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Register a new userTensor non-Gaussianity in chiral scalar-tensor theories of gravity
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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.
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We analyze junction conditions at a null or non-null hypersurface $Sigma$ in a large class of scalar-tensor theories in arbitrary $n(ge 3)$ dimensions. After showing that the metric and a scalar field must be continuous at $Sigma$ as the first junction conditions, we derive the second junctions conditions from the Einstein equations and the equation of motion for the scalar field. Subsequently, we study $C^1$ regular matching conditions as well as vacuum conditions at $Sigma$ both in the Jordan and Einstein frames. Our result suggests that the following configurations may be possible; (i) a vacuum thin-shell at null $Sigma$ in the Einstein frame, (ii) a vacuum thin-shell at null and non-null $Sigma$ in the Jordan frame, and (iii) a non-vacuum $C^1$ regular matching at null $Sigma$ in the Jordan frame. Lastly, we clarify the relations between the conditions for $C^1$ regularity and also for vacuum $Sigma$ in the Jordan and Einstein frames.
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We compute the spectrum of scalar models with a general coupling to the scalar curvature. We find that the perturbative states of these theories are given by two massive spin-0 modes in addition to one massless spin-2 state. This latter mode can be identified with the standard graviton field. Indeed, we are able to define an Einstein frame, where the dynamics of the massless spin-2 graviton is the one associated with the Einstein-Hilbert action. We also explore the interactions of all these degrees of freedom in the mentioned frame, since part of the coupling structure can be anticipated by geometrical arguments.
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