Dynamically generated inflation from non-Riemannian volume forms

D Benisty,S Pacheva,E I Guendelman,E Nissimov

doi:10.1140/epjc/s10052-019-7310-6

Abstract

We propose a simple modified gravity model without any initial matter fields in terms of several alternative non-Riemannian spacetime volume elements within the metric (second order) formalism. We show how the non-Riemannian volume-elements, when passing to the physical Einstein frame, create a canonical scalar field and produce dynamically a non-trivial inflationary-type potential for the latter with a large flat region and a stable low-lying minimum. We study the evolution of the cosmological solutions from the point of view of theory of dynamical systems. The theory predicts the spectral index n_s approx 0.96 and the tensor-to-scalar ratio r approx 0.002 for 60 e-folds, which is in accordance with the observational data. In the future Euclid and SPHEREx missions or the BICEP3 experiment are expected to provide experimental evidence to test those predictions.

Highlights

Planck units) cosmological constant of the present universe, is required.In a parallel development, extended gravity theories as alternatives/generalizations of the standard Einstein General Relativity are being extensively studied in the last decade or so
We propose a simple modified gravity model without any initial matter fields in terms of several alternative non-Riemannian spacetime volume elements within the metric formalism
We show how the nonRiemannian volume-elements, when passing to the physical Einstein frame, create a canonical scalar field and produce dynamically a non-trivial inflationary-type potential for the latter with a large flat region and a stable low-lying minimum

Summary

Introduction

Planck units) cosmological constant of the present universe, is required. In a parallel development, extended (modified) gravity theories as alternatives/generalizations of the standard Einstein General Relativity are being extensively studied in the last decade or so. Riemannian volume-elements, when passing to the physical Einstein frame, generate a canonical scalar field u and manage to create dynamically a non-trivial inflationary-type potential for u with a large flat region for large positive u and a stable low-lying minimum, i.e., u will play the role of a dynamically created “inflaton”. This dynamically generated inflationary potential turns out to be a generalization of the well-known Starobinsky potential [1]. 4 we propose our simple modified gravity model in terms of several non-Riemannian volume elements without any matter fields and derive the corresponding Einsteinframe description with the associated dynamical creation of a canonical scalar field with a non-trivial effective inflationary potential. Levi-Civita one in terms of gμν, there is no torsion, etc

The action

Einstein Frame: the Effective Scalar Potential

Evolution of the homogeneous solution

Perturbations

Conclusions