Some Issues In The Construction Of F(R) Theory

In2011SOL. PELL MATT BRIAN.SCHMIDT and ADAM.RIESS got the Nobel Prizein physics on account of the observation of the supernova.The result of the observation demon-strates that the universe is accelerating and cooling at the same time.To explain it,physicistsput forward many theories,such as Dark Energy and Modified Gravity Theory and so on.Thecosmological constant the scalar fieldModified Chaplygin Gas are common models ofdark energy,while modified gravity theory can account for the truth of the acceleration too,f(R)theory,for example,is very famous which has three kinds of formations.Since both dark energy model and modify theory can declare the acceleration of the expan-sion, additionally, the value of state parameter is restricted when the density of energy of f(R)can be written as ρR,the construction of f(R) can be obtained coming from ρ=ρR.Then basingon some suitable initial conditions and restricting relevant parameters,compares the result withtheformer f(R) which are proposed artificially.In this paper, considering about the model of Dark Energy which including the cosmo-logical constantscalar field dark energy modified Chapply gas(MCG) model to construct relevant expression of f(R) when matter couples with curvature arbitrarily and without couplingat all, then check whether the results do exist and can agree with the former f(R) model.Theresult is that the plus-minus formation of f(R) with respect to the curvature R can be receivedeasily which is similar to the former theory,however,the construction of MCG model may bemore complicated.Furthermore, by restricting some parameters,the state parameter ω satisfiesthe value which can explain the acceleration indeed.