  The early Universe inflation is well known as a promising theory to explain
the origin of large scale structure of the Universe, a causal theory for the
origin of primordial density fluctuations which may explain the observed
density inhomogeneities and cosmic microwave fluctuations in the very early
Universe, and to solve the early universe pressing problems for the standard
hot big bang theory. For a resonable inflation model, the potential during
inflation must be very flat in, at least, the direction of the inflaton. To
construct a resonable inflation model, or 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 for the quartic
term, the parameters in it are shown how to be constrained via the astrophysics
data observed and to be obtained to the expected accuracy by the soon lauched
MAP and PLANCK satellite missions, as well as the consistent cosmology
requirements. We find the effective inflaton mass parameter is in the TeV
range, and the quartic term's self-coupling constant tiny, needs fine-tunning.
