Parity Violating Metric-Affine Gravity Theories

Abstract

We study a parity violating Metric-Affine gravitational theory given by the Einstein-Hilbert action plus the so-called Holst term in vacuum. We find out that for a certain value of the Barbero-Immirzi parameter the total action possesses a remarkable invariance under particular transformations of the affine connection. We prove that in all cases, with appropriate gauge choices, the connection reduces to the Levi-Civita one and that the theory turns out to be equivalent to general relativity in vacuum. Subsequently, we generalize our discussion and analyze the case of Metric-Affine f (R) gravity plus the Holst term. In particular, we show that for f ′ (R) = constant the theory results to be on-shell equivalent to a metric-compatible torsionless Scalar-Tensor model. Matter coupling of the aforementioned models is also discussed, together with explicit examples and applications.

Metric-Affine Myrzakulov Gravity Theories

“…It would be worth it to further elaborate on cosmological applications of MAMG theories, especially in the presence of a cosmological hyperfluid [41,42] (see also [43]). Possible future developments may also regard the inclusion of parity violating terms in MAMG, in particular of the so-called Hojman term [44] (most of the time referred to as the Holst term [45]), following the lines of [46]. Always in this context, one might also consider the inclusion of a parity violating coupling of a scalar field to torsion, adding the contribution λ 3 t µ ∇ µ φ to the matter Lagrangian (11.1), where λ 3 is another constant parameter of the theory.…”

The Cosmology of Quadratic Torsionful Gravity

“…The tensor in (9) is the Ricci tensor of Γ, while in (10) we have the so-called homothetic curvature which vanishes for metric-compatible affine connections, and in (11) we have introduced a third tensor that is sometimes referred to as the co-Ricci tensor in the literature. In particular, for metric-compatible affine connections we have صν = −R µν (see also [19] for details).…”

“…Different restrictions of non-Riemannian geometry provide distinct frameworks for gravity theories formulations and the inclusion of torsion and non-metricity in gravitational theories has led to many fruitful applications in various areas of both mathematics and physics, among which, for instance, the ones recently presented in [6][7][8][9][10][11][12]. In particular, in the cosmological context, in [12] the most general form of acceleration equation in the presence of torsion and nonmetricity was derived and conditions under which torsion and non-metricity accelerate/decelerate the expansion rate of the Universe were discussed.…”

Toward Nonlocal Electrodynamics of Accelerated Systems

“…Observational consequences of the possible breakdown of parity and time-reversal invariance in the gravitational interaction have been considered by a number of authors; see, for instance, Refs. [67][68][69][70][71][72][73][74][75][76][77] and the references cited therein. On the other hand, there is no parity violation in standard general relativity.…”