Obtaining some constraints on the early universe based on WMAP-9 and Planck by using DECIGO and BBO detectors

The evolution stages of the universe such as: inflation, reheating, radiation, matter and acceleration can affect on the shape of the spectrum of relic gravitational waves. As well known, at the end of inflation, the scalar field ϕ oscillates quickly around some point where potential V(ϕ)=λϕn has a minimum. The potential V causes that the scale factor S obtains unusual growth during inflation, as the amount of this growth is given by eN, where N is the e-folding number. On the other hand the behaviour of the inflation and reheating stages are often known as power law expansion like S(η)∝η1+β,S(η)∝η1+βs respectively. The η is conformal time and β, βs constrained on the 1+β<0 and 1+βs>0. The waves being used to determine the reheating temperature in the range (106-109) GeV based on the BBO and DECIGO detectors. Hence we found constraints on the parameters N, β, βs and n corresponding to the range of reheating temperature, WMAP-9 and Planck. As these constraints give us valuable information about the manner of the evolution of universe and the waves during inflation and reheating stages.