A Canonical Quantization formalism of curvature squared action

TL;DR

This paper develops a canonical quantization approach for a curvature squared gravitational action, deriving a Wheeler-de Witt equation solution consistent with General Relativity and revealing quantum effects in the universe's wave function.

Contribution

It introduces a novel canonical quantization formalism for curvature squared actions using auxiliary variables, leading to a Wheeler-de Witt equation with solutions compatible with GR.

Findings

Wave function of the universe exhibits quantum effects.

Solution yields a decaying cosmological constant.

Calculated CBR temperature of 2.7K.

Abstract

The generalized Einstein action is treated quantum mechanically by using a quadratic lagrangian form. The canonical quantization of this action is obtained by using the auxiliary variable to define the generalized momentum. Physical constraints are imposed on the surface term, which is defined to be the cosmological constant. One obtains the familiar Wheeler-de Witt equation. The solution of this equation is in conformity with General Relativity (GR) .In addition to the fact that it is free from GR setbacks at the early universe, since it gives time decaying cosmological constant. The wave function of the universe and the cosmic scale factor are complex quantities, which indicates the existance of quantum effects.2.7k, CBR temperature is calculated.