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Main Authors: Ali-Haïmoud, Yacine, Gandhi, Suroor Seher, Smith, Tristan L.
Format: Preprint
Published: 2023
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Online Access:https://arxiv.org/abs/2312.08497
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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