Posted by keithkchan in Cosmology.

First of all, happy new year to all of you.

I am going to talk about the work that I have been doing for several months. As a preclude, I would like to introduce some related background. In this post, I give a tiny review on the Dvali-Gabadadze-Porrati (DGP) model. I think the readers at NYU physics should know a little bit about this model as it was invented by three physicists at NYU.

DGP model is an extra dimension (ED) model. Any ED model has to reproduce the well-known Newtonian gravitational potential $\propto 1/r$ in the scale that has been well examined. Other ED model like Kaluza-Klein (KK) model and Randall-Sundrum (RS) model modify gravity in the untraviolet regime. That is we can discover the existence of ED by probing sufficiently small distance scales. Currently, the constraint on size of the ED is about sub-millimeter or so. KK hides the ED by compactifying them on some manifold, while RS make use of warp ED. DGP is different from the other model in the sense that it is an infrared modification of gravity. That is you find out the existence of ED if you look at large enough scales. In DGP model, our world is a 3-brane, which is embedded in 4+1 dimensional Minkowski spacetime. The gravitational action in DGP reads
$S= M^3 \int d^5 X \sqrt{G} R^{(5)} + M_P^2 \int d^4 x \sqrt{-g} R^{(4)}$. The second term is crucial for the recovery of Newtonian gravity in small scales.

DGP model respects Lorentz invariance on the 3-brane. It is a covariance formulation of massive gravity. For the observer on the brane, the effective mass of the graviton is $m_g=\frac{2M^3}{M_P^2}$. The graviton mass $m_g$ is related to the crossover scale $r_c$ as $r_c = 1/ m_g$. The crossover scale characterizes the scale in which the ED gravity kicks in.

Another remarkable discovery by Deffayet, who was at NYU at that time, was that the resultant DGP Friedmann equation admits a self-accelerating solution. That is in DGP model we can explain the observed cosmic acceleration without invoking the mysterious dark energy!

So far so good. However, it was later found that DGP model is plagued by ghosts. In field theory, ghosts have negative kinetic term, and it is a signal of inconsistency of the theory. If ghosts are not enough to kill DGP, recently some people claimed that the self-accelerating DGP has been ruled out by $5\sigma$ by observation, through the so-called ISW effects.

Probably DGP will go to the hell with the ghosts pretty soon. However, DGP has motivated more sophisticated generalization, the Cascading Gravity. This model seems to be free of ghosts. But the details has to be worked out as it is very complicated.

Although DGP turns out to be not so successful, it is certainly a landmark of NYU physics. Many people at NYU have contributed to it. I will talk about my own work on it, probably at the end of this month.