Increasing the effective number of neutrinos with decaying particles

We present models of decaying particles for increasing the effective number of neutrinos N_nu after big bang nucleosynthesis but before the structure formation begins. We point out that our scenario not only solves the discrepancy between the constraints on N_nu from these two epochs, but also provides a possible answer to deeper inconsistency in the estimation of the matter power spectrum amplitude at small scales, represented by sigma_8, between the WMAP and some small scale matter power measurements such as the Lyman-alpha forest and weak lensing. We consider (a) saxion decay into two axions; (b) gravitino decay into axino and axion; (c) Dirac right-handed sneutrino decay into gravitino and right-handed neutrino.