Cosmological Perturbations of Extended NGR Model with Parity Violation

TL;DR

This work investigates an extended New General Relativity model that adds parity-odd, quadratic torsion terms to the teleparallel action. By performing a full cosmological perturbation analysis around a spatially flat FRW background, the authors derive the quadratic actions for tensor, vector, and scalar modes and identify the conditions under which ghost instabilities are avoided. They find that, in general, ghost-free configurations favor setting the parity-odd coefficient to zero, but there exists a narrow parameter region with a nonzero parity-odd term where all perturbation sectors can be healthy and dynamical. The degenerate case W=0 shows vacuum solutions with nontrivial evolution and further constraints on the dynamical DoFs. The results have implications for parity-violating gravity theories and gravitational-wave propagation, including birefringence and observational constraints from gravitational-wave events.

Abstract

Recently the modified teleparallel gravity models attracted a lot of interests. In this paper we consider more extensions to the New General Relativity (NGR) model with parity violations. This extended NGR model differs from the normal NGR model by the inclusion of additional parity-odd term that is quadratic in the torsion tensor. By investigating its cosmological perturbations of this model, we find that this model can avoid ghost instabilities in certain regions of the parameter space, where the coefficient of the parity-odd term does not vanish.

Figures (3)

• Figure 1: The allowed region of the case $d_1=0,\ d_2/d_4<0$.
• Figure 2: The allowed region of case where both the eigenvalues are positive, $c_2$ and $c_3$ are normalized with $c_1=\pm1$.
• Figure 3: (a): The allowed region of case $c_4=0,~Z=0,~2c_1-c_2\neq0$. (b): The allowed region of case $c_4=0,~2c_1-c_2=0,~Z\neq0$