Stability of selfaccelerating solutions in modified gravity models
Student thesis: Doctoral Thesis
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. Higherdimensional 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 DvaliGabadadzePorrati(DGP) model realizes this by having a 4D brane embedded in 5D spacetime. 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 selfaccelerating 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 spacetime 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 nonlinear 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 ghostfree normal branch with cosmological observations.
Whereas there seems to be no way of avoiding the ghost problem in the selfaccelerating branch of the DGP model, a generalization of it that removes the symmetry across the brane had been shown to be ghostfree in a flat background while retaining some form of latetime 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 selfaccelerating solutions. We present an extension of the BransDicke theory by adding a third order Galileon term to the BransDicke action that appears in the 4D effective theory of DGP gravity. An analysis of our model shows the presence of selfacceleration for a certain region of it’s parameter space, without any ghost or tachyonic instabilities.
In this thesis, after a brief introduction to the covered topics, we start by going beyond linearity to see if nonlinear 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 ghostfree normal branch with cosmological observations.
Whereas there seems to be no way of avoiding the ghost problem in the selfaccelerating branch of the DGP model, a generalization of it that removes the symmetry across the brane had been shown to be ghostfree in a flat background while retaining some form of latetime 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 selfaccelerating solutions. We present an extension of the BransDicke theory by adding a third order Galileon term to the BransDicke action that appears in the 4D effective theory of DGP gravity. An analysis of our model shows the presence of selfacceleration for a certain region of it’s parameter space, without any ghost or tachyonic instabilities.
Original language  English 

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Award date  Jul 2010 
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1.48 MB, PDF document
ID: 6061804