Torsional dark energy in quadratic gauge gravity

Abstract

The covariant canonical gauge theory of gravity (CCGG) is a gauge field formulation of gravity which a priori includes non-metricity and torsion. It extends the Lagrangian of Einstein’s theory of general relativity by terms at least quadratic in the Riemann–Cartan tensor. This paper investigates the implications of metric compatible CCGG on cosmological scales. For a totally anti-symmetric torsion tensor we derive the resulting equations of motion in a Friedmann–Lemaître–Robertson–Walker (FLRW) Universe. In the limit of a vanishing quadratic Riemann–Cartan term, the arising modifications of the Friedmann equations are shown to be equivalent to spatial curvature. Furthermore, the modified Friedmann equations are investigated in detail in the early and late times of the Universe’s history. It is demonstrated that in addition to the standard Lambda CDM behaviour of the scale factor, there exist novel time dependencies, emerging due to the presence of torsion and the quadratic Riemann–Cartan term. Finally, at late times, we present how the accelerated expansion of the Universe can be understood as a geometric effect of spacetime through torsion, rendering the introduction of a cosmological constant redundant. In such a scenario it is possible to compute an expected value for the parameters of the postulated gravitational Hamiltonian/Lagrangian and to provide a lower bound on the vacuum energy of matter.