A Low Matter Density Decaying Vacuum Cosmology from Complex Metric

TL;DR

This paper proposes a cosmological model where the universe's radius is a complex quantity, leading to a decaying vacuum scenario that addresses key cosmological problems and aligns with observational bounds.

Contribution

It introduces a novel complex metric approach to cosmology, deriving a scale factor that avoids singularities and solves classical cosmological issues.

Findings

The model predicts a finite initial radius comparable to the Planck length.

It confirms bounds on the current Hubble parameter consistent with observations.

The spacetime exhibits signature-changing properties and a peaked wave function in quantum cosmology.

Abstract

A low matter density decaying vacuum cosmology is proposed on the assumption that the universe's radius is a complex quantity \hat{R} if it is regarded as having a zero energy-momentum tensor. But we find that when the radius is real, it contains matter. Using the Einstein-Hilbert action principle, the physical scale factor R(t) =|\hat{R}| is obtained as equal to (R_0^{2} + t^{2})^{1/2} with R_0 representing the finite radius of the universe at t=0. The resulting physical picture is roughly a theoretical justification of the old Ozer-Taha model. The new model is devoid of all cosmological problems. In particular, it confirms the bounds on H_p, the present value of the Hubble parameter: 0.85 < H_p t_p < 1.91 and faces no age problem. We argue that the total energy density consists of parts corresponding to relativistic/non-relativistic matter, a positive vacuum energy and a form of matter with equation of state p_K = -(1/3) rho_K (textures or generally K-matter), and the following predictions are made for the present nonrelativistic era: Omega_{M,n.rel.} \approx 2/3, Omega_{V,n.rel.} \approx 1/3, Omega_ <<1, Omega_K \approx 1, where a parameter corresponding to K-matter is taken to be unity. It is shown that the spacetime with complex metric has signature changing properties. Using quantum cosmological considerations, it is shown that the wave function is peaked about the classical contour of evolution and the minimum radius R_0 of the nonsingular model is predicted as comparable with the Planck length. PACS No(s); 98.80 Hw, 04.20, 04.60