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Probing the Small Scale Matter Power Spectrum through Dark Matter Annihilation in the Early Universe

Recent observations of the cosmic microwave background (CMB) anisotropies and the distribution of galaxies, galaxy clusters, and the Lyman Alpha forest have constrained the shape of the power spectrum of matter fluctuations on large scales k < few h/Mpc. We explore a new technique to constrain the matter power spectrum on smaller scales, assuming the dark matter is a Weakly Interacting Massive Particle (WIMP) that annihilates at early epochs. Energy released by dark matter annihilation can modify the spectrum of CMB temperature fluctuations and thus CMB experiments such as Planck have been able to constrain the quantity f <sigma v> /m < 1/88 picobarn c / GeV, where f is the fraction of energy absorbed by gas, <sigma v> is the annihilation rate assumed constant, and m is the particle mass. We assume the standard scale-invariant primordial matter power spectrum of P_prim(k) ~ k^{n_s} at large scales k < k_p, while we adopt the modified power law of P_prim(k) ~ k_p^{n_s} (k/k_p)^{m_s} at small scales. We then aim at deriving constraints on m_s. For m_s > n_s, the excess small-scale power results in a much larger number of nonlinear small mass halos, particularly at high redshifts. Dark matter annihilation in these halos releases sufficient energy to partially ionize the gas, and consequently modify the spectrum of CMB fluctuations. We show that the recent Planck data can already be used to constrain the power spectrum on small scales. For a simple model with an NFW profile with halo concentration parameter c_200 = 5 and f <sigma v> / m = 1/100 picobarn c / GeV, we can limit the mass variance sigma_{max} < 100 at the 95% confidence level, corresponding to a power law index m_s < 1.43 (1.63) for k_p = 100 (1000) h/Mpc. Our results are also relevant to theories that feature a running spectral index.