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.
