An old Einstein - Eddington generalized gravity and modern ideas on branes and cosmology

TL;DR

This paper explores a generalized affine gravity theory in higher dimensions, incorporating additional fields that could explain dark energy, dark matter, and inflation, with models resembling brane cosmology from string theory.

Contribution

It introduces a new multidimensional affine gravity framework using a geometric Lagrangian, extending Einstein's approach to include dark energy, vector, and scalar fields.

Findings

The theory naturally includes dark energy as a cosmological constant.

It predicts the existence of massive or tachyonic vector and scalar fields coupled to gravity.

Models resemble brane cosmology scenarios from string theory.

Abstract

We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to determine the connection coefficients from a geometric Lagrangian that is an arbitrary function of the generalized Ricci curvature tensor and of other fundamental tensors. Such a theory supplements the standard Einstein gravity with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic) vector field vecton, and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation. The concrete choice of the geometric Lagrangian determines further details of the theory. The most natural geometric models look similar to recently proposed brane models of cosmology usually derived from string theory.