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Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalism of non-Riemannian spacetime volume-elements. The non-Riemannian volume element in the initial scalar field action leads to a hidden, nonlinear Noether symmetry which produces an energy-momentum tensor identified as the sum of a dynamically generated cosmological constant and dust-like dark matter. The non-Riemannian volume-element in the initial Einstein–Hilbert action upon passage to the physical Einstein-frame creates, dynamically, a second scalar field with a non-trivial inflationary potential and with an additional interaction with the dynamically generated dark matter. The resulting Einstein-frame action describes a fully dynamically generated inflationary model coupled to dark matter. Numerical results for observables such as the scalar power spectral index and the tensor-to-scalar ratio conform to the latest 2018 PLANCK data.
First, we propose a scale-invariant modified gravity interacting with a neutral scalar inflaton and a Higgs-like SU(2)×U(1) iso-doublet scalar field based on the formalism of non-Riemannian (metric-independent) spacetime volume-elements. This model describes, in the physical Einstein frame, a quintessential inflationary scenario driven by the “inflaton” together with the gravity-“inflaton” assisted dynamical spontaneous SU(2)×U(1) symmetry breaking in the post-inflationary universe, whereas the SU(2)×U(1) symmetry remains intact in the inflationary epoch. Next, we find the explicit representation of the latter quintessential inflationary model with a dynamical Higgs effect as an Eddington-type purely affine gravity.
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.