The Cosmological Constant as a Function of Extrinsic Curvature and Spatial Curvature

TL;DR

This paper proposes a model where the cosmological constant varies with extrinsic and spatial curvature, leading to new insights into dark energy and universe expansion consistent with observations.

Contribution

It introduces a novel approach where the cosmological constant depends on extrinsic and spatial curvature, challenging the notion of a constant dark energy component.

Findings

Models fit observational data of dark energy.

Cosmological constant can evolve with universe expansion.

Gradual change of the cosmological constant aligns with observations.

Abstract

In this paper we suppose that the cosmological constant will change when the universe expends. For a general consideration, the cosmological constant is assumed to be a function of scale factor and Hubble constant. According to the ADM formulation, to the FRW metric, the extrinsic curvature $I$ equals $-6H^{2}$ and spatial curvature $R$ equals $6k/a^{2}$. Therefore we suppose cosmological constant is a function of extrinsic curvature and spatial curvature. We investigate the cosmological evolution of FRW universe in these models. At last we investigate two particular models which could fit the observation data about dark energy well. Actually a changeless cosmological constant is not essential. If when the universe expands, the cosmological constant changes slowly and gradually flows to a constant, the observation data about dark energy could also be fitted well by this kind of theory.