Spinor fields in f(Q)-gravity

We present a tetrad--affine approach to $f(mathcal{Q})$ gravity coupled to spinor fields of spin-$rac{1}{2}$. 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 $f(mathcal{Q})=alphamathcal{Q}^n$. 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.