Preinflation with variable timescale and negative spatial curvature: Imprints of the ln(K)-spectrum on astrophysical scales

Abstract

In this work we propose a preinflationary model that describes the birth of the universe with nonzero spatial curvature, variable timescale and an initially null background energy density. We demonstrate that the spatial curvature must be negative k=−H02, in order for the equation of state can agree with recent CMBR observations ω̄=−1.03±0.04 (Workmanet et al. 2022). The field that drives the expansion of the universe and complies with such conditions is a phantom scalar field with negative kinetic energy density. In this model the cosmological parameter is given by the expectation value of the flow the field σˆ,μ, σ-being the geometric response to the quantum fluctuations of the phantom field. The ln(K)-spectrum of the varied scalar curvature and the anisotropies of the varied tensor metric fluctuations: δRˆK(xα) and δgˆ0i(K,xα), are studied for astrophysical scales.