Non-parametric reconstruction of an inflaton potential from Einstein–Cartan–Sciama–Kibble gravity with particle production

Shantanu Desai,Nikodem J Popławski

doi:10.1016/j.physletb.2016.02.014

Shantanu Desai, Nikodem J Popławski

Open Access

https://doi.org/10.1016/j.physletb.2016.02.014

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Abstract

The coupling between spin and torsion in the Einstein-Cartan-Sciama-Kibble theory of gravity generates gravitational repulsion at very high densities, which prevents a singularity in a black hole and may create there a new universe. We show that quantum particle production in such a universe near the last bounce, which represents the Big Bang gives the dynamics that solves the horizon, flatness, and homogeneity problems in cosmology. For a particular range of the particle production coefficient, we obtain a nearly constant Hubble parameter that gives an exponential expansion of the universe with more than 60 $e$-folds, which lasts about $\sim 10^{-42}$ s. This scenario can thus explain cosmic inflation without requiring a fundamental scalar field and reheating. From the obtained time dependence of the scale factor, we follow the prescription of Ellis and Madsen to reconstruct in a non-parametric way a scalar field potential which gives the same dynamics of the early universe. This potential gives the slow-roll parameters of cosmic inflation, from which we calculate the tensor-to-scalar ratio, the scalar spectral index of density perturbations, and its running as functions of the production coefficient. We find that these quantities do not significantly depend on the scale factor at the Big Bounce. Our predictions for these quantities are consistent with the Planck 2015 observations.

Highlights

It has been known since the 1970s that the standard hot Big Bang model suffers from the horizon, flatness, and homogeneity problems [1] and there must be another dynamical mechanism prior to Big Bang nucleosynthesis to alleviate these problems
The most widely accepted solution to these problems is the process of cosmic inflation, which is a brief period of exponential expansion, where the Universe is temporarily in a de Sitter phase dominated by the vacuum energy [2,3,4,5,6,7]
Most of the generic models of cosmic inflation are usually due to scalar field in the slow-roll approximation, where potential energy of the field dominates over its kinetic energy

Summary

Introduction

It has been known since the 1970s that the standard hot Big Bang model suffers from the horizon, flatness, and homogeneity problems [1] and there must be another dynamical mechanism prior to Big Bang nucleosynthesis to alleviate these problems. The basic predictions of single scalar field slow-roll inflation models, such as flatness, super-horizon correlations, adiabatic density perturbations, nearly scale-invariant spectrum of curvature perturbations, and no observable non-gaussianity, have been verified by the Cosmic Microwave Background (CMB) observations from Planck and WMAP [9,10,11]. Inflation provides a mechanism to seed the density perturbations which give rise to the observed structure in the universe Despite these predictions, many concerns have been raised about conceptual problems with models of inflation based on single-field scalar potentials [12]. Torsion provides the simplest and most natural mechanism that solves the singularity problem of the standard Big Bang cosmology. In order to make predictions for observables such as the tensor-to-scalar ratio and scalar spectral index of density fluctuations, we reconstruct a dynamically equivalent single-field scalar potential from the time dependence of the scale factor calculated in our model. We briefly discuss some other models of inflation based upon torsion and compare them with our approach

Universe in a black hole with torsion

Inflationary dynamics

Sensitivity to initial conditions

Other models of inflation with spin

Conclusions