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arXiv · 2608.21003

Cosmological Reconstruction in $f(Q, T)$ Gravity: $\Lambda$CDM Background and Matter-Sector Dependence

Shivank Pal·Gauree Shanker
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Abstract

In this work, we investigate the cosmological reconstruction of $f(Q, T)$ gravity, where $Q$ is the non-metricity scalar and $T$ is the trace of the energy-momentum tensor. We consider the functional form $f(Q,T)=f(Q)+\lambda T$ and reconstruct explicit forms of $f(Q)$ corresponding to the $\Lambda$CDM expansion history in Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. By employing the matter conservation equation and expressing the cosmological quantities in terms of $Q$, the reconstruction problem is formulated as a first-order linear differential equation for $f(Q)$. Analytical solutions for $f(Q)$ are obtained for various matter configurations, including dust-like matter, a perfect fluid with equation-of-state parameter $\omega=-1/3$, and a nonisentropic perfect fluid with a time-dependent barotropic index. Additionally, an e-folding formulation of the reconstruction is considered to examine the cosmological evolution in terms of the e-folding parameter. The resulting forms of $f(Q)$ confirm that the $\Lambda$CDM expansion history can be successfully realized within the $f(Q,T)$ framework across diverse matter sectors.

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Shivank Pal, Gauree Shanker. 2026-08-21. Cosmological Reconstruction in $f(Q, T)$ Gravity: $\Lambda$CDM Background and Matter-Sector Dependence. https://arxiv.org/abs/2608.21003

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