Dynamically generated inflationary two-field potential via non-Riemannian volume forms

Abstract

We consider a simple model of modified gravity interacting with a single scalar field φ with weakly coupled exponential potential within the framework of non-Riemannian spacetime volume-form formalism. The specific form of the action is fixed by the requirement of invariance under global Weyl-scale symmetry. Upon passing to the physical Einstein frame we show how the non-Riemannian volume elements create a second canonical scalar field u and dynamically generate a non-trivial two-scalar-field potential $U_{\mathrm{eff}}(u,\phi )$ with two remarkable features: (i) it possesses a large flat region for large u describing a slow-roll inflation; (ii) it has a stable low-lying minimum w.r.t. $(u,\phi )$ representing the dark energy density in the “late universe”. We study the corresponding two-field slow-roll inflation and show that the pertinent slow-roll inflationary curve $\phi =\phi (u)$ in the two-field space $(u,\phi )$ has a very small curvature, i.e., φ changes very little during the inflationary evolution of u on the flat region of $U_{\mathrm{eff}}(u,\phi )$. Explicit expressions are found for the slow-roll parameters which differ from those in the single-field inflationary counterpart. Numerical solutions for the scalar spectral index and the tensor-to-scalar ratio are derived agreeing with the observational data.