Explaining Gauss-Bonnet Term & Its Significance in Cosmology

[anuradha]

hi all,
anybody please give me a physical explanation for the Gauss-Bonnet invariant...
What is its significance in cosmology??does it contribute to the late time acceleration of the universe??
is it possible to find the variation of Gauss-bonnet term with respect to any given metric?if so, how??

-Anuradha

 

[Haelfix]

The Gauss-Bonnet term is defined to be a combination/contraction of various quadratic pieces of the renormalized Einstein Hilbert action.

Its something like G = R^2 - Ruv Ruv (one of those terms has all upper indices, the other all lower) + Ruvcd Ruvcd (same thing) where I have missed some constant factors here and there.

Anyway, you can look it up. The important thing is that its a topological invariant, so is nonrenormalized to all orders of perturbation theory. Being a topological invariant, it is also linked to the Euler characteristic of the manifold in question.

Now, it doesn't affect the field equations b/c it only contributes a surface term, which can be elimininated, however it still changes the dynamics b/c of the way it can couple to other terms (if so included).

Why is it important? Well, apart from making calculations easier in regular Einstein-Hilbert gravity, there is reason to believe that in modifications to GR it could play an important role. For instance Gauss-Bonnet gravity (one such modification that is a hot topic these days in gravity research) has a host of nice phenomenological and cosmological properties.

 

[Bruno5antos]

I've been doing calculations but not all terms are surface terms(maybe I am wrong) Has anyone do it?
I need to check this thing