DGP inside DGP

The first thing that happened this year here at CERN was Cosmo Coffee. TH Cosmo Coffee is similar to Amsterdam coffeshops in that you should not expect coffee being served. Last Wednesday, Michele Redi was talking about modified gravity theories from the DGP family.

One way to tackle the cosmological constant problem is to modify gravity at large distances. What one could hope to achieve by that is either accelerated expansion without a cosmological term in the lagrangian or filtering out the deadly effects of a large cosmological constant. Gravity, however, is not easily manipulated. In those instances when obvious inconsistencies are avoided, there always remain problematic features. For example, giving a mass to the graviton results in a strong coupling of its longitudinal polarization at some scale and, at distances smaller than that scale, non-linear effects become important. It pays to have a non-linear formulation in order to study the physical consequences of such modified gravities

The DGP model is an attempt along these lines that has a generally covariant non-linear formulation. DGP is the minimal 5D gravity with the 5th dimension infinite on one side and cut off by a 4D brane on the other side. The 4D brane carries a large gravity kinetic term (that is just the usual 4D Einstein-Hilbert term). Because of that brane kinetic term, gravity approximately obeys the 4D Newton law at small distances, while at large distances it switches to a 5D behaviour. One may hope that the weakening of gravity at large distances could help in solving some problems. Yet the DGP model is not quite satisfying in this respect. Self-accelerated solutions, although existing, are plagued by ghosts. Furthermore, the cosmological constant problem is not solved: loop effects would generate a cosmological term and destabilize the set-up.

The next thing to try is 6D gravity. However, a codimension-2 brane (here, a 4D brane embedded in 6D) is too singular. This means that divergences in the graviton propagator appear already at the classical level. Furthermore, codimension-2 brane typically leads to a ghost - the effective theory has a scalar excitation with a negative sign of the kinetic term.

In a recent paper, Michele et many al tried a funny regularization inspired by Russian folklore. A 4D brane with a gravity kinetic term is embedded into a 5D brane with a gravity kinetic term who, in turn, lives inside a 6D bulk. The model interpolates between 6D gravity at very large distances and 4D gravity at small distances, with a possible 5D intermediate region. This construction avoids any divergences at the classical level. The ghost persists in general, but it can be cured by adding a cosmological term on the 4D brane. A cosmological constant on a codimension-two brane has this peculiar feature that it does not curve the spacetime, so that the flat spacetime remains a solution to the Einstein equations.

At this moment it is not clear if this matroshka solves any problems or if it does not create problems of its own. Certainly, it is another example of a non-linear formulation of IR modified gravity. The interesting thing about this particular model is that, at the linearized level, the effective lagrangian for the graviton does not have the Pauli-Fierz structure. Such gravity theories have not been much studied before.