gravitational constant $G$ diminishing during the evolution of the universe. We also obtain a bound on the variation of $c$ to be $\Delta c/c \propto 10^{-5} >0$ which is at least one order of magnitude weaker than the quasar spectra observational bound.