Natural inflation from polymer quantization

Abstract

We study the polymer quantization of a homogeneous massive scalar field in the early universe using a prescription inequivalent to those previously appearing in the literature. Specifically, we assume a Hilbert space for which the scalar field momentum is well defined but its amplitude is not. This is closer in spirit to the quantization scheme of loop quantum gravity, in which no unique configuration operator exists. We show that in the semi-classical approximation, the main effect of this polymer quantization scheme is to compactify the phase space of chaotic inflation in the field amplitude direction. This gives rise to an effective scalar potential closely resembling that of hybrid natural inflation. Unlike polymer schemes in which the scalar field amplitude is well-defined, the semi-classical dynamics involves a past cosmological singularity; i.e., this approach does not mitigate the big bang. arXiv:1709.03960v3 [gr-qc]

Semiclassical cosmology with backreaction: The Friedmann-Schrödinger equation and inflation

“…Among these, with specific application to cosmology, is one that uses a fixed quantum state to compute the expectation value of the matter Hamiltonian. This "effective" Hamiltonian is then used in the Hamiltonian constraint to derive a modified classical dynamics [14][15][16];…”

Low Energy Consequences of Loop Quantum Gravity

“…The polymer quantization has been motivated from loop quantum gravity [1,2]. In fact, the polymer quantization of simple matter fields has been studied and the conclusions reached resemble the conclusions obtained in loop quantum gravity [3,4]. It has been demonstrated that the polymer quantization leads to radiation in inertial frames [5], and a modification of black body radiation at high temperatures [6].…”

“…We start by analyzing the effect polymer quantization would have on the Heisenberg algebra. It is known that in the polymer quantization, the usual phase space (x, p) can be replaced by [3,4] x…”

“…Now, as polymer quantization, and the modification of quantum mechanics by string theory, lead to the same first order corrections to the Heisenberg algebra, it can be argued that like string length scale, polymer length scale can also be several orders of magnitude larger than the Planck scale. In fact, it is possible that in nature two polymer scales exist, such that one of them is the gravitational polymer scale µ gr , and the other is the polymer scale for matter fields µ (as polymer quantization of matter fields has also been studied [3,4]), such that µ gr = gµ, where g is some coupling in a more fundamental theory. Under this similarity, it is possible to analyze physical consequences of polymer quantization on condensed matter systems in similar way to those of generalized uncertainty principle on such low energy system [8][9][10][11].…”