A tensor theory of space-time as a strained material continuum

TL;DR

This paper proposes a tensor-based theory of space-time as a strained continuum, incorporating elastic properties to explain cosmic inflation and acceleration, and successfully fitting supernova luminosity data.

Contribution

It introduces a novel elastic tensor framework for space-time, extending classical strain theory to cosmology and providing a unified explanation for inflation and late acceleration.

Findings

The theory accounts for initial inflation and late acceleration.

It fits supernova luminosity data satisfactorily.

Space-time is modeled as a strained material continuum.

Abstract

The classical theory of strain in material continua is reviewed and generalized to space-time. Strain is attributed to "external" (matter/energy fields) and intrinsic sources fixing the global symmetry of the universe (defects in the continuum). A Lagrangian for space-time is worked out, adding to the usual Hilbert term an "elastic" contribution from intrinsic strain. This approach is equivalent to a peculiar tensor field, which is indeed part of the metric tensor. The theory gives a configuration of space-time accounting both for the initial inflation and for the late acceleration. Considering also the contribution from matter the theory is used to fit the luminosity data of type Ia supernovae, giving satisfactory results.