We consider the ghost-free higher-order corrections to the Starobinsky model in the old-minimal supergravity , focusing on a sector among several scalar fields in the model that reproduces the scalaron potential in the original Starobinsky model .
In general , higher-order corrections can not be forbidden by symmetries , which likely violate the flatness of the scalaron potential and make inflation difficult in explaining the present Universe .
We find a severe constraint on the dimensionless coupling of the R ^ { 4 } correction as -5.5 \times 10 ^ { -8 } < s < 9.1 \times 10 ^ { -8 } from the recent results of the Planck observation .
If we start from the chaotic initial condition , the constraint becomes much more severe .
However , in the case in which the coupling of the R ^ { 4 } correction is positive , the scalaron potential has a local maximum with two local minima at the origin and infinity , which admits topological inflation .
In this case , inflation can take place naturally if the coupling satisfies the observational constraints .