Power spectrum for inflation models with quantum and thermal noises
  We determine the power spectrum for inflation models covering all regimes
from cold (isentropic) to warm (nonisentropic) inflation. We work in the
context of the stochastic inflation approach, which can nicely describe both
types of inflationary regimes concomitantly. A throughout analysis is carried
out to determine the allowed parameter space for simple single field polynomial
chaotic inflation models that is consistent with the most recent cosmological
data from the nine-year Wilkinson Microwave Anisotropy Probe (WMAP) and in
conjunction with other observational cosmological sources. We present the
results for both the amplitude of the power spectrum, the spectral index and
for the tensor to scalar curvature perturbation amplitude ratio. We briefly
discuss cases when running is present. Despite single field polynomial-type
inflaton potential models be strongly disfavored, or even be already ruled out
in their simplest versions in the case of cold inflation, this is not the case
for nonisentropic inflation models in general (warm inflation in particular),
though higher order polynomial potentials (higher than quartic order) tend to
become less favorable also in this case, presenting a much smaller region of
parameter space compatible with the recent observational cosmological data. Our
findings also remain valid in face of the recently released Planck results.
