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 $f^{\prime }(R)\ne \text{constant}$ 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.

38 pages

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