Chiral Primordial Gravitational Waves from a Lifshitz Point (0904.0554v3)

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.

• The paper presents a novel contribution by demonstrating that the inclusion of the Cotton tensor in Hořava-Lifshitz gravity produces chiral gravitational waves during inflation.
• It employs both analytical derivations and numerical simulations to quantify the degree of circular polarization as a distinctive signature of parity violation.
• The study outlines observational prospects via CMB and gravitational wave detection experiments, bridging theoretical quantum gravity and cosmological observations.

Chiral Primordial Gravitational Waves from a Lifshitz Point: An Overview

The paper of primordial gravitational waves (GWs) originating from quantum gravity at a Lifshitz point, as proposed by Hořava, provides a significant theoretical contribution to the field of cosmology and quantum gravity. This paper presents an analysis of the circular polarization of gravitational waves resulting from inflation within this framework, emphasizing the implications of parity violation induced by the Cotton tensor in the gravitational action.

Key Contributions and Findings

1. Theoretical Framework: The paper utilizes the Hořava-Lifshitz gravity, characterized by anisotropic scaling and foliation-preserving diffeomorphisms. This framework is distinct from conventional string theories, as it is not a unification theory but focuses on quantum gravity in 4D space-time. The theory's assumptions ensure power-counting renormalizability and offer a novel approach to exploring trans-Planckian physics.
2. Chirality and Parity Violation: Primordial gravitational waves are shown to exhibit chirality due to the inclusion of the Cotton tensor in the action, which inherently breaks parity invariance. This feature is a notable prediction of the quantum gravity model at a Lifshitz point and may be detectable through cosmic microwave background (CMB) observations and direct detection experiments.
3. Analytical and Numerical Approach: The authors derive the quadratic action for tensor perturbations and utilize a numerical approach to evaluate the degree of circular polarization of primordial gravitational waves. The numerical results indicate that significant circular polarization can be achieved under specific parameter conditions, notably the coupling constants involved in the theory.
4. Observational Prospects: The paper discusses the potential for observing circular polarization of primordial GWs. This could be done indirectly through CMB radiation or directly via experiments sensitive to stochastic gravitational wave backgrounds. The degree of polarization necessary for detection is shown to be within reach for various realistic scenarios, offering a tangible test of the theoretical predictions.

Theoretical and Practical Implications

The theoretical implications of this work are profound, as they provide a pathway to test quantum gravity effects at cosmological scales. The existence of circularly polarized gravitational waves is a robust prediction of the model and suggests an observable signature of trans-Planckian physics that is distinct from conventional spectrum modifications. This approach provides a theoretical consistency with current observations, such as the scale-free nature of the power spectrum for curvature perturbations.

From a practical perspective, the potential to detect these chiral signature imprints in cosmic structures can open new frontiers in observational cosmology, offering a unique probe into the early universe and the high-energy physics governing its dynamics.

Future Directions

Further work could focus on extending the analysis to include potential impacts on other cosmological observables and phenomena, such as non-Gaussianity or its interplay with other inflationary models. The search for exact solutions, like black hole solutions within this framework, and their analysis in terms of thermodynamics and spacetime structure could yield additional insights into the implications of Hořava-Lifshitz gravity. Moreover, exploring various cosmological and astrophysical contexts where this theory could have distinct observable consequences might provide further grounds for empirical validation or falsification.

In summary, this paper contributes to an evolving understanding of quantum gravity's role in the cosmological context. The predictions made for chiral gravitational waves provide a meaningful target for both theoretical exploration and empirical verification, offering a promising avenue for future research in connecting quantum gravitational theories to observable cosmological phenomena.