Growth of dark matter perturbations during kination

Kayla Redmond, Anthony Trezza, and Adrienne L. Erickcek

Phys. Rev. D 98, 063504 – Published 10 September 2018

Abstract

If the Universe’s energy density was dominated by a fast-rolling scalar field while the radiation bath was hot enough to thermally produce dark matter, then dark matter with larger-than-canonical annihilation cross sections can generate the observed dark matter relic abundance. To further constrain these scenarios, we investigate the evolution of small-scale density perturbations during such a period of kination. We determine that once a perturbation mode enters the horizon during kination, the gravitational potential drops sharply and begins to oscillate and decay. Nevertheless, dark matter density perturbations that enter the horizon during an era of kination grow linearly with the scale factor prior to the onset of radiation domination. Consequently, kination leaves a distinctive imprint on the matter power spectrum: scales that enter the horizon during kination have enhanced inhomogeneity. We also consider how matter density perturbations evolve when the dominant component of the Universe has a generic equation-of-state parameter $w$ . We find that matter density perturbations do not grow if they enter the horizon when $0 < w < 1 / 3$ . If matter density perturbations enter the horizon when $w > 1 / 3$ , their growth is faster than the logarithmic growth experienced during radiation domination. The resulting boost to the small-scale matter power spectrum leads to the formation of enhanced substructure, which effectively increases the dark matter annihilation rate and could make thermal dark matter production during an era of kination incompatible with observations.

Received 2 July 2018

DOI:https://doi.org/10.1103/PhysRevD.98.063504

Physics Subject Headings (PhySH)

Evolution of the Universe

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Kayla Redmond^*, Anthony Trezza, and Adrienne L. Erickcek^†

Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Phillips Hall CB3255, Chapel Hill, North Carolina 27599, USA

^*kayla.jaye@unc.edu
^†erickcek@physics.unc.edu

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Vol. 98, Iss. 6 — 15 September 2018

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Images

Figure 1
The evolution of dark matter density perturbations for two modes that enter the horizon during an era of kination. The left panel corresponds to scenarios where dark matter freezes in during an era of kination with $⟨ σ v ⟩ = 1.4 \times 10^{- 46} {cm}^{3} s^{- 1}$ . The right panel corresponds to scenarios where dark matter freezes out during an era of kination with $⟨ σ v ⟩ = 1 \times 10^{- 23} {cm}^{3} s^{- 1}$ and freeze-out occurring at $a_{F} = 2.5$ . The short-dashed line corresponds to the dark matter equilibrium density perturbation $δ_{χ, eq}$ . In both panels, $m_{χ} = 10^{5} GeV$ and kinaton-radiation equality occurs at $a_{KR} = 10^{4}$ . One mode has wave number $k = 3075 k_{KR}$ and enters the horizon at $a = 150$ , while the other mode has wave number $k = 43 k_{KR}$ and enters the horizon at $a = 1300$ .
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Figure 2
The evolution of $Φ$ given that the perturbation mode enters the horizon when the dominant component of the Universe has $w = 1, 0.75, 0.5, 0.33$ , or 0.25. All of these scenarios involve a mode with $k / H_{1} = 10^{- 5}$ , but they enter the horizon at varying values of $a$ .
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Figure 3
The evolution of $Φ$ for two modes that enter the horizon during an era of kination. In this figure, $m_{χ} = 10^{5} GeV$ , $⟨ σ v ⟩ = 1.4 \times 10^{- 46} {cm}^{3} s^{- 1}$ , and kinaton-radiation equality occurs at $a_{KR} = 10^{4}$ . One mode has wave number $k = 3075 k_{KR}$ and enters the horizon at $a = 150$ , while the other mode has wave number $k = 43 k_{KR}$ and enters the horizon at $a = 1300$ . The solid lines represent the numeric solution to Eq. (5) and the dashed lines represent the analytic approximations for $Φ$ using Eq. (10).
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Figure 4
Evolution of a dark matter density perturbation that enters the horizon during an era of kination. The left panel corresponds to scenarios where dark matter freezes in during an era of kination with $⟨ σ v ⟩ = 1.4 \times 10^{- 46} {cm}^{3} s^{- 1}$ . The right panel corresponds to scenarios where dark matter freezes out during an era of kination with $⟨ σ v ⟩ = 1 \times 10^{- 23} {cm}^{3} s^{- 1}$ and freeze-out occurring at $a_{F} = 2.5$ . In both panels, $m_{χ} = 10^{5} GeV$ and $a_{KR} = 10^{4}$ . The mode shown has wave number $k = 3075 k_{KR}$ and enters the horizon at $a = 150$ . The solid curve represents the numerical solution for $δ_{χ}$ using Eq. (4), the short-dashed line represents the analytical expression for $δ_{χ}$ using Eq. (15), and the long-dashed line corresponds to Eq. (18).
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Figure 5
The dark matter density perturbation evaluated at $100 a_{KR}$ for various $k$ modes. In this figure, $m_{χ} = 10^{5} GeV$ , $⟨ σ v ⟩ = 1.4 \times 10^{- 46} {cm}^{3} s^{- 1}$ , and kinaton-radiation equality occurs at $a_{KR} = 10^{4}$ . The solid curve represents the numeric evaluation of Eq. (4), while the long-dashed line and short-dashed line represent the analytical evolution via Eqs. (26) and (27).
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