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.