Irregular universe in the Nieh-Yan modified teleparallel gravity

TL;DR

This paper explores a modified teleparallel gravity model involving the Nieh-Yan density, revealing a new flat universe solution with coupled scalar and tensor perturbations, which could impact primordial cosmological observations.

Contribution

It introduces a new flat universe solution in Nieh-Yan modified teleparallel gravity with arbitrary connection, highlighting coupled perturbations at linear order.

Findings

New flat universe solution with arbitrary connection.

Coupling of scalar and tensor perturbations at linear level.

Implications for primordial perturbations from inflation.

Abstract

The Nieh-Yan modified teleparallel gravity is a model which modifies the general relativity equivalent teleparallel gravity by a coupling between the Nieh-Yan density and an axion-like field. This model predicts parity violations in the gravitational waves if the axion-like field has a non-trivial background, and more importantly it is ghost free and avoids the pathologies presented in other parity-violating gravity models. The cosmological dynamics and perturbations of the Nieh-Yan modified teleparallel gravity have been investigated in detail, but all these previous investigations rely on the symmetry requirement that in the background universe both the metric and affine connection are homogeneous and isotropic. In this paper we relax the symmetry constraint on the connection and leave it arbitrary at the beginning, after all the cosmological principle only needs the metric of the background spacetime to meet the symmetry requirement. We find a new flat universe solution for the Nieh-Yan modified teleparallel gravity, for which the background dynamics itself is unchanged but the perturbations around it present a new feature that the scalar and tensor perturbations are coupled together at the linear level. The implications of this peculiar feature in primordial perturbations from inflation are also discussed.