Early structure formation from primordial density fluctuations with a blue, tilted power spectrum

While observations of large-scale structure and the cosmic microwave background (CMB) provide strong constraints on the amplitude of the primordial power spectrum (PPS) on scales larger than 10 Mpc, the amplitude of the power spectrum on sub-galactic length scales is much more poorly constrained. We study early structure formation in a cosmological model with a blue-tilted PPS. We assume that the standard scale-invariant PPS is modified at small length scales as P(k) ∼ k^m, with m_s > 1. We run a series of cosmological hydrodynamic simulations to examine the dependence of the formation epoch and the characteristic mass of primordial stars on the tilt of the PPS. In models with m_s > 1, star-forming gas clouds are formed at z > 100 when the formation of hydrogen molecules is inefficient because the intense CMB radiation destroys chemical intermediates. Without efficient coolant, the gas clouds gravitationally contract while retaining a high temperature. The protostars formed in such "hot" clouds grow very rapidly through accretion to become extremely massive stars that may leave massive black holes with a few hundred solar masses at z > 100. The shape of the PPS critically affects the properties and the formation epoch of the first generation of stars. Future experiments on CMB polarization and spectrum distortion may provide important information on the nature of the first stars and their formation epoch, and hence on the shape of the small-scale power spectrum.