## Scalar Induced Gravitational Waves in Metric Teleparallel Gravity: Parity Violation and Energy Density

arXiv:2404.02922v1 Announce Type: new

Abstract: We investigate the scalar induced gravitational waves (SIGWs) in metric teleparallel gravity with the Nieh-Yan (NY) term, which results in parity violation during the radiation-dominated era. By solving the equations of motion of linear scalar perturbations from both the metric and tetrad fields, we obtain the corresponding analytic expressions. Then, we calculate the SIGWs in metric teleparallel gravity with the NY term and evaluate the energy density of SIGWs with a monochromatic power spectrum numerically. We find that the spectrum of the energy density of SIGWs in metric teleparallel gravity with the NY term is significantly different from that in general relativity (GR), which makes metric teleparallel gravity distinguishable from GR.

## Scalar Induced Gravitational Waves in Metric Teleparallel Gravity with the Nieh-Yan Term

In this article, we explore the phenomenon of scalar induced gravitational waves (SIGWs) in metric teleparallel gravity with the Nieh-Yan (NY) term. The presence of the NY term introduces parity violation during the radiation-dominated era, leading to interesting implications for gravitational wave production. By solving the equations of motion for linear scalar perturbations in both the metric and tetrad fields, we derive analytical expressions for the SIGWs. We then proceed to calculate the energy density of SIGWs with a monochromatic power spectrum, comparing it to that in general relativity (GR).

### Key Conclusions

- Metric teleparallel gravity with the NY term produces SIGWs with a distinct energy density spectrum compared to GR. This distinction allows us to differentiate between the two theories.

### Future Roadmap

While this study provides valuable insights into SIGWs in metric teleparallel gravity with the NY term, there are several avenues for future research:

- Further investigation can be done to understand the implications of the distinct energy density spectrum of SIGWs in metric teleparallel gravity. Are there observable consequences of this difference that can be tested? What astrophysical phenomena can be studied to explore this distinction?
- It would be interesting to explore the behavior of higher-order perturbations in metric teleparallel gravity with the NY term. Do higher-order perturbations exhibit similar distinctions from GR, or do they behave differently?
- Investigating the role of the NY term in other cosmological epochs and gravitational wave production scenarios can provide a comprehensive understanding of its impact on the overall dynamics of the universe. Are there additional epochs or scenarios where the NY term has a significant effect?

Challenges and Opportunities:

The challenges ahead involve theoretical modeling and numerical calculations to explore the observability of the differences in the energy density spectrum of SIGWs between metric teleparallel gravity and GR. Astrophysical observations and experiments may be necessary to test these predictions.

The opportunities lie in the potential for metric teleparallel gravity with the NY term to offer an alternative framework for studying gravitational waves and the fundamental nature of gravity. Exploring the implications of the NY term in various astrophysical contexts could lead to new insights and discoveries.