A self-consistent solution in affine space with scalar field

TL;DR

This paper explores how a conformal scalar field can induce non-metricity in affine connection spaces, potentially affecting early Universe cosmology through self-consistent solutions that modify Riemannian geometry.

Contribution

It demonstrates a self-consistent solution where scalar field conformal connection introduces non-metricity as a correction to Riemannian structure, relevant to early Universe models.

Findings

Non-metricity arises from scalar field conformal connection.

Non-metricity acts as a correction to Riemannian geometry.

Magnitude of non-metricity may be significant in the early Universe.

Abstract

Conformal connection of scalar field is shown to produce possible non-metricity in affine connection spaces. In case of self-consistent solution the non-metricity is a correction to background Riemannian structure with respect to gravitational constant and its magnitude may be essential in the early Universe.