Spinor fields in f(Q)-gravity

We present a tetrad-affine approach to f(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(Q) = alpha 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.