Constraints on polynomial inflation under power-law perturbations

We investigate perturbations in power-law monomial potentials within inflationary models driven by a single scalar field. By introducing a second term to the original potential, we study how this perturbation influences the slow-roll parameters and analyze the consequent changes in the spectral index, $n_s$, and the tensor-to-scalar ratio, $r$, treating the additional term as a correction to the monomial case. Comparing our numerical results with current cosmological data from the Planck satellite observations on $n_s$, $r$, and the clustering parameter, $σ_8$, we place significant constraints on the free parameter of our class of inflationary potentials. We found that the perturbative consistency method we analyze could be an interesting test to explore for more complex inflationary models, looking for features that better match the data that might highlight fundamental physics implications.

💡 Research Summary

The paper investigates how small polynomial corrections to the classic monomial inflaton potential affect observable inflationary parameters. Starting from the well‑studied single‑field slow‑roll framework, the authors first review the monomial case (V(\phi)=\alpha M_{\rm Pl}^4\tilde\phi^{,n}). They derive the standard slow‑roll parameters (\epsilon_V=n^2/(2\tilde\phi^2)) and (\eta_V=n(n-1)/\tilde\phi^2), obtain the field value at the end of inflation (\tilde\phi_e=n\sqrt{2}), and express the field at horizon crossing (\tilde\phi_) in terms of the number of e‑folds (N_). Using the relations (n_s-1=-6\epsilon_V+2\eta_V) and (r=16\epsilon_V), they find (n_s-1=-n(n+2)/\tilde\phi_^2) and (r=8n^2/\tilde\phi_^2). By normalising the scalar power spectrum to the Planck amplitude they fix (\alpha) as a function of (n). The monomial analysis reproduces the well‑known result that linear ((n=1)) and quadratic ((n=2)) potentials lie near the Planck 2018 contours for (N_*\sim55), but the tensor‑to‑scalar ratio constraint ((r\lesssim0.07) at 95 % C.L.) disfavors higher‑order monomials unless the number of e‑folds is unusually low.

The core of the work introduces a second term, treating the inflaton potential as a binomial \