Abstract
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.
Highlights
The main motivation for these developments was to overcome the limitations of the latter coming from: (i) cosmology—for solving the problems of dark energy and dark matter and explaining the large scale structure of the Universe [1–3]; (ii) quantum field theory in curved spacetime—because of the non-renormalizabilty of ultraviolet divergences in higher loops [4–9]; (iii) modern string theory—because of the natural appearance of higher-order curvature invariants and scalar-tensor couplings in low-energy effective field theories [10–14]. Another parallel crucial development is the emergence of the theoretical framework based on the concept of "inflation," which is a necessary part of the standard model of cosmology, since it provides the solution to the fundamental puzzles of the old Big Bang theory, such as the horizon, the flatness and the monopole problems [15–22]
A simple exponential potential does not comply with the above picture, here we present a simple modified gravity model naturally providing a dynamically generated scalar potential, whose inflationary dynamics are compatible with the recent observational data
In the present paper, starting from the basic first principle of Lagrangian field-theoretic actions combined with a non-canonical modification of gravity via employing non-Riemannian spacetime volume forms as alternatives to the standard Riemannian one given by − g, we have constructed a unified model of dynamically generated inflation with dark energy and dark matter coupled among themselves
Summary
In the last decade or so, a groundbreaking concept emerged regarding the intrinsic necessity to modify (extend) gravity theories beyond the framework of the norm—Einstein’s general relativity. In the present paper our principal aim is to construct a plausible unified model, i.e., describing (most of the) principal physical manifestations of a unification of inflation and dark energy interacting with dark matter, where the formalism of the non-Riemannian spacetime volume-elements will play a fundamental role.
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