Exploring Cosmological Implications of the Modified Raychaudhuri Equation in Non-Gravitating Vacuum Energy Theory

TL;DR

This paper explores how the modified Raychaudhuri Equation within Non-Gravitating Vacuum Energy theory affects cosmological models, revealing new geometric structures and scalar field solutions in a flat FLRW universe.

Contribution

It introduces a novel geometric framework based on NGVE theory and formulates modified cosmological models with scalar fields, expanding understanding of universe dynamics.

Findings

Derived scalar field solutions for exponential and power-law scale factors.

Analyzed the behavior of interaction terms in the modified Raychaudhuri Equation.

Studied caustic solutions and focusing theorem in the NGVE context.

Abstract

This article investigates the modified Raychaudhuri Equation (RE) in the context of Non-Gravitating Vacuum Energy (NGVE) theory and its implications for various cosmological characteristics. The equation is formulated based on the NGVE framework, in which global scale invariance generates a unique geometry. The newly developed geometry introduces a metric that is conformally connected to the conventional metric, with the conformal factor dependent on scalar field potentials. The cosmological study is carried out under the framework of a flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. Assuming matter behaves as an ideal fluid in the modified geometry, we formulate models for conditional expansion, collapse, and steady state, governed by the scalar field ($\phi$). In this context, the caustic solution and the focusing theorem are also studied. Scalar field solutions for exponential and power-law scale factors are also derived using NGVE theory's equations of motion. Finally, graphical analysis is used to investigate the behavior of the interaction terms that appear in the modified RE under these scale factors.