Energy transfer from spacetime into matter and a bouncing inflation from covariant canonical gauge theory of gravity

Abstract

Cosmological solutions for covariant canonical gauge theories of gravity are presented. The underlying covariant canonical transformation framework invokes a dynamical spacetime Hamiltonian consisting of the Einstein–Hilbert term plus a quadratic Riemann tensor invariant with a fundamental dimensionless coupling constant [Formula: see text]. A typical time scale related to this constant, [Formula: see text], is characteristic for the type of cosmological solutions: for [Formula: see text], the quadratic term is dominant, the energy–momentum tensor of matter is not covariantly conserved, and we observe modified dynamics of matter and spacetime. On the other hand, for [Formula: see text], 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 [Formula: see text]) 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 late epoch, the solution asymptotically behaves as the standard dust solution.