Energy transfer from space-time into matter and a bouncing inflation from Covariant Canonical Gauge theory of Gravity

TL;DR

This paper explores cosmological solutions within covariant canonical gauge theories of gravity, revealing a transition from quadratic Riemann tensor dominance to Einstein gravity, and identifies a bouncing universe scenario that approaches de-Sitter space.

Contribution

It introduces a covariant canonical gauge framework with a quadratic Riemann tensor term, analyzing its impact on cosmological evolution and identifying a novel bouncing solution.

Findings

Quadratic Riemann term dominates at early times, modifying matter and space-time dynamics.

Solutions converge to classical Einstein cosmology at late times.

A bouncing universe solution approaches de-Sitter space asymptotically.

Abstract

Cosmological solutions for covariant canonical gauge theories of gravity are presented. The underlying covariant canonical transformation framework invokes a dynamical space-time Hamiltonian consisting of the Einstein-Hilbert term plus a quadratic Riemann tensor invariant with a fundamental dimensionless coupling constant $g_1$. A typical time scale related to this constant, $\tau = \sqrt{8 \pi G g_1}$, is characteristic for the type of cosmological solutions: for $t \ll \tau$ the quadratic term is dominant, the energy-momentum tensor of the matter is not covariantly conserved, and we observe modified dynamics of matter and space-time. On the other hand, for $t \gg \tau$, the Einstein term dominates and the solution converges to classical cosmology. This is analyzed for different types of matter and dark energy with a constant equation of state. While for a radiation dominated universe solution the cosmology does not change, we find for a dark energy universe the well known de-Sitter space. However, we also identify a special bouncing solution (for $k=0$) which for large times approaches the de-Sitter space again. For a dust dominated universe (with no pressure) deviations are seen only in the early epoch. In the late epoch, the solution asymptotically behaves like the standard dust solution.