Cosmological Implications of Affine Gravity

TL;DR

This thesis explores affine gravity's unique properties and its implications for cosmological inflation, proposing a framework where metric tensors are generated rather than assumed, offering new insights into gravity and matter dynamics.

Contribution

It demonstrates that affine gravity naturally favors a unique metric tensor and provides a novel classical approach to inducing metric gravity without conformal transformations.

Findings

Affine gravity prefers a unique metric tensor for inflation.

The framework avoids conformal frames by redefining the inflaton.

Metric gravity can be induced solely from affine connection and scalar fields.

Abstract

The main aim of this thesis is to reveal some interesting aspects of the purely affine theory of gravity and its cosmological implication. A particular attention will be devoted to its consequences when applied to cosmological inflation. Primarily, affine spacetime, composed of geodesics with no notion of length and angle, accommodates gravity but not matter. The thesis study is expected to reveal salient properties of matter dynamics in affine spacetime and may reveal an intimate connection between vacuum state and metrical gravity. An interesting application of the framework is the inflationary regime, where it is shown that affine gravity prefers only a unique metric tensor such that the transition from nonminimal to minimal coupling of the inflaton is performed only via redefinition of the latter. This allows us to avoid the use of the so called conformal frames. In fact, unlike metric gravity, the metric tensor in affine gravity is generated and not postulated a priori, thus this tensor is absent in the actions and conformal transformation does not make sense. Last but not least, we try to show how metric gravity can be induced through a simple structure that contains only affine connection and scalar fields. General relativity arises classically only at the vacuum, and this view of gravity may be considered as a new way to inducing metric elasticity of space, not through quantum corrections as in standard induced gravity, but only classically. The thesis is concluded by analyzing affine gravity in a particular higher-dimensional manifold (product of two spaces) in an attempt to understand both, the cosmological constant and matter dynamically.