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