Breaking the degeneracy of non-canonical quartic inflation by reheating considerations

Here, the quartic inflationary potential $V(\phi )=\frac{\lambda }{4}{\phi }^4$ within a non-canonical framework characterized by a power-law Lagrangian is investigated. We demonstrate that the predictions of this model align with the Planck 2018 observational data. We explore how the predictions of the model depend on the non-canonical parameter $\alpha$ and the number of $e$-folds $N$. Notably, the sound speed, non-Gaussianity parameter, scalar spectral index, and tensor-to-scalar ratio are all affected by variations in $\alpha$. However, the scalar spectral index exhibits a degeneracy with respect to variation in $\alpha$, which can be broken by incorporating reheating consideration. By applying a combination of theoretical and observational constraints on $(r-n_{\mathrm{s}})$, non-Gaussianity, and reheating parameters, we find that the duration of inflation is constrained to the range $55\le N\le 55.7$ $e$-folds for $60\le \alpha \le 130$. Finally, we investigate relic gravitational waves and demonstrate that their energy density spectrum falls within the sensitivity range of gravitational waves detectors for this constrained range of $e$-folds.