Kinetic Isocurvature Perturbation

Abstract

We formulate a new class of primordial perturbations called $\textit{kinetic isocurvature perturbations}$, where the mass density of dark matter is constant relative to the photon number density while the kinetic energy of dark matter fluctuates in space. Such perturbations naturally arise in scenarios where a nonrelativistic heavy field decays into relativistic dark matter particles with a spatially modulated rate. As dark matter cools and becomes nonrelativistic, these fluctuations in kinetic energy leave large-scale density perturbations essentially unaffected and therefore evade the Cosmic Microwave Background bounds on isocurvature perturbations, yet survive as spatial variations in the free-streaming scale, resulting in patch-by-patch variation of the matter power spectrum.

Figures (6)

• Figure 1: Evolution of different density components in terms of $a/a_{i}$ for $m_{\chi} = 10^{-3} m_{\phi}$ and $\delta \Gamma = 0.2 \Gamma$. The blue lines show $\rho_\phi$ and $n_{\phi}$, the orange ones show $\rho_\chi$ and $n_{\chi}$, and the black ones depict the total density.
• Figure 2: Upper bound on $\delta_{\lambda}$ assuming $P_{\delta_{\lambda}}^{(\mathrm{delta})}(k)$ with the constraints from Buckley:2025zgh for $\lambda_{\mathrm{FS}}=0.1$ Mpc (top curves) and $1$ Mpc (bottom curves). Solid and dashed lines denote current and prospective bounds, respectively.
• Figure 3: Upper bound on $\delta_{\lambda}$ for given $\lambda_{\mathrm{FS}}$ assuming $P_{\delta_{\lambda}}^{\mathrm{(flat)}}(k)$ with the constraints given in Harigaya:2025pox and Buckley:2025zgh.
• Figure 4: The ratio $P_{PP}(k,K_{L}) / [ P_{m}(k)^2 P_{\delta_{\lambda}}(K_{L}) ]$ with the transfer function in Eq. \ref{['eq:transferfunction']} with $\beta = 2.4$ and $\gamma = -1.1$.
• Figure S1: Comparison of $\delta \rho_{\chi} / \rho_{\chi}$ between the result from solving the Boltzmann equation (blue) and that under the instantaneous-decay approximation (orange) for $m_{\chi} = 10^{-3} m_{\phi}$ and $\delta \Gamma = 0.2 \Gamma$.