Teleparallel Gravity And Its Cosmological Application

Although General Relativity(GR)has achieved great success,it faces the difficulties in both theoretically and observationally,such as singularity of the universe,dark matter and dark energy.GR is now generally considered as an effective theory and thought to be modified at high energy and/or large length scales.Since the fundamental object that describes gravitational effects in GR is Riemann tensor which contains second time derivative of metric,it is difficult to construct gravity models which are no higher-derivative effects.For this reason,this paper will study modified gravity models based on teleparallel gravity and symmetric teleparallel gravity,which are all equivalent of general relativity and do not contain higher-derivative effects.In the framework of teleparallel gravity,we proposed a healthy parity violating gravity model which we call it Nieh-Yan modified teleparallel gravity(NYTG),whose action is based on the Einstein-Hilbert action with the addition of the Nieh-Yan term coupled with a scalar field.The perturbation expansion of the model on the cosmological background shows that the velocities of left-and right-handed GWs are different and more importantly,NYTG model is free from ghost.This is exactly what we want in a modified gravity model with parity breaking effects and no ghost fields.This is also different from the Chern-Simons modified gravity based on general relativity,which has parity violating effects but the tensor perturbations will appear ghost fields at high energy scale.This can be treated as an advantage for modified gravity models based on teleparallel gravity.In the framework of symmetric teleparallel gravity,although some papers have considered the possible parity violating gravity models,they only studied the tensor perturbations of those models on the cosmological background,and found that gravitational waves have parity breaking effect.We did a complete cosmological perturbation analysis of it in follow-up studies.We first studied the simplest parity violating model and found that it does have parity breaking signals(left-and right-handed GWs propagate with different velocities),but vector perturbations will appear ghost fields at high energy scale.In order to solve the ghost problem in this simplest parity breaking model,we considered its scalar-tensor extension and found that as long as the coefficients in the extended model meet certain conditions,a modified gravity model with parity breaking effects and no ghost fields can be obtained.Symmetric teleparallel gravity can be considered as a constrained metric-affine theory,with metric and connection as independent fundamental variables.For a particular spacetime,according to GR we can easily have the form of the metric,but we do not know which connection is suitable.Meanwhile,choosing arbitrary affine connection may lead the equations of motion to be inconsistent.Therefore,this paper also presents an improved method to choose suitable connection for given spacetime.