  We calculate the spectral index and tensor-to-scalar ratio for patch
inflation defined by $H^2\approx \beta^2_q V^q$ and $\dot{\phi}\approx -V'/3H$,
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 $V=V_0\phi^p$ 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.
