We present a numerical integration of the cosmological scalar perturbation equations in warm inflation. The initial conditions are provided by a discussion of the thermal fluctuations of an inflaton field and thermal radiation using a combination of thermal field theory and thermodynamics. The perturbation equations include the effects of a damping coefficient $\Gamma$ and a thermodynamic potential V. We give an analytic expression for the spectral index of scalar fluctuations in terms of a new slow-roll parameter constructed from $\Gamma .$ A series of toy models, inspired by spontaneous symmetry breaking and a known form of the damping coefficient, lead to a spectrum with $n_s>1\mathrm{}$ on large scales and $n_s<1\mathrm{}$ on small scales.

We show that inflation can naturally occur at a finite temperature $T>H$ that is sustained by dissipative effects, when the inflaton field corresponds to a pseudo Nambu-Goldstone boson of a broken gauge symmetry. Similar to the Little Higgs scenarios for electroweak symmetry breaking, the flatness of the inflaton potential is protected against both quadratic divergences and the leading thermal corrections. We show that, nevertheless, nonlocal dissipative effects are naturally present and are able to sustain a nearly thermal bath of light particles despite the accelerated expansion of the Universe. As an example, we discuss the dynamics of chaotic warm inflation with a quartic potential and show that the associated observational predictions are in very good agreement with the latest Planck results. This model constitutes the first realization of warm inflation requiring only a small number of fields; in particular, the inflaton is directly coupled to just two light fields.

We investigate the phenomenology of warm inflation and present generic results about the evolution of the inflaton and radiation fields. The general conditions required for warm inflation to take place are derived and discussed. A comprehensive approach is presented for the generation of thermally induced adiabatic and isocurvature perturbations and the amplitude of their spectra calculated. In addition we derive the ratio of tensor-to-scalar perturbations and find the spectral indices for adiabatic, isocurvature and tensor perturbations formed in the warm inflationary era. These results are presented in a simplified and compact approach that is generally applicable. Our results are illustrated by inflation models with polynomial and exponential potentials. We compare our analytic results against numerical models and find excellent agreement. Finally, presently available data are used to put constraints on warm inflation and we discuss how near-future observations may distinguish the warm inflationary scenario from standard supercooled inflation. The main observable difference is the different scalar-to-tensor ratio, and that the consistency relation between this and the slope of tensor perturbations does not hold for warm inflation.

The implications of the recently proposed trans-Planckian censorship conjecture (TCC) are analyzed in the context of warm inflation. It is found that for a single-stage accelerated expansion the constraints imposed by the censorship are roughly the same as for cold inflation. Next, we study how a two-stage inflationary expansion with an intermediate radiation-dominated era can alleviate the bounds imposed by the censorship. For a demonstrative toy model we found $r<{10}^{-23}$, but can be $r<{10}^{-5}$ for a weaker form of TCC for the later stages of expansion, while still satisfying the other swampland conditions.

In the past decade, the importance of dissipation and fluctuation to inflationary dynamics has been realized and has led to a new picture of inflation called warm inflation. Although these phenomena are common to condensed matter systems, for inflation models their importance has only recently started to be appreciated. The article describes the motivation for these phenomena during inflation and then examines their origins from first principles quantum field theory treatments of inflation models. Cosmology today is a data intensive field and this is driving theory to greater precision and predictability. This opens the possibility to consider tests for detecting observational signatures of dissipative processes, which will be discussed. In addition, it will be discussed how particle physics and cosmology are now working in tandem to push the boundaries of our knowledge about fundamental physics.