Probing single-field inflation: predictions, constraints, and theoretical viewpoints

TL;DR

This work studies a single-field inflation model within the K-essence framework by introducing a coupling $\alpha$ between the canonical Lagrangian and the potential. Through both numerical analyses and analytical expansions for two representative potentials $V(\phi)=\tfrac{1}{2}m^{2}\phi^{2/5}$ and $V(\phi)=\tfrac{1}{2}M^{2}\phi$, the authors show that the coupling modifies the slow-roll dynamics and lowers the tensor-to-scalar ratio $r$ while producing $n_s$ values compatible with Planck and BK observations. They derive explicit analytical expressions for $N(\phi)$, $r$, and $n_s$ as series in small parameters $\beta=\alpha m^{2}/2$ and $\tilde{\beta}=\alpha M^{2}/2$, and identify ranges of these parameters that satisfy observational constraints. The results suggest that the $\alpha$-coupled model provides a viable extension to canonical single-field inflation, achieving consistency with current cosmological data and offering a testable alternative for early-universe dynamics.

Abstract

This work investigates a single-field inflationary model, a specific class of the K-essence models where a coupling term exists between canonical Lagrangian and the potential. This coupling term has many effects on key inflationary parameters consisting of the power spectral, the spectral index, the tensor-to-scalar ratio, the Hubble parameter, the equation of state parameter, and the slow-roll parameter. By solving the equations numerically and deriving analytical results, how this modification affects inflationary dynamics can be analyzed. Our results show that the coupling term, $α$, decreases the inflationary parameters, such as the tensor-to-scalar ratio, $r$, and improves the consistency with observational constraints from Planck and BICEP/Keck at the $68 \%$ and $95 \%$ confidence. These findings indicate that the studied model provides a promising alternative to the early universe dynamics while aligning with recent cosmological observations.

Figures (12)

• Figure 1: The evolution of the Hubble parameter as a function of the number of e-folds for $V(\phi) \sim \phi^{n}$, $N= 60$, $\beta = 0.212$ and $\tilde{\beta} = 0.031$.
• Figure 2: The evolution of the power spectrum of curvature and tensor perturbations as a function of the number of e-folds for $V(\phi)=\phi^{2/5}$, $N= 60$ and $\beta = 0.212$
• Figure 3: The evolution of the power spectrum of curvature and tensor perturbations as a function of the number of e-folds for $V(\phi)=\phi$, $N=60$ and $\tilde{\beta} = 0.031$.
• Figure 4: The evolution of the power spectrum of curvature using the slow-roll approximation and solving the Mukhanov-Sasaki equation numerically as a function of the number of e-folds for $V(\phi)=\phi^{2/5}$, $N= 60$ and $\beta = 0.212$
• Figure 5: The evolution of the power spectrum of curvature using the slow-roll approximation and solving the Mukhanov-Sasaki equation numerically as a function of the number of e-folds for $V(\phi)=\phi$, $N=60$ and $\tilde{\beta} = 0.031$.