EINSTEIN GRAVITY AND BRANEWORLD IN LOW ENERGY EFFECTIVE REGIME AND EXTRA DIMENSION - (NIM: 302 03 007), Arianto
Abstrct: In this dissertation, we consider the Einstein theory of gravity with more than four dimensions (extra dimensions) such as supergravity and braneworld gravity in five dimensional space-time. The bulk is taken to have the topology of an orbifold . First, we give an overview of extra dimensional physics in the perspective of the Einstein theory of gravity, from the Kaluza-Klein picture up to modern braneworld. We describe the different models (Randall-Sundrum, Arkani-Hamed-Dimopoulos-Dvali, Dvali Gabadadze-Porrati) and their impacts on cosmology. We consider compactification of five dimensional ungauged supergravity coupled to vector multiplet and hypermultiplets on orbifold . In the model, the vector multiplets scalar manifold is arbitrary while the hypermultiplet scalars span a generalized self dual Einstein manifold constructed by Calderbank and Pedersen. The bosonic and the fermionic sectors of the low energy effective supergravity in four dimensions are derived. From the geometry of orbifold , we then investigate five-dimensional braneworld. We develop the covariant curvature formalism for extracting four-dimensional information from the five-dimensional Einstein equations governing the bulk geometry. We start with two -symmetric branes at fixed points of an orbifold 2 and derive the induced Einstein equations on both branes. Two additional terms appear in the four-dimensional Einstein equations: a local quadratic term in the sources and a non local term which is a projection of the five-dimensional Weyl tensor. This last tensor, which it acts as a radiation term, modifies the Friedmann equations. Moreover, we apply the covariant curvature formalism of low energy expansion method in the bulk to study the Randall-Sundrum models with an emphasis of the effective equation of motions on the brane. Through the junction condition, we deduce in the zeroth order fine tuning for RS model. The modified Einstein equation is derived from the first order expansion. We also clarify the emergence of the AdS/CFT correspondence for the case of the higher order expansion in a low energy iteration scheme. Furthermore, we consider a cosmology scenario with two branes moving in a five dimensional bulk. As in the case of born-again-braneworld (BAB) model, it is possible that the branes collide. The energy-momentum tensor is taken to describe a perfect fluid on the positive tension brane and a time dependent cosmological on the negative tension brane. The dynamics of the radion (scalar field on the brane) contains information about the proper distance between the branes. We then generalize the Randall-Sundrum two branes scenario allowing for a third brane to live in the bulk. The three parallel 3-branes system with both positive and negative tension is studied in a low energy regime. The effective equations of motion on the brane are derived and in particular we examine, in the first order, the radion effective lagrangian for this system. In this case, we show the solution of the modified Friedmann equation with dark radiation on the middle brane and the other branes by direct elimination of the radion fields and Weyl scaling of the metric on the branes. The result shows that the interpretation given to the radion field in two brane scenario can be generalized to a three brane scenario. In this case both the two radion fields contribute to the realization of effective theory on each brane. Furthermore, we discuss the effective gravitational field equations at low energies on the braneworld where Lorentz violation occurs in the bulk space along the extra dimension. In the Lorentz violation model, we find that the evolution of Weyl tensor is given by contributions of the matter fields on the brane and a constant of integration which corresponds to perturbations due to gravitational waves in the bulk. This result affects the gravitational coupling of the effective gravitational field equations on the brane. Upon introducing the FRW metric and perfect fluid matter on the brane, we consider the effective dynamical equations for the brane scale factor with various kinds of matter. Finally, the impact of Lorentz violation on the dynamics of a scalar field is investigated. In particular, we study the dynamics of a scalar field in the scalar-vector-tensor theory where the vector field is constrained to be unity and time like. By taking a generic form of the scalar field action, a generalized dynamical equation for the scalar-vector-tensor theory of gravity is obtained to describe the cosmological solutions. We present a class of solutions for an ordinary scalar field or phantom field corresponding to a power law coupling vector and the Hubble parameter. As the results, we find a constant equation of state in de Sitter space-time and power law expansion with the quadratic of coupling vector, while a dynamic equation of state is obtained for n more than 2. Then, we reconsider the inflationary scenario based on the Lorentz violating scalar-vector-tensor theory of gravity. In particular, the coupling between the scalar fields and the Lorentz violating vector is incorporated in our model. Finally, we use the dynamical system formalism to study the attractor behavior of a cosmological model containing a scalar field endowed with a quadratic coupling vector and a chaotic potential.