Cosmological perturbation theory in metric-affine gravity

We formulate cosmological perturbation theory around the spatially curved FLRW background in the context of metric-affine gauge theory of gravity which includes torsion and nonmetricity. Performing scalar-vector-tensor decomposition of the spatial perturbations, we find that the theory displays a rich perturbation spectrum with helicities 0, 1, 2, and 3, on top of the usual scalar, vector, and tensor metric perturbations arising from Riemannian geometry. Accordingly, the theory provides a diverse phenomenology, e.g. the helicity-2 modes of the torsion and/or nonmetricity tensors source helicity-2 metric tensor perturbation at the linear level leading to the production of gravitational waves. As an immediate application, we study linear perturbation of the nonmetricity helicity-3 modes for a general parity-preserving action of metric-affine gravity which includes quadratic terms in curvature, torsion, and nonmetricity. We then find the conditions to avoid possible instabilities in the helicity-3 modes of the spin-3 field.