Cosmological constraints from Gauss-Bonnet braneworld with large-field potentials

We calculate the spectral index and tensor-to-scalar ratio for patch inflation defined by $H^2\approx {\beta }_q^2{V}^q$ and $\dot{\varphi }\approx -V^{\mathrm{\prime }}\mathrm{/}3H$, using the slow-roll expansion. The patch cosmology arisen from the Gauss-Bonnet braneworld consists of Gauss-Bonnet (GB), Randall-Sundrum (RS), and 4D general relativistic (GR) cosmological models. In this work, we choose large-field potentials of $V=V_0{\varphi }^p$ to compare with the observational data. Since second-order corrections are rather small in the slow-roll limit, the leading-order calculation is sufficient to compare with the data. Finally, we show that it is easier to discriminate between quadratic potential and quartic potential in the GB cosmological model rather than the GR or RS cosmological models.