Primordial Gravitational Waves in Parity-violating Symmetric Teleparallel Gravity

Technical Deep Dive: Primordial Gravitational Waves in Parity-violating Symmetric Teleparallel Gravity

Overview

This work investigates the generation of primordial gravitational waves (GWs) within the theoretical framework of parity-violating (PV) extensions of symmetric teleparallel gravity (STG). The key findings are:

• PV extensions of STG introduce interactions between the scalar field and parity-odd terms in the nonmetricity tensor, leading to velocity birefringence in tensor perturbations.
• During inflation, when the inflaton rapidly traverses a steep "cliff" in its potential, one circular polarization state of tensor modes experiences significant amplification due to tachyonic instability.
• The resulting primordial GW signal is predicted to be dominated by the left-handed polarization and exhibit a distinct multi-peak energy spectrum, potentially detectable by LISA and Taiji interferometers.
• The chirality of this GW signal could be determined using the LISA-Taiji network.

Problem & Context

• The detection of gravitational waves (GWs) by LIGO-Virgo has opened new avenues to probe the early universe and the nature of gravity.
• Primordial GWs generated during inflation carry valuable information, but for simple inflation models, their predicted amplitude is too small to be detected by current or near-future interferometers.
• Parity-violating (PV) gravity theories, such as PV extensions of teleparallel and symmetric teleparallel gravity (STG), can lead to observable signatures in the primordial GW spectrum.

Methodology

• The authors consider PV extensions of STG, which introduce interactions between the scalar field and parity-odd terms in the nonmetricity tensor.
• They apply this PV STG framework to the context of axion inflation, studying its impact on the evolution of tensor perturbations during inflation.
• Key steps:
  • Derive the field equations in a flat FRW background
  • Analyze the behavior of tensor perturbations, focusing on the velocity birefringence induced by PV terms
  • Numerically solve the background equations and study the time evolution of tensor power spectra

Results

• The PV terms lead to a double-peak structure in the term |H\dot{\phi}^2 + \dot{\phi}\ddot{\phi}|/(m^2H), with a more pronounced positive peak.
• For certain modes, the condition \omega_A^2(k) < 0 is satisfied near the positive peak, leading to tachyonic instability and significant amplification of the left-handed tensor mode.
• The resulting primordial GW signal is dominated by the left-handed polarization and exhibits a distinctive multi-peak energy spectrum.
• The predicted GW energy spectrum falls within the sensitive frequency ranges of LISA and Taiji interferometers, potentially allowing detection of the chiral GW signal.

Interpretation

• The one-handed polarization and multi-peak structure of the predicted primordial GW signal are unique signatures that distinguish it from other inflationary scenarios.
• Detection of such a chiral GW signal would provide invaluable insights into the physics of inflation and the nature of gravity, probing PV extensions of STG.

Limitations & Uncertainties

• The analysis is limited to the specific PV extensions of STG considered in the paper, and the results may depend on the details of the model.
• The parameter choices, while constrained by current CMB observations, still involve some degree of tuning to ensure the GW signal falls within the optimal sensitivity range of future detectors.

What Comes Next

• The authors suggest that further investigation of PV gravity theories and their potential signatures in the primordial GW spectrum could yield additional testable predictions.
• Ongoing and future GW interferometer experiments, such as LISA and Taiji, will be crucial for detecting and characterizing the predicted chiral GW signal, potentially providing a new window into the early universe.