The metric-affine squared scalaron: parameter-free inflation

We present a model of slow-roll inflation in metric-affine gravity, where the connection is independent of the metric. We require that the Einstein-Hilbert term is the only operator that breaks three out of four shift-symmetries of the connection, and impose them on the metric-affine Starobinsky term αR(Γ) squared. This replaces it by α squared, the square of the invariant part of the scalar curvature. The theory propagates only the graviton and one healthy scalar, the metric-affine squared scalaron. Its potential approaches a plateau polynomially, U U 0(1-μ 2/χ 2), with μ= sqrt 6,M P fixed by the curvature of the connection. Once α 2 times10 8 is set by the scalar amplitude, the model has no free parameters. It predicts n s 1-3/(2N*) and r 2 sqrt3,N*-3/2 at leading order in N*, and n s=0.968 -- 0.974 and r=0.011 - 0.008 with exact slow-roll for N*=50 - 60 e-folds. These values agree with current data, and r is within reach of the next generation of B-mode measurements.