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

## TL;DR

This paper presents a modified gravity model with a non-Riemannian volume form that naturally generates a two-field inflationary potential, leading to slow-roll inflation consistent with observations and a stable dark energy minimum.

## Contribution

It introduces a novel two-scalar-field potential derived from non-Riemannian volume forms, unifying inflation and dark energy within a single framework.

## Key findings

- The model produces a large flat inflationary region with slow-roll behavior.
- Numerical results for spectral index and tensor-to-scalar ratio match observational data.
- The potential has a stable minimum corresponding to dark energy.

## Abstract

We consider a simple model of modified gravity interacting with a single scalar field $\varphi$ 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 $U_{\rm eff}(u,\varphi)$ 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. $(u,\varphi)$ 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 $\varphi = \varphi(u)$ in the two-field space $(u,\varphi)$ has a very small curvature, i.e., $\varphi$ changes very little during the inflationary evolution of $u$ on the flat region of $U_{\rm eff}(u,\varphi)$. 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.