The Ultra Slow-Roll Phase Of Warm Inflation In Braneworld Cosmology

TL;DR

The paper analyzes ultra slow-roll (USR) dynamics in warm inflation embedded within RS-II and DGP braneworld cosmologies. By deriving modified slow-roll parameters $\epsilon_1$ and $\epsilon_2$, the e-fold count $N_e$, and the curvature power spectrum $P$, and by numerically evolving linear and cubic potentials, it shows that brane-induced high-energy corrections are largely suppressed during USR, leaving the dynamics effectively four-dimensional. The results indicate that USR warm inflation is robust to braneworld modifications, with brane terms fading as the USR condition tightens, while dissipative effects shape the spectrum more than brane tension. This robustness simplifies phenomenological predictions and motivates future work on Gauss-Bonnet extensions and PBH/non-Gaussian analyses within USR scenarios.

Abstract

Slow-roll of the inflaton (inflationary field) defines the standard dynamics of the inflationary epoch. However, the inflaton deviates from slow-roll when it encounters an extremely flat region in the inflationary potential, and enters a phase dubbed Ultra Slow Roll (USR). In previous studies, there have been various theories which modify the theory of general relativity, all of them having different motivations based on different paradigms. Among these, braneworld gravity, motivated from string theory; is one of the most prominent theories as it provides a geometrical explanation for the weakness of gravity. In this article, we explore two possible braneworld background theories, the Randall-Sundrum (RS-II) model and the Dvali-Gabadadze-Porratai (DGP) model, and then realize an USR phase in a particularly interesting inflationary scenario, called warm inflation. In the warm inflationary scenario, a thermal radiation bath coexists with the inflationary energy density as an effect of the dissipative dynamics. We then derive inflationary slow roll parameters and the primordial power spectrum of scalar curvature perturbations in such a setup. We then numerically investigate the evolution of the inflaton and the primordial power spectrum of scalar curvature perturbations. Our analysis shows that the braneworld contributions become progressively suppressed as the USR conditions are made more stringent, indicating that the USR phase effectively diminishes brane-induced corrections to standard inflationary dynamics.

Figures (1)

• Figure 1: Comparison of inflaton evolution and primordial power spectra for linearized and cubic potentials under different values of $M$. Each subplot illustrates the dependence of the inflaton field $\phi$ and the primordial power spectrum $P$ on dissipation, brane tension, and dark radiation parameters.