Alternatives to the Standard GTR

Chapter 5

Abstract

1. Introduction

experiments.

75

Cosmological Solutions to

Keywords: affine gravity, exact solutions, cosmological models

when one wants to conciliate both standard models,

<sup>1</sup> Besides the standard model of particles, there is a standard model of cosmology.

Torsion-Free Sector

Polynomial Affine Gravity in the

Oscar Castillo-Felisola, José Perdiguero and Oscar Orellana

We find possible cosmological models of the polynomial affine gravity described by connections that are either compatible or not with a metric. When possible, we compare them with those of general relativity. We show that the set of cosmological vacuum solutions in general relativity are a subset of the solutions of polynomial affine gravity. In our model, the cosmological constant appears as an integration constant, and, additionally, we show that some forms of matter can be emulated by the affine structure—even in the metric compatible case. In the case of connections not compatible with a metric, we obtain formal families of solutions, which should be constrained by physical arguments. We show that for a certain parametrisation of the connection, the affine Ricci-flat condition yields the cosmological field equations of general relativity coupled with a perfect fluid, pointing towards a geometrical emulation of—what is interpreted in general relativity as—matter effects.

All of the fundamental physics is described by four interactions: electromagnetic, weak, strong and gravitational. The former three are bundled into what is known as standard model of particle physics, which explains very accurately the physics at very short scales. These three interactions share common grounds, for example, they are modelled by connections with values in a Lie algebra, they have been successfully quantised and renormalised, and the simplest of them—quantum electrodynamics—gives the most accurate results when compared with the

On the other hand, the model that explains gravitational interaction (general relativity) is a field theory for the metric, which can be thought as a potential for the gravitational connection [1, 2]. Although general relativity is the most successful theory, we have to explain gravity [3–5], it cannot be formulated as a gauge theory (in four dimensions), the standard quantisation methods lead to inconsistencies, and it is non-renormalisable, driving the community to believe it is an effective theory of a yet unknown fundamental one. Within the framework of cosmology,

<sup>1</sup> it was noticed that nearly 95%

## Chapter 5
