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We study the stability of relativistic stars in scalar-tensor theories with a nonminimal coupling of the form $F(phi)R$, where $F$ depends on a scalar field $phi$ and $R$ is the Ricci scalar. On a spherically symmetric and static background, we incorporate a perfect fluid minimally coupled to gravity as a form of the Schutz-Sorkin action. The odd-parity perturbation for the multipoles $l geq 2$ is ghost-free under the condition $F(phi)>0$, with the speed of gravity equivalent to that of light. For even-parity perturbations with $l geq 2$, there are three propagating degrees of freedom arising from the perfect-fluid, scalar-field, and gravity sectors. For $l=0, 1$, the dynamical degrees of freedom reduce to two modes. We derive no-ghost conditions and the propagation speeds of these perturbations and apply them to concrete theories of hairy relativistic stars with $F(phi)>0$. As long as the perfect fluid satisfies a weak energy condition with a positive propagation speed squared $c_m^2$, there are neither ghost nor Laplacian instabilities for theories of spontaneous scalarization and Brans-Dicke (BD) theories with a BD parameter $omega_{rm BD}>-3/2$ (including $f(R)$ gravity). In these theories, provided $0<c_m^2 le 1$, we show that all the propagation speeds of even-parity perturbations are sub-luminal inside the star, while the speeds of gravity outside the star are equivalent to that of light.
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Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from general relativity in the strong-field regime. In these theories, the $N$-tuple of scalar fields takes values in a coordinate patch of an $N$-dimensional Riemannian target-space manifold whose properties are poorly constrained by weak-field observations. Here we introduce for simplicity a non-trivial model with two scalar fields and a maximally symmetric target-space manifold. Within this model we present a preliminary investigation of spontaneous scalarization for relativistic, perfect fluid stellar models in spherical symmetry. We find that the scalarization threshold is determined by the eigenvalues of a symmetric scalar-matter coupling matrix, and that the properties of strongly scalarized stellar configurations additionally depend on the target-space curvature radius. In preparation for numerical relativity simulations, we also write down the $3+1$ decomposition of the field equations for generic tensor-multi-scalar theories.
In this work we shall study the implications of a subclass of $E$-models cosmological attractors, namely of $a$-attractors, on hydrodynamically stable slowly rotating neutron stars. Specifically, we shall present the Jordan frame theory of the $a$-attractors, and by using a conformal transformation we shall derive the Einstein frame theory. We discuss the inflationary context of $a$-attractors in order to specify the allowed range of values for the free parameters of the model based on the latest cosmic-microwave-background-based Planck 2018 data. Accordingly, using the notation and physical units frequently used in theoretical astrophysics contexts, we shall derive the Tolman-Oppenheimer-Volkoff equations in the Einstein frame. Assuming a piecewise polytropic equation of state, the lowest density part of which shall be chosen to be the WFF1, or APR or the SLy EoS, we numerically solve the Tolman-Oppenheimer-Volkoff equations using a double shooting python-based LSODA numerical code. The resulting picture depends on the value of the parameter $a$ characterizing the $a$-attractors. As we show, for large values of $a$, which do not produce a viable inflationary era, the $M-R$ graphs are nearly identical to the general relativistic result, and these two are discriminated at large central densities values. Also, for large $a$-values, the WFF1 equation of state is excluded, due to the GW170817 constraints. In addition, the small $a$ cases produce larger masses and radii compared to the general relativistic case and are compatible with the GW170817 constraints on the radii of neutron stars. Our results indicate deep and not yet completely understood connections between non-minimal inflationary attractors and neutron stars phenomenology in scalar-tensor theory.
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 study the viability conditions for the absence of ghost, gradient and tachyonic instabilities, in scalar-torsion $f(T,phi)$ gravity theories in the presence of a general barotropic perfect fluid. To describe the matter sector, we use the Sorkin-Schutz action and then calculate the second order action for scalar perturbations. For the study of ghost and gradient instabilities, we found that the gravity sector keeps decoupled from the matter sector and then applied the viability conditions for each one separately. Particularly, we verified that this theory is free from ghost and gradient instabilities, obtaining the standard results for matter, and for the gravity sector we checked that the corresponding speed of propagation satisfies $c_{s,g}^2=1$. On the other hand, in the case of tachyonic instability, we obtained the general expressions for the mass eigenvalues and then evaluated them in the scaling matter fixed points of a concrete model of dark energy. Thus, we found a space of parameters where it is possible to have a stable configuration respecting the constraints from the CMB measurements and the BBN constraints for early dark energy. Finally, we have numerically corroborated these results by solving the cosmological equations for a realistic cosmological evolution with phase space trajectories undergoing scaling matter regimes, and then showing that the system presents a stable configuration throughout cosmic evolution.
In scalar-vector-tensor theories with $U(1)$ gauge invariance, it was recently shown that there exists a new type of hairy black hole (BH) solutions induced by a cubic-order scalar-vector interaction. In this paper, we derive conditions for the absence of ghosts and Laplacian instabilities against odd-parity perturbations on a static and spherically symmetric background for most general $U(1)$ gauge-invariant scalar-vector-tensor theories with second-order equations of motion. We apply those conditions to hairy BH solutions arising from the cubic-order coupling and show that the odd-parity stability in the gravity sector is always ensured outside the event horizon with the speed of gravity equivalent to that of light. We also study the case in which quartic-order interactions are present in addition to the cubic coupling and obtain conditions under which black holes are stable against odd-parity perturbations.
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