Isocurvature Perturbation of Weakly Interacting Massive Particles and Small Scale Structure

The adiabatic perturbation of dark matter is damped during the kinetic decoupling due to the collision with a relativistic component on subhorizon scales. However, the isocurvature part is free from damping and could be large enough to make a substantial contribution to the formation of small scale structure. We explicitly study the weakly interacting massive particles as dark matter with an early matter dominated period before radiation domination and show that the isocurvature perturbation is generated during the phase transition and leaves an imprint in the observable signatures for small scale structure.

Figure 1

The evolution of the energy densities of the scalar (black), radiation (red), and DM (blue), respectively, with respect to the initial total energy density. The blue dashed line is the equilibrium energy density of WIMP, and green dashed lines denote the asymptotic behavior of radiation energy density. DM freezes out at $a/a_i\simeq 20$ and RD starts from $a/a_i\simeq 300$.

Figure 2

The evolution of the density contrast of the radiation (red), DM (blue), and the isocurvature perturbation (brown) with respect to the initial gravitational potential for $k_{\mathrm{kd}}^{-1}<k^{-1}$ ($k=0.1k_{\mathrm{kd}}$, left), $k_{\mathrm{reh}}^{-1}<k^{-1}<k_{\mathrm{kd}}^{-1}$ ($k=5k_{\mathrm{kd}}=0.5k_{\mathrm{reh}}$, middle), and $k_{\mathrm{fr}}^{-1}<k^{-1}<k_{\mathrm{reh}}^{-1}$ ($k=50k_{\mathrm{kd}}=5k_{\mathrm{reh}}=0.8k_{\mathrm{fr}}$, right). We have set $M=5\mathrm{TeV}$, $T_{\mathrm{reh}}=0.1\mathrm{GeV}$, and $T_{\mathrm{kd}}=0.01\mathrm{GeV}$.

Figure 3

Density contrast of DM with $M=5\mathrm{TeV}$, $T_{\mathrm{reh}}=0.1\mathrm{GeV}$, and $T_{\mathrm{kd}}=0.01\mathrm{GeV}$.