Observational constraints on degeneracy of non-canonical inflation driven by quartic potential

Here, the quartic inflationary potential $V(\phi)=\frac{\lambda}{4}\phi^4$ in non-canonical framework with a power-law Lagrangian is investigated. We demonstrate that the predictions of this potential in non-canonical framework align with the observational data of Planck 2018. We determine how the predictions of the model vary with changes in the non-canonical parameter $\alpha$ and the number of $e$-folds $N$. The sound speed, non-Gaussianity parameter, scalar spectral index, and tensor-to-scalar ratio are all influenced by $\alpha$. However, the scalar spectral index exhibits degeneracy with respect to changes in $\alpha$. It is found that, this degeneracy does not break through reheating consideration. But the length of the reheating epoch constrains the length of the inflation period and the value of $\alpha$. Therefore, we investigate relic gravitational waves (GWs) and show that, the degeneracy of the model with respect to the $\alpha$ parameter can be broken using the relic GWs. Additionally, the density of relic GWs falls within the sensitivity range of GWs detectors for the specific $e$-folds number between 55 and 55.7.
Comment: 25 pages, 6 figures, 3 tables