# Observational effects of varying speed of light in quadratic gravity cosmological models

## TL;DR

This paper investigates how the speed of light can vary in quadratic gravity models and demonstrates that models with a variable speed of light better fit supernova data than those with a constant speed.

## Contribution

It introduces the concept of variable speed of light in quadratic gravity theories and tests its implications against supernova observations.

## Key findings

- Variable speed of light models are favored by supernova data.
- The causal structure constant can become variable in certain gravity theories.
- Varying speed of light impacts luminosity distance calculations.

## Abstract

We study different manifestations of the speed of light in theories of gravity where metric and connection are regarded as independent fields. We find that for a generic gravity theory in a frame with locally vanishing affine connection, the usual degeneracy between different manifestations of the speed of light is broken. In particular, the space-time causal structure constant ($c_{ST}$) may become variable in that local frame. For theories of the form $f(R,R^{\mu\nu} R_{\mu\nu})$, this variation in $c_{ST}$ has an impact on the definition of the luminosity distance (and distance modulus), which can be used to confront the predictions of particular models against Supernovae type Ia (SN Ia) data. We carry out this test for a quadratic gravity model without cosmological constant assuming i) a constant speed of light and ii) a varying speed of light, and find that the latter scenario is favored by the data.