Reheating and relic gravitational waves as remedies for degeneracies of non-canonical natural inflation

Abstract

Here, a natural non-canonical inflationary model based on a power-law Lagrangian is investigated. We analyze the scalar spectral index $n_{\mathrm{s}}$ and the tensor-to-scalar ratio $r$ of the model and identify their degeneracies with respect to the free parameters. Notably, $n_{\mathrm{s}}$ and $r$ show effective independence from the model parameters due to degeneracies in the slow-roll parameters that leads to unresolved parameter degeneracies. Employing the constraints on reheating parameters such as the reheating duration $N_{\mathrm{reh}}$, the reheating temperature $T_{\mathrm{reh}}$, and the equation of state parameter ${\omega }_{\mathrm{reh}}$, is found to be insufficient to fully break these degeneracies. However, the relic gravitational wave spectrum provides a way to break degeneracy with respect to the non-canonical parameter $\alpha$, degeneracy with respect to the potential parameter $f$ persist. Finally, we specify the allowed ranges for the inflationary duration $N$ and the parameter $\alpha$, in light of the latest observational data. These results highlight the role of relic gravitational waves in refining inflationary models and illustrate the challenges in fully resolving parameter degeneracies.

24 pages, 6 figures, 2 tables

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