Allowed parameter regions for a general inflation moded

Abstract

The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of Universe and to solve the early universe pressing problems. For a resonable inflation model, the potential during inflation must be very flat in, at least, the direction of the inflaton. To construct the inflaton potential all the known related astrophysics observations should be included. For a general tree-level hybrid inflation potential, which is not discussed fully so far, the parameters in it are shown how to be constrained via the astrophysics data observed and to be obtained to the expected accuracy, and consistent cosmology requirements.