The parity violating gravity models based on the symmetric teleparallel gravity have been considered in the literature, but their applications in cosmology and especially the modifications to cosmological perturbations have not been fully explored. In this paper we consider such a simple model which modifies general relativity by a parity non-conserved coupling, within the framework of the symmetric teleparallel gravity. We study in detail its cosmological applications and focus on its cosmological perturbation theory. Besides the already known parity violation in the tensor perturbations, we find that the vector perturbations in this model are promoted to be dynamical degrees of freedom, and the left- and right-handed vector modes propagate with different velocities. More importantly, we find that one of the vector modes is a ghost at high momentum scales, which will give rise to the problem of vacuum instability in the quantum theory of cosmological perturbations.
In this paper we consider the parity violating gravity model within the framework of teleparallel gravity. The parity violations are caused by the couplings of a scalar field to the scalar invariants which are parity-odd and quadratic in the torsion tensor. Totally there are two such type independent invariants, and one of them is the Nieh-Yan density. Through investigations on the cosmological perturbations of this model, we find that in general it suffers from the difficulties of ghost instability in the scalar and vector perturbations. But in the special case only the coupling to the Nieh-Y…
Many parity violating gravity models suffer from the ghost instability problem. In this paper, we consider a symmetric teleparallel gravity model that extends the general relativity equivalent model by several parity violating interactions between the gravitational field and a scalar field. These interactions exclude higher derivatives and are quadratic in the nonmetricity tensor. Through investigations on the linear cosmological perturbations, our results show that, in general, this model suffers from the difficulty caused by the existence of ghost mode in the vector perturbations. However, i…
The discovery of gravitational waves (GWs) from the compact binary components by LIGO/Virgo Collaboration provides an unprecedented opportunity for testing gravity in the strong and highly dynamical field regime of gravity. Currently a lot of model-independent tests have been performed by LIGO/Virgo Collaboration and no any significant derivation from general relativity has been found. In this paper, we study the parity violating effects on the propagation of GWs in the Nieh-Yan modified teleparallel gravity, a theory which modifies general relativity by a parity violating Nieh-Yan term. We ca…
Symmetric teleparallel gravity (STG) is an alternative description of the gravitational field as an effect of the nonmetricity rather than the curvature of the spacetime. For an specific choice of the symmetric teleparallel lagrangian, the STG dynamics is equivalent to the general relativity (GR), and it is called Symmetric teleparallel equivalent to general relativity (STEGR). We propose a local Lorentz violating dynamics in the gravitational sector in the STEGR framework. The Lorentz violation is trigged by the vacuum expectation value (vev) of the well-known bumblebee field, whose vev coupl…
In this paper we consider a parity violating gravity model without higher derivatives, thus ghost free. This model is constructed from the tetrad and its derivatives and coupled to a dynamical scalar field, like axion. It can be reduced from the Nieh-Yan term within the framework of teleparallel gravity. We apply this model to cosmology and investigate its consequences on cosmological perturbation theory. We find that the coupled dynamical scalar field lost its independent dynamics at the linear order and the parity violating term itself behaves like a viscosity. For gravitational waves, this …
General Relativity and its higher derivative extensions have symmetric teleparallel reformulations in terms of the non-metricity tensor within a torsion-free and flat geometry. These notes present a derivation of the exact propagator for the most general infinite-derivative, even-parity and generally covariant theory in the symmetric teleparallel spacetime. The action made up of the non-metricity tensor and its contractions is decomposed into terms involving the metric and a gauge vector field and is found to complement the previously known non-local ghost- and singularity-free theories.
The recently proposed Nieh-Yan modified teleparallel gravity is a parity-violating gravity model that modifies the general relativity equivalent teleparallel gravity by a Nieh-Yan term. This model is healthy and simple in form. In this paper, we consider the application of this model to the Solar System and investigate its slow-motion and weak-field approximation in terms of the parametrized post-Newtonian formalism. We find that all the post-Newtonian parameters of the model are the same as those of general relativity, which makes the model compatible with the Solar System experiments.
In this Letter we consider a general quadratic parity-preserving theory for a general flat connection. Imposing a local symmetry under the general linear group singles out the general teleparallel equivalent of General Relativity carrying both torsion and non-metricity. We provide a detailed discussion on the teleparallel equivalents of General Relativity and how the two known equivalents, formulated on Weitzenböck and symmetric teleparallel geometries respectively, can be interpreted as two gauge-fixed versions of the general teleparallel equivalent. We then explore the viability of the gener…
The observer's frame is the more elementary description of the gravitational field than the metric. The most general covariant, even-parity quadratic form for the frame field in arbitrary dimension generalises the New General Relativity by nine functions of the d'Alembertian operator. The degrees of freedom are clarified by a covariant derivation of the propagator. The consistent and viable models can incorporate an ultra-violet completion of the gravity theory, an additional polarisation of the gravitational wave, and the dynamics of a magnetic scalar potential.
Scalar quasinormal modes of rotating black holes in parity-violating gravity
Tokyo Metropolitan University（东京都立大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；College of Humanities and Sciences, Nihon University（日本大学文理学部）；Chulalongkorn University（朱拉隆功大学）；The University of Tokyo（东京大学）
We consider gravitational waves (GWs) in generic parity-violating gravity including recently proposed ghost-free theories with parity violation as well as Chern-Simons (CS) modified gravity, and study the implications of observational constraints from GW170817/GRB 170817A. Whereas GWs propagate at the speed of light, c, in CS gravity, we point out that this is specific to CS gravity and the GW propagation speed deviates from c, in general, in parity-violating gravity. Therefore, contrary to the previous literature in which only CS gravity is studied as a concrete example, we show that GW170817…
We generalize the world line EFT formalism to account for parity violating finite size effects. Results are presented for potentials and radiating moments of a binary inspiral for the parity conserving sector, and agreement is found with, previous calculations. Furthermore, we generate new results in this sector, calculating the current quadrupole moment induced by finite size gravitomagnetic effects. We also present novel results for parity violating sources, which might be due to beyond standard model physics, and show that they generate GW signals with the unique signature that the current-…
We revisit models, within the Einstein-Cartan theory, where the cosmological constant $Λ$ is promoted to a variable, at the cost of allowing for torsion even in the absence of spinors. We remark that some standard notions about FRW Universes collapse in these theories, most notably spatial homogeneity and isotropy may now co-exist with violations of parity invariance. The parity violating solutions have non-vanishing Weyl curvature even within FRW models. The presence of parity violating torsion opens up the space of possible such theories with relevant FRW modifications: in particular the Pon…
