- 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 Ueff(u,ϕ) 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,ϕ) 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 ϕ = ϕ(u) in the two-field space (u,ϕ) has a very small curvature, i.e., ϕ changes very little during the inflationary evolution of u on the flat region of Ueff(u,ϕ). 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.
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