The spectrum of primordial fluctuations from inflation can be obtained using a mathematically controlled, and systematically extendable, uniform approximation. Closed-form expressions for power spectra and spectral indices may be found without making explicit slow-roll assumptions. Here we provide details of our previous calculations, extend the results beyond leading-order in the approximation, and derive general error bounds for power spectra and spectral indices. Already at next-toleading-order, the errors in calculating the power spectrum are less than a percent. This meets the accuracy requirement for interpreting next-generation cosmic microwave background observations.

Inflationary cosmology provides a natural mechanism for the generation of primordial perturbations which seed the formation of observed cosmic structure and lead to specific signals of anisotropy in the cosmic microwave background radiation. In order to test the broad inflationary paradigm as well as particular models against precision observations, it is crucial to be able to make accurate predictions for the power spectrum of both scalar and tensor fluctuations. We present detailed calculations of these quantities utilizing direct numerical approaches as well as error-controlled uniform approximations, comparing with the (uncontrolled) traditional slow-roll approach. A simple extension of the leading-order uniform approximation yields results for the power spectra amplitudes, the spectral indices, and the running of spectral indices, with accuracy of the order of 0.1% -approximately the same level at which the transfer functions are known. Several representative examples are used to demonstrate these results.

The hybrid model with a scalar "inflaton" field coupled to a "Higgs" field with a broken symmetry potential is one of the promising models for inflation and (p)reheating after inflation. We consider the nonequilibrium evolution of the quantum fields of this model with quantum back reaction in the Hartree approximation, in particular the transition of the Higgs field from the metastable "false vacuum" to the broken symmetry phase. We have performed the renormalization of the equations of motion, of the gap equations and of the energy density, using dimensional regularization. We study the influence of the back reaction on the evolution of the classical fields and of the quantum fluctuations. We observe that back reaction plays an important role over a wide range of parameters. Some implications of our investigation for the preheating stage after cosmic inflation are presented.

We consider the out-of-equilibrium evolution of a classical condensate field ϭ͗⌽͘ and its quantum fluctuations for a ⌽ 4 model in 1ϩ1 dimensions with a double well potential. We use the two-particle pointirreducible ͑2PPI͒ formalism in the two-loop approximation. We compare our results to those obtained in the Hartree approximation, in the bare vertex approximation, and in the two-particle irreducible next-to-leading order large-N approach, with thermal initial conditions. In the 2PPI scheme, we find that the system tends to the symmetric configuration at late times, as expected in the absence of spontaneous symmetry breaking.

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a Φ 4 model in 1 + 1 dimensions with a symmetric and a double well potential. We use the 2PPI formalism and go beyond the Hartree approximation by including the sunset term. In addition to the mean field φ(t) = Φ the 2PPI formalism uses as variational parameter a time dependent mass M 2 (t) which contains all local insertions into the Green function. We compare our results to those obtained in the Hartree approximation. In the symmetric Φ 4 theory we observe that the mean field shows a stronger dissipation than the one found in the Hartree approximation. The dissipation is roughly exponential in an intermediate time region. In the theory with spontaneous symmetry breaking, i.e., with a double well potential, the field amplitude tends to zero, i.e., to the symmetric configuration. This is expected on general grounds: in 1 + 1 dimensional quantum field theory there is no spontaneous symmetry breaking for T > 0, and so there should be none at finite energy density (microcanonical ensemble), either. Within the time range of our simulations the momentum spectra do not thermalize and display parametric resonance bands.