# Covariant c-flation: a variational approach

## TL;DR

This paper introduces a covariant variational framework for theories where fundamental constants like the speed of light, gravitational constant, and cosmological constant vary, providing new insights into early universe cosmology without requiring inflation.

## Contribution

It develops a general action principle for variable constants, preserving covariance, and applies it to solve initial condition puzzles in cosmology through scalar field dynamics.

## Key findings

- Provides a covariant action for variable $c$, $G$, and $\\Lambda$
- Demonstrates mechanisms for horizon and flatness problem solutions without inflation
- Shows scalar field dynamics can address early universe initial conditions

## Abstract

We develop an action principle to construct the dynamics that give rise to a minimal generalization of Einstein's equations, where the speed of light ($c$), the gravitational constant ($G$) and the cosmological constant ($\Lambda$) are allowed to vary. Our construction preserves general covariance of the theory, which yields a general dynamical constraint on $c$, $G$ and $\Lambda$. This action is general and can be applied to describe different cosmological solutions. We apply this formulation to the initial condition puzzles of the early universe and show that it generates a dynamical mechanism to obtain the homogeneous and flat universe we observe today. We rewrite the conditions necessary to solve the horizon and flatness problems in this framework, which does not necessarily lead to an accelerated expansion as in inflation. Then, we show how the dynamics of the scalar field that represents $c$ or $G$ (and $\Lambda$) can be used to solve the problems of the early universe cosmology by means of different ways to c-inflate the horizon in the early universe. By taking $\Lambda = 0$, we show that the dynamics of the scalar field representing $c$ can be described once a potential is given.