Growth of Gravitational Wave Spectrum from Sound Waves in a Universe with Generic Expansion Rate
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908523231707136 |
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| author | Xiao, Yang Guo, Huai-Ke Hu, Jiahang Yang, Jin Min Zhang, Yang |
| author_facet | Xiao, Yang Guo, Huai-Ke Hu, Jiahang Yang, Jin Min Zhang, Yang |
| contents | We derive a compact analytical expression for the growth factor $Υ$, which characterizes how the gravitational wave spectrum sourced by sound waves evolves in a universe with a generic expansion history. Assuming the dominant energy density scales as $ρ\propto a^{-3(1+w)}$, we obtain $Υ=\frac{2[1-y^{3(w-1)/2}]}{3(1-w)}$, where $y = a(t)/a(t_s)$ is the ratio of the scale factor at a later time $t$ to that at $t_s$ when gravitational wave production from sound waves starts. This general result reduces to known forms in radiation-and matter-dominated eras, thereby extending previous formulas to a broader class of cosmological backgrounds. The derivation assumes only that the source is stationary, making $Υ$ a universal factor that captures gravitational wave growth in various scenarios-not limited to phase transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Growth of Gravitational Wave Spectrum from Sound Waves in a Universe with Generic Expansion Rate Xiao, Yang Guo, Huai-Ke Hu, Jiahang Yang, Jin Min Zhang, Yang General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology We derive a compact analytical expression for the growth factor $Υ$, which characterizes how the gravitational wave spectrum sourced by sound waves evolves in a universe with a generic expansion history. Assuming the dominant energy density scales as $ρ\propto a^{-3(1+w)}$, we obtain $Υ=\frac{2[1-y^{3(w-1)/2}]}{3(1-w)}$, where $y = a(t)/a(t_s)$ is the ratio of the scale factor at a later time $t$ to that at $t_s$ when gravitational wave production from sound waves starts. This general result reduces to known forms in radiation-and matter-dominated eras, thereby extending previous formulas to a broader class of cosmological backgrounds. The derivation assumes only that the source is stationary, making $Υ$ a universal factor that captures gravitational wave growth in various scenarios-not limited to phase transitions. |
| title | Growth of Gravitational Wave Spectrum from Sound Waves in a Universe with Generic Expansion Rate |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2410.23666 |