Quantum Cosmology via Quantization of Point-Like Lagrangian

TL;DR

This paper introduces a novel approach to quantum cosmology by quantizing a classical point-like Lagrangian, applied to various gravity theories, revealing the importance of a positive cosmological constant and potential inflation explanations.

Contribution

It proposes a new method of studying quantum cosmology through classical point-like Lagrangian quantization, differing from traditional minisuperspace models.

Findings

The cosmological constant is essential and positive.

Exact solutions suggest inflation can be explained quantum mechanically.

The approach is applicable to Einstein, cosmological constant, and $f(R)$-gravity.

Abstract

The purpose of this paper is to introduce a new way to inquire the quantum cosmology for a certain gravitational theory. Normally, the quantum cosmological model is introduced as the minisuperspace theory which is obtained by reducing the superspace where the Wheel-DeWitt equation is defined on using the symmetry provided by cosmological principle. Unlike that, the key of our approach is to reinterpret the cosmology in a classical dynamical way using a point-like Lagrangian and then quantize the point-like model. We apply the method into Einstein gravity, gravity with a cosmological constant and the $f(R)$-gravity, and get their wave equations respectively. By analsysing the exact solution for the quantum cosmology with and without a cosmological constant we demonstrate that the cosmological constant is essential and being a tiny positive number. We also show the possibility of explaining inflation under the quantum version of cosmology.