In the early Universe, energy stored in small-scale density perturbations is quickly dissipated by Silkdamping, a process that inevitably generates µand y-type spectral distortions of the cosmic microwave background (CMB). These spectral distortions depend on the shape and amplitude of the primordial power spectrum at wavenumbers k 10 4 Mpc −1 . Here we study constraints on the primordial power spectrum derived from COBE/FIRAS and forecasted for PIXIE. We show that measurements of µ and y impose strong bounds on the integrated small-scale power, and we demonstrate how to compute these constraints using k-space window functions that account for the effects of thermalization and dissipation physics. We show that COBE/FIRAS places a robust upper limit on the amplitude of the small-scale power spectrum. This limit is about three orders of magnitude stronger than the one derived from primordial black holes in the same scale range. Furthermore, this limit could be improved by another three orders of magnitude with PIXIE, potentially opening up a new window to early Universe physics. To illustrate the power of these constraints, we consider several generic models for the small-scale power spectrum predicted by different inflation scenarios, including running-mass inflation models and inflation scenarios with episodes of particle production. PIXIE could place very tight constraints on these scenarios, potentially even ruling out running-mass inflation models if no distortion is detected. We also show that inflation models with sub-Planckian field excursion that generate detectable tensor perturbations should simultaneously produce a large CMB spectral distortion, a link that could potentially be established by PIXIE.

It has been proposed that cosmic acceleration or inflation can be driven by replacing the EinsteinHilbert action of general relativity with a function fR of the Ricci scalar R. Such fR gravity theories have been shown to be equivalent to scalar-tensor theories of gravity that are incompatible with Solar System tests of general relativity, as long as the scalar field propagates over Solar System scales. Specifically, the parameterized post-Newtonian (PPN) parameter in the equivalent scalar-tensor theory is 1=2, which is far outside the range allowed by observations. In response to a flurry of papers that questioned the equivalence of fR theory to scalar-tensor theories, it was recently shown explicitly, without resorting to the scalar-tensor equivalence, that the vacuum field equations for 1=R gravity around a spherically symmetric mass also yield 1=2. Here we generalize this analysis to fR gravity and enumerate the conditions that, when satisfied by the function fR, lead to the prediction that 1=2.

Superhorizon perturbations induce large-scale temperature anisotropies in the cosmic microwave background (CMB) via the Grishchuk-Zel'dovich effect. We analyze the CMB temperature anisotropies generated by a single-mode adiabatic superhorizon perturbation. We show that an adiabatic superhorizon perturbation in a ÃCDM universe does not generate a CMB temperature dipole, and we derive constraints to the amplitude and wavelength of a superhorizon potential perturbation from measurements of the CMB quadrupole and octupole. We also consider constraints to a superhorizon fluctuation in the curvaton field, which was recently proposed as a source of the hemispherical power asymmetry in the CMB.

The thermal and expansion history of the Universe before big bang nucleosynthesis is unknown. We investigate the evolution of cosmological perturbations through the transition from an early matter era to radiation domination. We treat reheating as the perturbative decay of an oscillating scalar field into relativistic plasma and cold dark matter. After reheating, we find that subhorizon perturbations in the decay-produced dark matter density are significantly enhanced, while subhorizon radiation perturbations are instead suppressed. If dark matter originates in the radiation bath after reheating, this suppression may be the primary cutoff in the matter power spectrum. Conversely, for dark matter produced nonthermally from scalar decay, enhanced perturbations can drive structure formation during the cosmic dark ages and dramatically increase the abundance of compact substructures. For low reheat temperatures, we find that as much as 50% of all dark matter is in microhalos with M 0.1M⊕ at z ≃ 100, compared to a fraction of ∼ 10 −10 in the standard case. In this scenario, ultradense substructures may constitute a large fraction of dark matter in galaxies today. * Electronic address: erickcek@cita.utoronto.ca † Electronic address: krs@physics.ubc.ca