Tensor non-Gaussianity in chiral scalar-tensor theories of gravity

Abstract

Violation of parity symmetry in the gravitational sector, which manifests into unequal left and right circular polarization states of primordial gravitational waves, represents a way to test high-energy modifications to general relativity. In this paper we study inflation within recently proposed chiral scalar-tensor theories of gravity, that extend Chern-Simons gravity by including parity-violating operators containing first and second derivatives of the non-minimally coupled scalar (inflaton) field. Given the degeneracy between different parity-violating theories at the level of the power spectrum statistics, we make a detailed analysis of the parity violation on primordial tensor non-Gaussianity. We show, with an explicit computation, that no new contributions arise in the graviton bispectra if the couplings in the new operators are constant in a pure de Sitter phase. On the other hand, if the coupling functions are time-dependent during inflation, the tensor bispectra acquire non-vanishing contributions from the parity-breaking operators even in the exact de Sitter limit, with maximal signal in the squeezed and equilateral configurations. We also comment on the consistency relation of the three-point function of tensor modes in this class of models and discuss prospects of detecting parity-breaking signatures through Cosmic Microwave Background B-mode bispectra.

Bootstrapping Large Graviton non-Gaussianities

“…This suppression was also noted in [47]. In this paper we have restricted ourselves to exact scale invariance, and away from this limit other shapes are possible [46]. As we mentioned above, it would be very interesting to pick out this EFToI subset of our full catalogue directly at the level of the correlator rather than going back to the Lagrangian.…”

“…In turn this may only happen when 2n ∂η + n ∂i ≤ 3, where n ∂η and n ∂i are respectively the number of time and space derivatives in the parity-odd interaction 5 . This explains on general grounds why parity-odd correlators where found to vanish in the scale-invariant limit in a number of explicit calculations [31,46,48].…”

“…Progress in understanding boost-breaking gravitational interactions has been achieved using effective field theories and the Lagrangian approach in a series of recent papers [42][43][44][45][46][47]. This approach is quite general and intuitive but its computational complexity grows quickly as one considers operators with an increasing number of derivatives.…”

Ghost instability in the teleparallel gravity model with parity violations

“…(3.5)- (3.6) and (3.39)-(3.40) in Ref. [11]. It is very difficult to have a ghost-free PV gravity model within the framework of Riemannian geometry.…”

Gravitational wave constraints on Lorentz and parity violations in gravity: high-order spatial derivative cases

“…In these theories, the parity violating terms can also be written in the form of high-order odd-order spatial derivatives. Various implications of parity violations on the gravitational waves have been extensively explored in [40][41][42][43][44][45][46][47][48]. Note that in [49][50][51][52], a parity-violating effects induced by lower dimemnsion operators have also been proposed and their phenomenological effects have been explored.…”