On The Modified Teleparallel Equivalent Of General Relativity

Grand unification has been the dream of physics for over a centery.However,the two pillars of the modern physics,General Relativity(GR)and quantum gauge field theory,seem not to be consistent with each other.Shortly after General Relativity,Eistein himself proposed the Teleparallel Equivalent of General Relativity(TEGR),also known as the Teleparallelism,aiming to unified gravity and electromagnetism.Although this attempt at unification was not successful,it was found that TEGR is a gauge description of gravity.In this sense,the study of TEGR and its modification can be seen as a theoretical step towards bringing gravity into the framework of unified gauge field theory.As the name indicates,TEGR is equivalent to GR.Thus TEGR is also beset with the cosmological problems that GR has encountered in recent years,including cosmological constant,accelerating expanding,small scale problems,etc.Similar to the modified gravities that developed from GR,modifications to TEGR have also been proposed to tackle these problems.By the use of data fitting,as well as numerical and analytical methods,the current work investigates the large scale evolution of the Universe,Solar system tests and structure formation in modified Teleparallelism,i.e.f(T)gravity.In Chapter 2 and 3,we review the basis of TEGR as the gauge description of gravity and its extension to f(T)gravity,including both minimal and non-minimal torsion-matter couping cases,as well as the f(T,?)gravity.In Chapter 4,we study several concrete models of f(T)gravity,and fit the model parameters of them with the observation data set of type Ia supernovae(SNe Ia),cosmic micro background radiation(CMB)and baryon acoustic oscillation(BAO).With appropriate model parameters,the models can describe the large scale evolution history of the Universe,but they predict distinct fates of the Universe.In Chapter 5,we study the weak field limit of the static spherical symmetric solution of f(T)gravity,and use it to investigate the Solar system tests including gravitationalredshift,perihelion precession and geodetic effect.By comparing the theoretical predictions to the experiments,we give addtional constraints on the model parameters.For the concrete models considered in the current work,appropriately chosen parameters according to the cosmological fitting can give consistent results of the Solar system tests.In Chapter 6,we use the cosmological equations to study the spherical top-hat collapse,virialization and structure formation in f(T) gravity.