$\Lambda$CDM cosmology with a quiescent anisotropy in a higher dimensional steady state universe

TL;DR

This paper explores a higher-dimensional steady state universe model, showing how internal space dynamics influence observable anisotropy, and suggests it could explain the lower-than-expected CMB quadrupole fluctuations.

Contribution

It demonstrates that a higher-dimensional negative cosmological constant can produce effects similar to a positive cosmological constant and anisotropy in a $ ext{Lambda}$CDM framework, offering new insights.

Findings

Exact Friedmann equations match standard $ ext{Lambda}$CDM

Higher-dimensional effects mimic dark energy and anisotropy

Potential explanation for low CMB quadrupole fluctuations

Abstract

In this work, which follows a series of studies on the higher-dimensional steady state universe idea and prepared for Professor Tekin Dereli's Festschrift, we show the influence of the dynamical internal (unobservable) space on the evolution of the possible anisotropy of the external (observable) space. We obtain mathematically exactly the same Friedmann equation of the standard $\Lambda$CDM model for the external space, but with some remarkable physical differences. In particular, the higher-dimensional negative cosmological constant plays the role of the four-dimensional positive cosmological constant and the expansion anisotropy, viz., the shear scalar, of the external space mimics a negative cosmological constant; it would mimic a stiff fluid when allowed on top of the standard $\Lambda$CDM model. This latter feature gives us the opportunity to manipulate the CMB quadrupole temperature fluctuation, suggesting a possible answer to the fact that its observed value is lower than that predicted by the standard $\Lambda$CDM model.