Nieh-Yan Modified Teleparallel Gravity

Discrete symmetries,including the charge conjugation,parity,time reversal and their combinations have played important roles in the exploration of the Standard Model of particle physics.Since the parity violation was discovered in weak interactions,we gradually know that most of them are not exact in the nature.So people began to explore the possibility that discrete symmetries are broken in other interactions.Whether or not these discrete symmetries are broken in gravity is unclear to us,but recently there were lots of studies on the parity violating gravity in the literature,stimulated by the experimental detections of gravitational waves and the developments in the cosmic microwave background radiation experiments.If there are parity violations in gravity,the left and right polarized gravitational waves should have different behaviors and corresponding signals are possibly to be captured by well-designed experiments.The most famous parity-violating gravity is the Chern-Simons gravity,which is the simplest theory of parity-violating gravity based on Riemannian geometry.But the Chern-Simons gravity faces the problem of ghost instability,and its extension based on Riemannian geometry not only fails to properly avoid ghost instability,but also makes the theoretical form too complicated.So we want to construct a parity-violating gravity that is simple and ghost free.In response to this problem,we propose the Nieh-Yan modified Teleparallel gravity,which is a parity-violating gravity that is simple in form and ghost free.The framework of Teleparallel gravity is a framework for gravity theory that describes gravity in terms of torsion rather than curvature.Within the framework of Teleparallel gravity,a gravity theory equivalent to General Relativity can be constructed.Within the framework of Teleparallel gravity,by introducing the odd-parity topological term composed of torsion,we construct a parity-violating gravity theory with a simple form and no higher-order derivatives,which is called the Nieh-Yan modified Teleparallel gravity.In order to demonstrate that the Nieh-Yan modified Teleparallel gravity is indeed ghost free,and to explore the specific parity-violating signal of the Nieh-Yan modified Teleparallel gravity,we study the cosmological perturbations of the Nieh-Yan modified Teleparallel gravity.For tensor perturbations,we find that left-handed and right-handed gravitational waves have different propagation velocities.This phenomenon is called velocity birefringence,which is a clear physical signal of parity violation.For vector perturbations,we find that there are no dynamical degrees of freedom.For scalar perturbations,there is a dynamical degree of freedom that is missing in the flat universe but reappears in the curved universe.More importantly,through the quadratic actions of scalar,vector and tensor perturbations,we confirm that the Nieh-Yan modified Teleparallel gravity is ghost free.Next,In order to explore whether the Nieh-Yan modified Teleparallel gravity is compatible with the Solar System experiments,we study the parametrized postNewtonian limit of the Nieh-Yan modified Teleparallel gravity.For the dynamical Nieh-Yan modified Teleparallel gravity,its post-Newtonian parameters can naturally match the current experimental limits.But for the non-dynamical Nieh-Yan modified Teleparallel gravity,its post-Newtonian parameters cannot naturally match the current experimental limits.Finally,in order to explore whether there are other simple and ghost free parityviolating gravity theories within the framework of Teleparallel gravity,we generalize the Nieh-Yan modified Teleparallel gravity and consider the most general parityviolating term which is quadratic in the torsion tensor.By studying the cosmological perturbations of this general parity-violating gravity,we find that this general parityviolating gravity will face the problem of ghost instability again,unless it completely reduces to the Nieh-Yan modified Teleparallel gravity.This means that within the framework of Teleparallel gravity,among the parity-violating terms which are quadratic in the torsion tensor,only the Nieh-Yan term is ghost free.