Quantized Cosmology

TL;DR

This paper presents a quantization approach to cosmology that modifies the Friedmann equation with quantum corrections, potentially impacting observable cosmic microwave background anisotropies and offering insights into inflation.

Contribution

It introduces a novel quantization method that preserves classical equations as quantum operators and reveals significant quantum corrections to the Friedmann equation.

Findings

Quantum correction to Friedmann equation significant at small scale factors

Potential observable effects on cosmic microwave background anisotropies

Framework applicable to studying chaotic and eternal inflation

Abstract

This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, one can quantize the problem in a way which parallels the classical discussion. The result is that two of the Einstein equations arise as exact equations of motion and one of the usual Einstein equations (suitably quantized) survives as a constraint equation to be imposed on the space of physical states. However, the Friedmann equation, which is also a constraint equation and which is the basis of the Wheeler-DeWitt equation, acquires a welcome quantum correction that becomes significant for small scale factors. We discuss the extension of this result to a full quantum mechanical derivation of the anisotropy ($\delta \rho /\rho$) in the cosmic microwave background radiation, and the possibility that the extra term in the Friedmann equation could have observable consequences. Finally, we suggest interesting ways in which these techniques can be generalized to cast light on the question of chaotic or eternal inflation. In particular, we suggest one can put an experimental lower bound on the distance to a universe with a scale factor very different from our own, by looking at its effects on our CMB radiation.