Parity Violating Teleparallel Gravity And Vacuum Instability Of Cosmological Perturbation

As a discrete symmetry parity trasformation is usually studied in physics.Since parity violation was discovered in the beta decay of weak interaction,it has been gradually explored whether parity violation also exists in other fundamental interactions including gravity.On the one hand,albeit parity violation has not been detected in gravity,as technology and accuracy of experiments improves by leaps and bounds,it’s likely to acquire different results compared with the past in the future.On the other hand,from the perspective of theory,during the last decades there has been a lot of research on parity violation,one of the most famous parity violating gravity model is the ChernSimons modified gravity.It adds a parity violating term which is called Chern-Simons term based on Einstein-Hilbert action,and there is a clear evidence suggesting that parity is violated by calculating the linear order equation of motivation for tensor perturbation.Nevertheless,the quadratic action for tensor perturbation shows that the coefficient of kinetic term is negative which will lead to vacuum instability when gravity is quantized.After that,some gravity theories appeared to modify the ChernSimons theory,but the problem of vacuum instability was still not solved.In addition to Riemannian geometry,Teleparallel gravity is also an alternative theoretical framework,then a new modified gravity based on Teleparallel gravity was proposed which is celled Nieh-Yan modified Teleparallel gravity model.This theory contains a quadratic term of torsion known as Nieh-Yan term which bring about parity violation without vacuum instability.Within the Teleparallel gravity,other parity violating terms which are also quadratic torsion terms can be constructed except Nieh-Yan term,it’s crucial to take them into account.Therefore,we consider a more general model consists of all parity violating quadratic terms and apply the model to spatially-flat FRW universe to clarify whether there is still vacuum instability.Through cosmological perturbation,we find that the quadratic action for tensor perturbation still indicate parity violation,but unfortunately the quadratic action for scalar and vector demonstrates that some degrees of freedom result in vacuum instability.In order to solve the problem we have to let the model degenerate into Nieh-Yan modified Teleparallel gravity model.Thus we conclude that if all the parity violating quadratic terms are considered,then Nieh-Yan modified Teleparallel gravity model is the only parity violating theory without vacuum instability.