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.

Non-Markovian stochastic Langevin-like equations of motion are compared to their corresponding Markovian (local) approximations. The validity of the local approximation for these equations, when contrasted with the fully nonlocal ones, is analyzed in detail. The conditions for when the equation in a local form can be considered a good approximation are then explicitly specified. We study both the cases of additive and multiplicative noises, including system-dependent dissipation terms, according to the fluctuation-dissipation theorem.

System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case, it is useful to resort to simplified models relying on effective stochastic equations. A natural consideration is to assume that there is a noisy contribution from the environment, such that the parameters that characterize it are not constant but instead fluctuate around their characteristic values. From this perspective, we propose a stochastic generalization of the nonlocal Fisher-KPP equation where, as a first step, environmental fluctuations are Gaussian white noises, both in space and time. We apply analytical and numerical techniques to study how noise affects stability and pattern formation in this context. Particularly, we investigate noise-induced coherence by means of the complementary information provided by the dispersion relation and the structure function.

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The nonequilibrium dynamics of an homogeneous scalar field is studied using Langevin equations. Microscopic derivations based on quantum field theory methods can lead to complicated nonlocal equations of motion. Here we study, numerically, the results obtained by appropriately approximating these equations in a local form (the Markovian approximation) and compare with results obtained with suitable prescriptions for accounting for the nonlocal terms, i.e. the non-Markovian form. We use a prescription for the nonlocal equations motivated by the results obtained from previous derivations using nonequilibrium quantum field theory methods.