Spinor fields in $f(\mathcal{Q})$-gravity

TL;DR

This paper develops a tetrad-affine formulation of $f( ext{Q})$ gravity coupled with spin-1/2 fields, deriving field equations, conservation laws, and analytical solutions for Bianchi type-I cosmologies, showing isotropization and possible accelerated expansion.

Contribution

It introduces a new tetrad-affine approach to $f( ext{Q})$ gravity with spinor fields and provides analytical solutions for cosmological models with specific $f( ext{Q})$ functions.

Findings

Conservation law of spin density ensures antisymmetric Einstein-like equations vanish.

Analytical solutions for Bianchi type-I models with $f( ext{Q})=\alpha\mathcal{Q}^n$ are derived.

Solutions exhibit isotropization and potential accelerated expansion depending on the parameter $n$.

Abstract

We present a tetrad-affine approach to $f(\mathcal{Q})$ gravity coupled to spinor fields of spin-1/2. After deriving the field equations, we derive the conservation law of the spin density, showing that the latter ensures the vanishing of the antisymmetric part of the Einstein-like equations, just as it happens in theories with torsion and metricity. We then focus on Bianchi type-I cosmological models proposing a general procedure to solve the corresponding field equations and providing analytical solutions in the case of gravitational Lagrangian functions of the kind $f(\mathcal{Q})=\alpha\mathcal{Q}^n$. At late time such solutions are seen to isotropize and, depending on the value of the exponent $n$, they can undergo an accelerated expansion of the spatial scale factors.