Modified Gravity With Warped Extra Dimension And Cosmology

General relativity has been proved to be one of the most successful theories in physics.Despite of the successes it has gained,the theory suffers from some long lived pathologies such as the singularity problem and the renormalization problem.It contradicts with the other one of the two pillars of modern physics,quantum mechanics.Furthermore,in order to explain the cosmic accelerating expansion,one has to include the dark energy.The nature of this dark component is still a mystery and unknown.Given all of these consid-erations,physicists believe that general relativity should be modified and the spacetime should be described by some other gravity theories.On the other hand,the developments on extra dimension theory provided a new gate to go beyond the Standard Model of particle physics and of cosmology.It has been shown that extra dimension(s)could be the solution of some open problems,for example the gauge hierarchy problem,the cosmological constant problem,and the fermion mass hierarchy problem,etc.Hence the study on extra dimension theory will help us have a better understanding of the fundamental physics.It is really interesting to consider what would happen if we combine the modified gravity theories and the idea of extra dimension(s).In this thesis we pay special attention to the gravity theories with modified source,which is contrary to the theory with modified geometry.In the first chapter we introduce some basics of modified gravity theories and the developments of the extra dimension theories.In the second chapter we consider the f(R,T)gravity theory(with T being the trace of the energy momentum tensor)in five dimensions.The fifth dimension is warped because of the bulk scalar field.We consider the stability of the background configuration by analyzing the full linear perturbations.The effective gravity theory in four dimensions can be reproduced provided that some constraints on the formalism of the action are satisfied.We then move to the work on Palatini f(R)theory of gravity,which by definition is not metric theory.However,it can be transformed to be a metric theory with a modified source part.We get the first exact thick braneworld solution in which the background scalar field is a domain wall configuration.The analysis on the tensor perturbations shows that the model is free of tachyon instability.Due to the existence of massive Kaluza-Klein modes of graviton,the effective theory of gravity in four dimensions has a tiny difference with the four-dimensional general relativity.We calculated the correction to the Newtonian potential.With some approximations,the correction goes like?1/r2.The scalar perturbations are considered in the frame work of scalar tensor theory since the original Palatini f(R)theory gives higher derivatives to the source part.In this frame work there are two background scalar fields.However,we show that there is only one independent scalar degree of freedom.There is a danger that the effective theory in four dimensions would have an additional long range interaction if the massless mode of the scalar perturbation is localized.We study the condition avoiding this unacceptable phenomenology.These constraints rule out some of the background solutions and also impose some conditions on the form of f(R).At last,we study an inflation model originated from higher dimension theory,namely Fibre Inflation.It is based on a flux compactification of Type IIB superstring theory.There are two versions of realization in Fibre Inflation,namely the single field theory and the two-field theory.For the single field theory,we consider the preheating stage realized by self-resonance after inflation.The inflaton field simply oscillates around the minimum of the potential,hence provides the possibility of parametric resonance for the inflaton perturbation.For the two-field theory,the situation is completely different.If the inflation is driven by multiple scalar fields,there would be entropy modes which are orthogonal to the adiabatic mode.At large scales,the entropy modes seed the evolution of the adiabatic mode.If the entropy mode is amplified at large scales,the curvature perturbation,which is directly related to the Comic Microwave Background(CMB)power spectrum observed today,would have an exponential increase.This would violate the present observations.For the Fibre Inflation we considered here,we show that the model is safe.