Forecasting constraints on the no-hair theorem from the stochastic gravitational wave background
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| Format: | Preprint |
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2023
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| author | Tan, Chen Wang, Ke |
| author_facet | Tan, Chen Wang, Ke |
| contents | Although the constraints on general relativity (GR) from each individual gravitational-wave (GW) event can be combined to form a cumulative estimate of the deviations from GR, the ever-increasing number of GW events used also leads to the ever-increasing computational cost during the parameter estimation. Therefore, in this paper, we will introduce the deviations from GR into GWs from all events in advance and then create a modified stochastic gravitational-wave background (SGWB) to perform tests of GR. More precisely, we use the $\mathtt{pSEOBNRv4HM\_PA}$ model to include the model-independent hairs and calculate the corresponding SGWB with a given merger rate. Then we turn to the Fisher information matrix to forecast the constraints on the no-hair theorem from SGWB at frequency $10[{\rm Hz}]\lesssim f\lesssim10^3[{\rm Hz}]$ detected by the third-generation ground-based GW detectors, such as the Cosmic Explorer. We find that the forecasting constraints on hairs at $68\%$ confidence range are $δω_{220}=0\pm0.1296$ and $δτ_{220}=0\pm0.0678$ when the flat priors about the merger rate are added but $δω_{220}=0\pm0.0903$ and $δτ_{220}=0\pm0.0608$ when the non-flat priors about the merger rate are added. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_17767 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Forecasting constraints on the no-hair theorem from the stochastic gravitational wave background Tan, Chen Wang, Ke General Relativity and Quantum Cosmology Although the constraints on general relativity (GR) from each individual gravitational-wave (GW) event can be combined to form a cumulative estimate of the deviations from GR, the ever-increasing number of GW events used also leads to the ever-increasing computational cost during the parameter estimation. Therefore, in this paper, we will introduce the deviations from GR into GWs from all events in advance and then create a modified stochastic gravitational-wave background (SGWB) to perform tests of GR. More precisely, we use the $\mathtt{pSEOBNRv4HM\_PA}$ model to include the model-independent hairs and calculate the corresponding SGWB with a given merger rate. Then we turn to the Fisher information matrix to forecast the constraints on the no-hair theorem from SGWB at frequency $10[{\rm Hz}]\lesssim f\lesssim10^3[{\rm Hz}]$ detected by the third-generation ground-based GW detectors, such as the Cosmic Explorer. We find that the forecasting constraints on hairs at $68\%$ confidence range are $δω_{220}=0\pm0.1296$ and $δτ_{220}=0\pm0.0678$ when the flat priors about the merger rate are added but $δω_{220}=0\pm0.0903$ and $δτ_{220}=0\pm0.0608$ when the non-flat priors about the merger rate are added. |
| title | Forecasting constraints on the no-hair theorem from the stochastic gravitational wave background |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2311.17767 |