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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2312.08497 |
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| _version_ | 1866918002835849216 |
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| author | Ali-Haïmoud, Yacine Gandhi, Suroor Seher Smith, Tristan L. |
| author_facet | Ali-Haïmoud, Yacine Gandhi, Suroor Seher Smith, Tristan L. |
| contents | Elastic scattering of dark matter (DM) particles with baryons induce cosmological signals that may be detectable with modern or future telescopes. For DM-baryon scattering cross sections scaling with negative powers of relative velocity, $σ_{χb}(v) \propto v^{-2}, v^{-4}$, such interactions introduce a momentum-exchange rate that is nonlinear in DM-baryon bulk relative velocities, thus not amenable for inclusion as-is into standard linear cosmological Boltzmann codes. Linear ansatzes have been adopted in past works, but their accuracy is unknown as they do not arise from first-principles derivations. In this work, for the first time, we construct a rigorous framework for computing linear-cosmology observables as a perturbative expansion in $σ_{χb}$. We argue that this approach is accurate for Cosmic Microwave Background (CMB) angular power spectra when most or all of the DM is scattering with baryons with cross section $σ_{χb}(v) \propto v^{-2}, v^{-4}$. We derive exact formal expressions for CMB power spectra at linear order in $σ_{χb}$, and show that they only depend on a specific velocity integral of the momentum-exchange rate. Consequently, we can obtain the exact power spectra at linear order in $σ_{χb}$ by substituting the original nonlinear momentum-exchange rate with a uniquely specified linear rate. Serendipitously, we find that the exact substitution we derive from first principles precisely coincides with the most widely used linear ansatz, thus placing previous CMB-anisotropy upper bounds on a more solid footing. In addition to finally providing an exact cosmological solution to the DM-baryon scattering problem in a well-defined region of parameter space, the framework we construct opens the way to computing higher-order correlation functions, beyond power spectra, which are promising yet unexplored probes of DM-baryon scattering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08497 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exact treatment of weak dark matter-baryon scattering for linear-cosmology observables Ali-Haïmoud, Yacine Gandhi, Suroor Seher Smith, Tristan L. Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology Elastic scattering of dark matter (DM) particles with baryons induce cosmological signals that may be detectable with modern or future telescopes. For DM-baryon scattering cross sections scaling with negative powers of relative velocity, $σ_{χb}(v) \propto v^{-2}, v^{-4}$, such interactions introduce a momentum-exchange rate that is nonlinear in DM-baryon bulk relative velocities, thus not amenable for inclusion as-is into standard linear cosmological Boltzmann codes. Linear ansatzes have been adopted in past works, but their accuracy is unknown as they do not arise from first-principles derivations. In this work, for the first time, we construct a rigorous framework for computing linear-cosmology observables as a perturbative expansion in $σ_{χb}$. We argue that this approach is accurate for Cosmic Microwave Background (CMB) angular power spectra when most or all of the DM is scattering with baryons with cross section $σ_{χb}(v) \propto v^{-2}, v^{-4}$. We derive exact formal expressions for CMB power spectra at linear order in $σ_{χb}$, and show that they only depend on a specific velocity integral of the momentum-exchange rate. Consequently, we can obtain the exact power spectra at linear order in $σ_{χb}$ by substituting the original nonlinear momentum-exchange rate with a uniquely specified linear rate. Serendipitously, we find that the exact substitution we derive from first principles precisely coincides with the most widely used linear ansatz, thus placing previous CMB-anisotropy upper bounds on a more solid footing. In addition to finally providing an exact cosmological solution to the DM-baryon scattering problem in a well-defined region of parameter space, the framework we construct opens the way to computing higher-order correlation functions, beyond power spectra, which are promising yet unexplored probes of DM-baryon scattering. |
| title | Exact treatment of weak dark matter-baryon scattering for linear-cosmology observables |
| topic | Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2312.08497 |