Gauge-invariant cosmological perturbations in Type 3 New General Relativity and background-hierarchy bounds

TL;DR

This paper analyzes background-hierarchy bounds in Type 3 New General Relativity, identifying parameter regions where linear cosmological perturbation theory remains valid, and clarifies gauge choices and mode propagation.

Contribution

It provides a detailed perturbative analysis of Type 3 NGR, deriving background-hierarchy bounds and clarifying gauge-invariant mode identification in cosmological settings.

Findings

Derived background-hierarchy bounds for scalar, vector, and tensor modes.

Identified parameter space where linear perturbation theory is valid.

Clarified gauge choices and mode propagation in Type 3 NGR.

Abstract

In this paper, we investigate background-hierarchy bounds in Type~3 of New General Relativity (NGR). These bounds arise when the contribution associated with the evolution of the background spacetime exceeds that of the quadratic kinetic term in the perturbed Lagrangian. Type~3 of NGR has two free parameters and preserves diffeomorphism invariance and spatial rotations, while breaking Lorentz-boost invariance. We first review Type~3 and identify preferable gauge choices for metric-affine gauge theories of gravity with Weitzenb\"ock connection, including NGR, from the viewpoint of symmetry in both Dirac--Bergmann analysis and linear perturbation theory. We then revisit the perturbative analysis of Type~3 and show that the propagating modes are correctly identified even when the perturbed Lagrangian is not written solely in terms of gauge-invariant variables. Finally, we derive the background-hierarchy bounds for the scalar, transverse-vector, and tensor modes around a flat FLRW background, and identify the region of parameter space in which the linear perturbation theory of Type~3 remains viable for cosmological applications.