Reconstruction of $\Lambda$CDM Universe in $f(Q)$ Gravity

TL;DR

This paper reconstructs $f(Q)$ gravity models that exactly reproduce the $ ext{Lambda}$CDM cosmological expansion history, providing explicit functions and demonstrating how various FLRW cosmologies can emerge from specific $f(Q)$ theories.

Contribution

The paper introduces explicit $f(Q)$ functions that admit $ ext{Lambda}$CDM expansion and shows how to reconstruct cosmologies using $f(Q)$ gravity, including in terms of e-folding.

Findings

Derived explicit $f(Q)$ functions matching $ ext{Lambda}$CDM.

Reconstructed cosmological evolution for specific $f(Q)$ models.

Demonstrated how any FLRW cosmology can be obtained from $f(Q)$ gravity.

Abstract

In this manuscript, we present a number of fascinating explicit reconstructions for the $f(Q)$ gravity from the background of Friedmann-La\^imatre-Robertson-Walker (FLRW) evolution history. We find the more general functions of non-metricity scalar $Q$ that admit exact $\Lambda$CDM expansion history. Adding extra degrees of freedom to the matter sector is the only method to get the scale factor to behave in this manner for more generic functions of $Q$. In addition, a cosmological reconstruction for modified $f(Q)$ gravity is constructed in terms of e-folding. It is shown how any FLRW cosmology can arise from a specific $f(Q)$ theory. We also reconstruct the well-known cosmological evolution for the specific examples of $\Lambda$CDM cosmology.