Minimal $k$-inflation in light of the conformal metric-affine geometry

摘要: We motivate a minimal realization of slow-roll $k$-inflation by incorporating the local conformal symmetry and broken global $\mathrm{SO}(1,1)$ in metric-affine geometry. With use geometry where both metric affine connection are treated as independent variables, can be preserved each term Lagrangian thus higher derivatives scalar fields easily added conformally invariant way. Predictions this $k$-inflation, $n_\mathrm{s}\sim 0.96$, $r\sim 0.005$, $c_\mathrm{s}\sim 0.03$, not only consistent with current observational data but also have prospect to tested forthcoming observations.