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Register a new userSpin-orbit effects for compact binaries in scalar-tensor gravity
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Gravitational waves provide us with a new window into our Universe, and have already been used to place strong constrains on the existence of light scalar fields, which are a common feature in many alternative theories of gravity. However, spin effects are still relatively unexplored in this context. In this work, we construct an effective point-particle action for a generic spinning body that can couple both conformally and disformally to a real scalar field, and we show that requiring the existence of a self-consistent solution automatically implies that if a scalar couples to the mass of a body, then it must also couple to its spin. We then use well-established effective field theory techniques to conduct a comprehensive study of spin-orbit effects in binary systems to leading order in the post-Newtonian (PN) expansion. Focusing on quasicircular nonprecessing binaries for simplicity, we systematically compute all key quantities, including the conservative potential, the orbital binding energy, the radiated power, and the gravitational-wave phase. We show that depending on how strongly each member of the binary couples to the scalar, the spin-orbit effects that are due to a conformal coupling first enter into the phase at either 0.5PN or 1.5PN order, while those that arise from a disformal coupling start at either 3.5PN or 4.5PN order. This suppression by additional PN orders notwithstanding, we find that the disformal spin-orbit terms can actually dominate over their conformal counterparts due to an enhancement by a large prefactor. Accordingly, our results suggest that upcoming gravitational-wave detectors could be sensitive to disformal spin-orbit effects in double neutron star binaries if at least one of the two bodies is sufficiently scalarised.
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By means of the Greens function method, we computed the spectral indices up to third order in the slow-roll approximation for a general scalar-tensor theory in both the Einstein and Jordan frames. Using quantities which are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field, we showed that the frames are equivalent up to this order due to the underlying assumptions. Nevertheless, care must be taken when defining the number of $e$-folds.
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In $f(R)$ gravity and Brans-Dicke theory with scalar potentials, we study the structure of neutron stars on a spherically symmetric and static background for two equations of state: SLy and FPS. In massless BD theory, the presence of a scalar coupling $Q$ with matter works to change the star radius in comparison to General Relativity, while the maximum allowed mass of neutron stars is hardly modified for both SLy and FPS equations of state. In Brans-Dicke theory with the massive potential $V(phi)=m^2 phi^2/2$, where $m^2$ is a positive constant, we show the difficulty of realizing neutron star solutions with a stable field profile due to the existence of an exponentially growing mode outside the star. As in $f(R)$ gravity with the $R^2$ term, this property is related to the requirement of extra boundary conditions of the field at the surface of star. For the self-coupling potential $V(phi)=lambda phi^4/4$, this problem can be circumvented by the fact that the second derivative $V_{,phi phi}=3lambdaphi^2$ approaches 0 at spatial infinity. In this case, we numerically show the existence of neutron star solutions for both SLy and FPS equations of state and discuss how the mass-radius relation is modified as compared to General Relativity.
We analyze the propagation of high-frequency gravitational waves (GW) in scalar-tensor theories of gravity, with the aim of examining properties of cosmological distances as inferred from GW measurements. By using symmetry principles, we first determine the most general structure of the GW linearized equations and of the GW energy momentum tensor, assuming that GW move with the speed of light. Modified gravity effects are encoded in a small number of parameters, and we study the conditions for ensuring graviton number conservation in our covariant set-up. We then apply our general findings to the case of GW propagating through a perturbed cosmological space-time, deriving the expressions for the GW luminosity distance $d_L^{({rm GW})}$ and the GW angular distance $d_A^{({rm GW})}$. We prove for the first time the validity of Etherington reciprocity law $d_L^{({rm GW})},=,(1+z)^2,d_A^{({rm GW})}$ for a perturbed universe within a scalar-tensor framework. We find that besides the GW luminosity distance, also the GW angular distance can be modified with respect to General Relativity. We discuss implications of this result for gravitational lensing, focussing on time-delays of lensed GW and lensed photons emitted simultaneously during a multimessenger event. We explicitly show how modified gravity effects compensate between different coefficients in the GW time-delay formula: lensed GW arrive at the same time as their lensed electromagnetic counterparts, in agreement with causality constraints.
Kinetic mixing between the metric and scalar degrees of freedom is an essential ingredient in contemporary scalar-tensor theories. This often makes hard to understand their physical content, especially when derivative mixing is present, as it is the case for Horndeski action. In this work we develop a method that allows to write a Ricci curvature-free scalar field equation and discuss some of the advantages of such rephrasing in the study of stability issues in the presence of matter, the existence of an Einstein frame and the generalization of the disformal screening mechanism. For quartic Horndeski theories, such procedure leaves, in general, a residual coupling to curvature, given by the Weyl tensor. This gives rise to a binary classification of scalar-tensor theories into stirred theories, for which the curvature can be substituted for, and shaken theories for which a residual coupling to curvature remains. Quite remarkably, we have found that generalized DBI Galileons belong to the first class. Finally, we discuss kinetic mixing in quintic theories for which non-linear mixing terms appears and in the recently proposed theories beyond Horndeski which display a novel form of kinetic mixing, in which the field equation is sourced by derivatives of the energy-momentum tensor.
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