# Gravitational Waves in Axion Dark Matter

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Gravitational Waves in Dynamical Chern–Simons Gravity

#### Action of Gravitational Waves

## 3. Gravitational Waves Propagating in Axion Dark Matter

## 4. Parametric Resonances

#### 4.1. Coherence Length

#### 4.2. One More Consistency Check

## 5. Gravitational Faraday Rotation

## 6. Velocity of Gravitational Waves

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Abbott, B.P.; Abbott, R.; Abbott, T.D.; Abernathy, M.R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.X.; et al. Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett.
**2016**, 116, 061102. [Google Scholar] [CrossRef] - Abbott, B.P.; Abbott, R.; Abbott, T.D.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.X.; Adya, V.; et al. GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Phys. Rev. Lett.
**2017**, 119, 161101. [Google Scholar] [CrossRef] [Green Version] - Abbott, B.P.; Abbott, R.; Abbott, T.D.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.X.; Adya, V.; et al. Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A. Astrophys. J.
**2017**, 848, L13. [Google Scholar] [CrossRef] - Nishizawa, A. Generalized framework for testing gravity with gravitational-wave propagation. I. Formulation. Phys. Rev. D
**2018**, 97, 104037. [Google Scholar] [CrossRef] [Green Version] - Arai, S.; Nishizawa, A. Generalized framework for testing gravity with gravitational-wave propagation. II. Constraints on Horndeski theory. Phys. Rev. D
**2018**, 97, 104038. [Google Scholar] [CrossRef] [Green Version] - Nishizawa, A.; Kobayashi, T. Parity-violating gravity and GW170817. Phys. Rev. D
**2018**, 98, 124018. [Google Scholar] [CrossRef] [Green Version] - Visinelli, L.; Bolis, N.; Vagnozzi, S. Brane-world extra dimensions in light of GW170817. Phys. Rev. D
**2018**, 97, 064039. [Google Scholar] [CrossRef] [Green Version] - Casalino, A.; Rinaldi, M.; Sebastiani, L.; Vagnozzi, S. Alive and well: Mimetic gravity and a higher-order extension in light of GW170817. Class. Quant. Grav.
**2019**, 36, 017001. [Google Scholar] [CrossRef] [Green Version] - Campbell, B.A.; Duncan, M.J.; Kaloper, N.; Olive, K.A. Gravitational dynamics with Lorentz Chern–Simons terms. Nucl. Phys. B
**1991**, 351, 778. [Google Scholar] [CrossRef] [Green Version] - Lue, A.; Wang, L.M.; Kamionkowski, M. Cosmological signature of new parity-violating interactions. Phys. Rev. Lett.
**1999**, 83, 1506. [Google Scholar] [CrossRef] [Green Version] - Jackiw, R.; Pi, S.Y. Chern–Simons modification of general relativity. Phys. Rev. D
**2003**, 68, 104012. [Google Scholar] [CrossRef] [Green Version] - Yoshida, D.; Soda, J. Electromagnetic waves propagating in the string axiverse. PTEP
**2018**, 2018, 041E01. [Google Scholar] [CrossRef] [Green Version] - Yoshida, D.; Soda, J. Exploring the string axiverse and parity violation in gravity with gravitational waves. Int. J. Mod. Phys. D
**2018**, 27, 1850096. [Google Scholar] [CrossRef] [Green Version] - Soda, J.; Yoshida, D. Exploring String Axions with Gravitational Waves. Galaxies
**2017**, 5, 96. [Google Scholar] [CrossRef] [Green Version] - Arvanitaki, A.; Dimopoulos, S.; Dubovsky, S.; Kaloper, N.; March-Russell, J. String Axiverse. Phys. Rev. D
**2010**, 81, 123530. [Google Scholar] [CrossRef] [Green Version] - Satoh, M.; Kanno, S.; Soda, J. Circular Polarization of Primordial Gravitational Waves in String-inspired Inflationary Cosmology. Phys. Rev. D
**2008**, 77, 023526. [Google Scholar] [CrossRef] [Green Version] - Satoh, M.; Soda, J. Higher Curvature Corrections to Primordial Fluctuations in Slow-roll Inflation. J. Cosmol. Astropart. Phys.
**2008**, 2008, 019. [Google Scholar] [CrossRef] [Green Version] - Marsh, D.J.E. Axion Cosmology. Phys. Rept.
**2016**, 643, 1. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Oikonomou, V.K.; Popov, A.A. Propagation of Gravitational Waves in Chern–Simons Axion Einstein Gravity. Phys. Rev. D
**2019**, 100, 084009. [Google Scholar] [CrossRef] [Green Version] - Odintsov, S.D.; Oikonomou, V.K. f(R) Gravity Inflation with String-Corrected Axion Dark Matter. Phys. Rev. D
**2019**, 99, 064049. [Google Scholar] [CrossRef] [Green Version] - Dyda, S.; Flanagan, E.E.; Kamionkowski, M. Vacuum Instability in Chern–Simons Gravity. Phys. Rev. D
**2012**, 86, 124031. [Google Scholar] [CrossRef] [Green Version] - Takahashi, T.; Soda, J. Chiral Primordial Gravitational Waves from a Lifshitz Point. Phys. Rev. Lett.
**2009**, 102, 231301. [Google Scholar] [CrossRef] [Green Version] - Yagi, K.; Yunes, N.; Tanaka, T. Gravitational Waves from Quasi-Circular Black Hole Binaries in Dynamical Chern–Simons Gravity. Phys. Rev. Lett.
**2012**, 109, 251105. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ali-Haimoud, Y.; Chen, Y. Slowly-rotating stars and black holes in dynamical Chern–Simons gravity. Phys. Rev. D
**2011**, 84, 124033. [Google Scholar] [CrossRef] [Green Version] - Jung, S.; Kim, T.; Soda, J.; Urakawa, Y. Constraining the gravitational coupling of axion dark matter at LIGO. arXiv
**2003**, arXiv:2003.02853. [Google Scholar] - Khlopov, M.; Sakharov, A.; Sokoloff, D. The large scale modulation of the density distribution in standard axionic CDM and its cosmological and physical impact. arXiv
**1998**, arXiv:9812286. [Google Scholar] - Zhang, H. Axion Stars. Symmetry
**2019**, 12, 25. [Google Scholar] [CrossRef] [Green Version] - Nakayama, K. Vector Coherent Oscillation Dark Matter. J. Cosmol. Astropart. Phys.
**2019**, 2019, 019. [Google Scholar] [CrossRef] [Green Version] - Nomura, K.; Ito, A.; Soda, J. Pulsar timing residual induced by ultralight vector dark matter. Eur. Phys. J. C
**2020**, 80, 1–10. [Google Scholar] [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chu, C.-S.; Soda, J.; Yoshida, D.
Gravitational Waves in Axion Dark Matter. *Universe* **2020**, *6*, 89.
https://doi.org/10.3390/universe6070089

**AMA Style**

Chu C-S, Soda J, Yoshida D.
Gravitational Waves in Axion Dark Matter. *Universe*. 2020; 6(7):89.
https://doi.org/10.3390/universe6070089

**Chicago/Turabian Style**

Chu, Chong-Sun, Jiro Soda, and Daiske Yoshida.
2020. "Gravitational Waves in Axion Dark Matter" *Universe* 6, no. 7: 89.
https://doi.org/10.3390/universe6070089