Conformal cosmology with a positive effective gravitational constant

TL;DR

This paper revises conformal cosmology by applying a non-Hermitian Hamiltonian approach, resulting in a positive effective gravitational constant and a theory similar to Einstein-based cosmology.

Contribution

It demonstrates that using a non-Hermitian Hamiltonian approach resolves the negative G issue in conformal cosmology, aligning it with conventional Einstein cosmology.

Findings

Effective gravitational constant G is positive after reformulation.

The Hamiltonian spectrum is bounded below with the new approach.

The revised model closely resembles Einstein-based cosmology.

Abstract

The conformal cosmological model presented by Mannheim predicts a negative value for the effective gravitational constant, G. It also involves a scalar field, S, which is treated classically. In this paper we point out that a classical treatment of S is inappropriate, because the Hamiltonian is non-Hermitean, and the theory must be developed in the way pioneered by Bender and others. When this is done, we arrive at a Hamiltonian with an energy spectrum that is bounded below, and also a G that is positive. The resulting theory closely resembles the conventional cosmology based on Einstein relativity.