### Abstract

The observed accelerated expansion of the universe is one of the big issues of modern cosmology. One possible way of understanding it is by modifying General Relativity so that gravity is weaker at large scales. Higher-dimensional models that offer infrared modifications of gravity provide just that. Braneworld models are a subclass of these, where standard matter is confined to a p dimensional brane living in a p+d dimensional “bulk” space. Gravitons, however, can access the extra d dimensions. The Dvali-Gabadadze-Porrati(DGP) model realizes this by having a 4D brane embedded in 5D space-time. By including an induced gravity term in the action, standard 4D gravity is recovered at small scales, whereas at large scales gravity is 5D. This model is particularly interesting because of its phenomenology, namely the existence of two cosmological branches, one of which, called the self-accelerating branch, exhibits late time cosmic acceleration even when no matter is present in the brane. However, such cosmologies, at the linear level, have been found to be plagued by ghost instabilities that cause a catastrophic instability of space-time thus automatically excluding the model as a viable explanation of reality.In this thesis, after a brief introduction to the covered topics, we start by going beyond linearity to see if non-linear interactions might change previous results on the presence of the ghost. We did this for a cosmological background and, in the process, derived the equations that form the basis of structure formation tests in the DGP model. Our analysis however, proves the validity of the linearized solutions and, thus, the presence of the ghost. We then used a numeric algorithm to solve the full 5D set of dynamical equations for the scalar perturbations in the DGP model. Our numeric solutions are the basis for comparison of the ghost-free normal branch with cosmological observations.

Whereas there seems to be no way of avoiding the ghost problem in the self-accelerating branch of the DGP model, a generalization of it that removes the symmetry across the brane had been shown to be ghost-free in a flat background while retaining some form of late-time acceleration (given the name of stealth acceleration) in certain limits. We study the spectrum of perturbations for a de Sitter background in the same setup. Our analysis showed that the only way to avoid a ghost is precisely to have Minkowski branes.

Finally, yet another generalization of the DGP model, in this case a generalization of its 4D effective action called the Galileon model, is shown to possess the self-accelerating solutions. We present an extension of the Brans-Dicke theory by adding a third order Galileon term to the Brans-Dicke action that appears in the 4D effective theory of DGP gravity. An analysis of our model shows the presence of self-acceleration for a certain region of it’s parameter space, without any ghost or tachyonic instabilities.

Date of Award | Jul 2010 |
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Original language | English |

Supervisor | Kazuya Koyama (Supervisor) |