Single-field slow roll inflation (please refer note below, if you dont know about slow roll inflation) is a compelling solution to the difficulties of standard Big Bang cosmology and provides a natural explanation for the primordial perturbations observed in Cosmic Microwave Background (CMB) anisotropies. However, it has challenges such as the generation of radiative corrections to the potential by generic Planck-suppressed operators which give rise to a “flatness problem”. We can avoid these corrections if the inflaton is a pseudo-Nambu-Goldstone boson (pNGB) that enjoys a weakly-broken shift symmetry. As a result, such a pNGB (henceforth axion) provides an elegant candidate for the inflaton.

But, although the use of an axion as the inflation avoids the issues of radiative corrections to the potential, it has other implications for the dynamics of inflation. Like, the inflation generally couples to gauge sector and such a coupling generates a thermal bath during inflation, which can significantly alter the predictions of inflation. And thats what is shown by William DeRocco and colleagues in their recent paper.

“As the axion slow-rolls during inflation, this coupling can cause the production of a non-diluting thermal bath, a situation known as “warm inflation.” This thermal bath can dramatically alter inflationary dynamics and observable predictions.”

— they said.

They demonstrated that, this bath is an attractor solution in significant parts of axion inflation parameter space and in those regions, axion inflation will generate the bath for a wide variety of initial conditions, including starting from zero initial temperature in the universe means if inflation begins in a vacuum.

“In other words, for those parts of inflation model parameter space, the presence of thermal bath is not optional and thermal effects can not be neglected when accessing the viability of an axion inflation model.”

— they said.

They added that the coupling to gauge group must be very weak i.e. f ≳ 10^{15} GeV; in order to remain safely in a cold inflationary regime, though this limit is modified in the presence of light fermions.

Furthermore, they found that, axion inflation becomes warm over a large range of couplings, and explicitly map the parameter space for two axion inflation potentials: one for the pure gauge case (as shown in fig 1 & 2) and second for light fermions case (as shown in fig 3 and 4).

Finally, it has been concluded that, in large regions of parameter space, “cold” axion inflation models are often warmer than one might expect.

**Note**: The most straightforward theories of inflation assume there exists some scalar field ϕ that permeates the Universe and drives inflation. Over time this scalar field changes, and the rate of change is given by ϕ˙. There is also some “potential energy” associated with the scalar field, which is given by some function V(ϕ). The specific functional form of V(ϕ) is given by whatever theory of inflation that a theorist has postulated. The “slow roll approximation” simply states that ϕ˙≪V(ϕ)ϕ˙≪V(ϕ). In other words, the “kinetic energy” of the field is negligible compared to the “potential energy” of the field. Under this assumption, it is possible to show that the equation of motion of the expansion of the Universe leads to approximately exponential expansion, i.e., inflation. The slow roll approximation simplifies the equations of motion and guarantees that inflation will occur.

**Reference***: William DeRocco, Peter W. Graham, and Saarik Kalia, “Warming up cold inflation”, Arxiv, pp. 1-14, 2021. **arXiv:2107.07517*

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