Does Gauss-Bonnet Accelerate Our Universe?

As is well known our universe is expanding from BigBang. But the answer to the discussion about the expansion of acceleration or deceleration was given till1998. The Supernova Cosmology Project leading by S.Perlmutter and high-z supernova search team leading by B.Schmidt, observed the outbreak of the supernova which is far from us, and described the universe which we live in. By calculating the distance between supernova and us, and the velocity they leaved or red shift, we find that our universe is accelerating expansion. And the data of WMAP make sure that this conclusion is right. Thus, many cosmology model were made by physicist to explain the accelerating expansion of the universe.First, we review the actuality of cosmology, cosmological principle and the standard cosmological model. We emphasize that beside state parameter there is another most important parameter---the deceleration parameter q, and discuss the relationship with expansion. Then we roughly describe some models which our universe is accelerating expansion, such as inflation model, cosmological constant model and Kaluza-Klein theory which describe the high-dimensional cosmology, we also make a general review about the characteristics and the shortage of these models. After then, we consider the M theory which is under the framework of Kaluza-Klein theory, and how it comes from string theory and superstring theory, and we focus on the brane world model which is belong to M theory. This theory made our universe as a1+3brane which is embedded in the bulk of1+3+d dimension. Our standard particles are tied on the brane, while the gravity can cross freely in the bulk. This model can recover to the general relativity during the low energy case, but in high-energy condition, gravity leak into the bulk, show a real high dimensional way. Then we enumerate two typical examples in brane world model, RS-1and RS-2, introduce some kinetic properties.At last, we go back to brane world cosmology, and we introduce Gauss-Bonnet term in action of brane world, because the equation of motion has no more than second derivatives of metric and the theory is free of ghosts. The lagrangian is a pure divergence in four or less dimensions, but in more than four dimensional theories, the Gauss-Bonnet term has dynamically physical meanings, it can be interpreted as the reason of accelerating expansion. So, we could use the supernova cosmology which we talked before, and take the data of Type la Supernova, and fit the coupling parameter of this model. Then we plot the images of function of state, Hubble parameter and deceleration parameter specially, to check whether Gauss-Bonnet term can be a good candidate of accelerating expansion.