Chiral Primordial Gravitational Waves from a Lifshitz Point

TL;DR

This paper investigates inflation within Ho\u030cava-Lifshitz gravity, where anisotropic scaling and foliation-preserving diffeomorphisms yield a parity-violating Cotton-tensor contribution. The authors derive the tensor perturbation dynamics, showing right- and left-handed gravitational waves evolve differently due to a parity-violating term, which produces a nonzero circular polarization $\Pi$ in the primordial gravitational-wave background. By solving the mode equations with adiabatic vacuum initial conditions, they quantify $\Pi$ as a function of model parameters $\beta$ and $\gamma$, finding that detectable chirality is possible via CMB observations or direct GW experiments, while the scalar perturbations remain scale-free and consistent with current data. The work proposes a robust, falsifiable signature of Lifshitz-point quantum gravity and outlines observational paths to test this framework, presenting a potential smoking gun for new gravitational physics.

Abstract

We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho${\rm\check{r}}$ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.

Figures (2)

• Figure 1: The time evolution of the power is depicted. The thick solid line represents the evolution for the conventional Einstein gravity. The thin solid line and the dotted line show the time evolution of right handed mode and left handed mode, respectively.
• Figure 2: The degree of circular polarization $\Pi$ for various $\gamma$ as a function of $\beta$ are shown. As can be seen from the figure, $\Pi$ grows as the $\beta$ becomes large. The dependence on $\gamma$ is not monotonic rather there is a value which gives the maximum polarization for fixed $\beta$.