Spectral Running and Non-Gaussianity from Slow-Roll Inflation in Generalised Two--Field Models

TL;DR

This work analyzes slow-roll inflation in theories with two scalar fields that are coupled both in the potential and through non-canonical kinetic terms via $e^{2b(\varphi)}$. It derives general slow-roll expressions for the running of the adiabatic, isocurvature, and cross-spectra ($\alpha_\zeta$, $\alpha_S$, $\alpha_C$) using the transfer-matrix formalism and then computes inflationary non-Gaussianity $f_{\rm NL}$ with the $\delta N$ approach, focusing on product and sum potentials. Through explicit scalar-tensor examples, notably Jordan–Brans–Dicke and BD-type models, it shows the coupling parameter controls certain slow-roll quantities but does not lead to observable enhancements in $f_{\rm NL}$ (typically $|f_{\rm NL}| \sim 1/(2N)$). Numerical analyses corroborate the analytic slow-roll results, indicating that, within the studied regimes, non-Gaussianity remains small and spectral runnings stay within observational bounds. The framework enables applying these results to broader multi-field, non-canonical inflation models and informs constraints from Planck-like data.

Abstract

Theories beyond the standard model such as string theory motivate low energy effective field theories with several scalar fields which are not only coupled through a potential but also through their kinetic terms. For such theories we derive the general formulae for the running of the spectral indices for the adiabatic, isocurvature and correlation spectra in the case of two field inflation. We also compute the expected non-Gaussianity in such models for specific forms of the potentials. We find that the coupling has little impact on the level of non-Gaussianity during inflation.

Figures (6)

• Figure 1: The spectral index ($(n_\zeta -1)/\epsilon$) and running of $n_\zeta$ and $n_C$ in terms of $\epsilon$ for model 1-a.
• Figure 2: Spectral index ($n_\zeta -1$) and running of $n_\zeta$ and $n_C$ for model 2-a. We used $\beta=0.1\epsilon$ here.
• Figure 3: Running of $n_S$ for Models 1 and 2. $\alpha_S$ is independent of $\Delta$.
• Figure 4: Spectral index ($n_\zeta -1$) and running of $n_\zeta$ and $n_C$ in terms of $\epsilon$ for model 3. Values of $\beta=0.1\sqrt{\epsilon}$ and $r e^{-2b}=2$ have been assumed.
• Figure 5: Running of $n_S$ for Models 3 and 4. $\alpha_S$ is independent of $\Delta$.