Massive Scalar-tensor Theories Research Articles

Binary neutron star mergers in massive scalar-tensor theory: Properties of postmerger remnants

We investigate the properties of postmerger remnants of binary neutron star mergers in the framework of Damour–Esposito-Farese-type scalar-tensor theory of gravity with a massive scalar field by numerical relativity simulation. It is found that the threshold mass for prompt collapse is raised in the presence of the excited scalar field. Our simulation results also suggest the existence of a long-lived ϕ mode in hypermassive neutron stars due to the presence of the massive scalar field that enhances the quasiradial oscillation in the remnant. We investigate the descalarization condition in hypermassive neutron stars and discover a distinctive signature in postmerger gravitational waves. Published by the American Physical Society 2024

Binary neutron star mergers in massive scalar-tensor theory: Quasiequilibrium states and dynamical enhancement of the scalarization

Binary neutron star mergers in massive scalar-tensor theory: Quasiequilibrium states and dynamical enhancement of the scalarization

Spontaneous scalarization as a new core-collapse supernova mechanism and its multimessenger signals

We perform multi-dimensional core-collapse supernova (CCSN) simulations in a massive scalar-tensor theory for the first time with a realistic equation of state and multi-energy neutrino radiation. Among the set of our models varying the scalar mass and the coupling strength between the scalar and gravitational fields, a particular model allows for recurrent spontaneous scalarizations (SSs) in the proto-neutron star (PNS). Each SS induces the PNS collapse and subsequent bounce, from which devastating shock waves emanate and eject the PNS envelope. The explosion energy can easily exceed $\mathcal O(10^{51})$ erg. This study reveals new aspects of SS as the explosion mechanism of CCSNe. We also discuss its characteristic multi-messenger signals: neutrinos and gravitational waves.

Gravitational Waves from Accretion-Induced Descalarization in Massive Scalar-Tensor Theory.

Many classes of extended scalar-tensor theories predict that dynamical instabilities can take place at high energies, leading to the formation of scalarized neutron stars. Depending on the theory parameters, stars in a scalarized state can form a solution-space branch that shares a lot of similarities with the so-called mass twins in general relativity appearing for equations of state containing first-order phase transitions. Members of this scalarized branch have a lower maximum mass and central energy density compared to Einstein ones. In such cases, a scalarized star could potentially overaccrete beyond the critical mass limit, thus triggering a gravitational phase transition where the star sheds its scalar hair and migrates over to its nonscalarized counterpart. Such an event resembles, but is distinct from, a nuclear or thermodynamic phase transition. We dynamically track a gravitational transition by first constructing hydrostatic, scalarized equilibria for realistic equations of state, and then allowing additional material to fall onto the stellar surface. The resulting bursts of monopolar radiation are dispersively stretched to form a quasicontinuous signal that persists for decades, carrying strains of order ≳10^{-22} (kpc/L)^{3/2} Hz^{-1/2} at frequencies of ≲300 Hz, detectable with the existing interferometer network out to distances of L≲10 kpc, and out to a few hundred kpc with the inclusion of the Einstein Telescope. Electromagnetic signatures of such events, involving gamma-ray and neutrino bursts, are also considered.

On Shapiro time delay in massive scalar-tensor theories

The problem of defenition of the post-Newtonian parameter γ in massive scalar-tensor theories is considered. We demonstrate an equivalent correspondence between the post-Newtonian parameter γ and the parameter appearing in the equation of a null geodesic in massive scalar-tensor theories. We show that massive scalar-tensor theories can be distinguished from general relativity via the Shapiro time delay. All calculations are performed for hybrid metric-Palatini f(R)-gravity for the sake of illustration. The expression for Shapiro time delay in hybrid f(R)-gravity is obtained for the first time.

Uniqueness of the Inflationary Higgs Scalar for Neutron Stars and Failure of Non-Inflationary Approximations

Neutron stars are perfect candidates to investigate the effects of a modified gravity theory, since the curvature effects are significant and more importantly, potentially testable. In most cases studied in the literature in the context of massive scalar-tensor theories, inflationary models were examined. The most important of scalar-tensor models is the Higgs model, which, depending on the values of the scalar field, can be approximated by different scalar potentials, one of which is the inflationary. Since it is not certain how large the values of the scalar field will be at the near vicinity and inside a neutron star, in this work we will answer the question, which potential form of the Higgs model is more appropriate in order for it to describe consistently a static neutron star. As we will show numerically, the non-inflationary Higgs potential, which is valid for certain values of the scalar field in the Jordan frame, leads to extremely large maximum neutron star masses; however, the model is not self-consistent, because the scalar field approximation used for the derivation of the potential, is violated both at the center and at the surface of the star. These results shows the uniqueness of the inflationary Higgs potential, since it is the only approximation for the Higgs model, that provides self-consistent results.

Scalar gravitational wave signals from core collapse in massive scalar–tensor gravity with triple-scalar interactions

The spontaneous scalarization during the stellar core collapse in the massive scalar–tensor theories of gravity introduces extra polarizations (on top of the plus and cross modes) in gravitational waves, whose amplitudes are determined by several model parameters. Observations of such scalarization-induced gravitational waveforms therefore offer valuable probes into these theories of gravity. Considering a triple-scalar interactions in such theories, we find that the self-coupling effects suppress the magnitude of the scalarization and thus reduce the amplitude of the associated gravitational wave signals. In addition, the self-interacting effects in the gravitational waveform are shown to be negligible due to the dispersion throughout the astrophysically distant propagation. As a consequence, the gravitational waves observed on the Earth feature the characteristic inverse-chirp pattern. Although not with the on-going ground-based detectors, we illustrate that the scalarization-induced gravitational waves may be detectable at a signal-to-noise ratio level of with future detectors, such as Einstein Telescope and Cosmic Explorer.

Scalarized neutron stars in massive scalar-tensor gravity: X-ray pulsars and tidal deformability

Neutron stars (NSs) in scalar-tensor theories of gravitation with the phenomenon of spontaneous scalarization can develop significant deviations from general relativity. Cases with a massless scalar have been studied widely. We compare the NS scalarizations in Damour--Esposito-Far\`ese theory, Mendes-Ortiz theory, and $\ensuremath{\xi}$ theory with a massive scalar field. Numerical solutions for slowly rotating NSs are obtained. They are used to construct the x-ray pulse profiles of a pair of extended hot spots on the surface of NSs. We also calculate the tidal deformability for NSs with spontaneous scalarization, which is done for the first time with a massive scalar field. We show the universal relation between the moment of inertia and the tidal deformability. The x-ray pulse profiles, the tidal deformability, and the universal relation may help us to constrain the massive scalar-tensor theories in x-ray and gravitational-wave observations of NSs, including the Neutron star Interior Composition Explorer satellite, the Square Kilometre Array telescope, and LIGO/Virgo/KAGRA laser interferometers.

Polar Quasinormal Modes of Neutron Stars in Massive Scalar-Tensor Theories

We study polar quasinormal modes of relativistic stars in scalar-tensor theories, where we include a massive gravitational scalar field and employ the standard Brans-Dicke coupling function. For the potential of the scalar field we consider a simple mass term as well as a potential associated withR2gravity. The presence of the scalar field makes the spectrum of quasinormal modes much richer than the spectrum in General Relativity. We here investigate radial modes (l= 0) and quadrupole modes (l= 2). The general relativisticl= 0 normal modes turn into quasinormal modes in scalar-tensor theories, that are able to propagate outside of the stars. In addition to the pressure-led modes new scalar-ledϕ-modes arise. We analyze the dependence of the quasinormal mode frequencies and decay times on the scalar field mass.

The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms

Here we perform the Kaluza–Klein dimensional reduction from D+1 to D dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein–Hilbert theory, linearized unimodular gravity and scalar tensor models. We obtain simple expressions in terms of gauge invariant field combinations and show that unitarity is preserved in all cases. After fixing a gauge, the reduced model becomes a massive scalar tensor theory. We show that the diffeomorphism (Diff) symmetry, instead of TDiff, is a general feature of the massless sector of consistent massive scalar tensor models. We discuss some subtleties when eliminating Stückelberg fields directly at action level as gauge conditions. A non local connection between the massless sector of the scalar tensor theory and the pure tensor TDiff model leads to a parametrization of the non conserved source which naturally separates spin-0 and spin-2 contributions in the pure tensor theory. The case of curved backgrounds is also investigated. If we truncate the non minimal couplings to linear terms in the curvature, vector and scalar constraints require Einstein spaces as in the Diff and WTDiff (Weyl plus Diff) cases. We prove that our linearized massive scalar tensor models admit those curved background extensions.

Constraining the equation of state in modified gravity via universal relations

Modern multi-messenger astronomical observations and heavy ion experiments provide new insights into the structure of compact objects. Nevertheless, much ambiguity remains when it comes to super dense matter above the nuclear saturation density such as that found within neutron stars. This work explores equation of state (EOS)-independent universal relations between the physical parameters of static neutron stars at the maximum-mass point, previously proven for General Relativity (GR) and used to constraint EOS candidates within the GR framework. We explore 53 different EOS candidates and prove that these relations hold for scalarized neutron stars in massive scalar-tensor theories, exploring also the effect of non-baryonic EOS. We further show that the relation's fit parameters are highly dependent on the theory's parameters. On the basis of these relations multiple constraints on the EOS can be derived and it turns out that they can be significantly different than the GR ones. This demonstrates the importance of taking into account the modified gravity effects even when imposing constraints on the EOS.

Orbital and epicyclic frequencies in massive scalar-tensor theory with self-interaction

Testing modified theories of gravity with direct observations of the parameters of a neutron star is not the optimal way of testing gravitational theories. However, observing electromagnetic signals originating from the close vicinity of the compact object my turn out an excellent way of probing spacetime in strong field regime. A promising candidate for doing so are the so-called quasi-periodic oscillations, observed in the X-ray light curves of some pulsars. Although the origin of those oscillations is unknown, one thing most of the models describing them have in common is that in one way or another they incorporate the radius of the innermost stable circular obit, and the orbital and the epicyclic frequencies of particles moving around the compact object. In this paper we study the aforementioned quantities in the context of massive scalar-tensor theory and massive scalar-tensor theory with self-interaction, both of which in strong regime allow for significant deviations from General relativity for values for the free parameters of the theory in correlation with the observations.

Axial quasinormal modes of scalarized neutron stars with massive self-interacting scalar field

We study the axial quasi-normal modes of neutron stars in scalar-tensor theories with massive scalar field including a self-interacting term in the potential. Various realistic equations of state including nuclear, hyperonic and hybrid matter are employed. Although the effect of spontaneous scalarization of neutron stars can be very large, binary pulsar observations and gravitational wave detections significantly constrain the massless scalar-tensor theories. If we consider a properly chosen nonzero mass for the scalar field, though, the scalar-tensor parameters cannot be restricted by the observations, resulting in large deviation from pure general relativity. With this motivation in mind, we extend the universal relations for axial quasi-normal modes known in general relativity to neutron stars in massive scalar-tensor theories with self-interaction using a wide range of realistic EOS. We confirm the universality of the scaled frequency and damping time in terms of the compactness and scaled moment of inertia for neutron stars with and without massive scalarization.

Rapidly rotating neutron stars with a massive scalar field—structure and universal relations

We construct rapidly rotating neutron star models in scalar-tensor theories with a massive scalar field. The fact that the scalar field has nonzero mass leads to very interesting results since the allowed range of values of the coupling parameters is significantly broadened. Deviations from pure general relativity can be very large for values of the parameters that are in agreement with the observations. We found that the rapid rotation can magnify the differences several times compared to the static case. The universal relations between the normalized moment of inertia and quadrupole moment are also investigated both for the slowly and rapidly rotating cases. The results show that these relations are still EOS independent up to a large extend and the deviations from pure general relativity can be large. This places the massive scalar-tensor theories amongst the few alternative theories of gravity that can be tested via the universal I-Love-Q relations.

Slowly rotating neutron stars in scalar-tensor theories with a massive scalar field

In the scalar-tensor theories with a massive scalar field the coupling constants, and the coupling functions in general, which are observationally allowed, can differ significantly from those in the massless case. This fact naturally implies that the scalar-tensor neutron stars with a massive scalar field can have rather different structure and properties in comparison with their counterparts in the massless case and in general relativity. In the present paper we study slowly rotating neutron stars in scalar-tensor theories with a massive gravitational scalar. Two examples of scalar-tensor theories are examined - the first example is the massive Brans-Dicke theory and the second one is a massive scalar-tensor theory indistinguishable from general relativity in the weak field limit. In the later case we study the effect of the scalar field mass on the spontaneous scalarization of neutron stars. Our numerical results show that the inclusion of a mass term for the scalar field indeed changes the picture drastically compared to the massless case. It turns out that mass, radius and moment of inertia for neutron stars in massive scalar-tensor theories can differ drastically from the pure general relativistic solutions if sufficiently large masses of the scalar field are considered.

Astrophysical Black Holes as Natural Laboratories for Fundamental Physics and Strong-Field Gravity

Astrophysical tests of general relativity belong to two categories: 1) "internal", i.e. consistency tests within the theory (for example, tests that astrophysical black holes are indeed described by the Kerr solution and its perturbations), or 2) "external", i.e. tests of the many proposed extensions of the theory. I review some ways in which astrophysical black holes can be used as natural laboratories for both "internal" and "external" tests of general relativity. The examples provided here (ringdown tests of the black hole "no-hair" theorem, bosonic superradiant instabilities in rotating black holes and gravitational-wave tests of massive scalar-tensor theories) are shamelessly biased towards recent research by myself and my collaborators. Hopefully this colloquial introduction aimed mainly at astrophysicists will convince skeptics (if there are any) that space-based detectors will be crucial to study fundamental physics through gravitational-wave observations.

Gravitational waves from quasicircular extreme mass-ratio inspirals as probes of scalar-tensor theories

A stellar-mass compact object spiraling into a supermassive black hole, an extreme-mass-ratio inspiral (EMRI), is one of the targets of future gravitational-wave detectors and it offers a unique opportunity to test General Relativity (GR) in the strong-field. We study whether generic scalar-tensor (ST) theories can be further constrained with EMRIs. We show that in the EMRI limit, all such theories universally reduce to massive or massless Brans-Dicke theory and that black holes do not emit dipolar radiation to all orders in post-Newtonian (PN) theory. For massless theories, we calculate the scalar energy flux in the Teukolsky formalism to all orders in PN theory and fit it to a high-order PN expansion. We derive the PN ST corrections to the Fourier transform of the gravitational wave response and map it to the parameterized post-Einsteinian framework. We use the effective-one-body framework adapted to EMRIs to calculate the ST modifications to the gravitational waveform. We find that such corrections are smaller than those induced in the early inspiral of comparable-mass binaries, leading to projected bounds on the coupling that are worse than current Solar System ones. Brans-Dicke theory modifies the weak-field, with deviations in the energy flux that are largest at small velocities. For massive theories, superradiance can lead to resonances in the scalar energy flux that can lead to floating orbits outside the innermost stable circular orbit and that last until the supermassive black hole loses enough mass and spin-angular momentum. If such floating orbits occur in the frequency band of LISA, they would lead to a large dephasing (~1e6 rads), preventing detection with GR templates. A detection that is consistent with GR would then rule out floating resonances at frequencies lower than the lowest observed frequency, allowing for the strongest constraints yet on massive ST theories.

Exact cosmological solution of a scalar-tensor gravity theory compatible with theΛCDMmodel

We consider the massive scalar-tensor theory in the Jordan frame $F(\ensuremath{\Phi})={K}^{2}{\ensuremath{\Phi}}^{2}$ and $U(\ensuremath{\Phi})=(1/2){m}^{2}{\ensuremath{\Phi}}^{2}$, where $F(\ensuremath{\Phi})$ corresponds to a constant Brans-Dicke parameter ${\ensuremath{\omega}}_{\mathrm{BD}}=1/4{K}^{2}$. The constraint of the Solar System experiments is ${K}^{2}<(1/400{)}^{2}$. For dustlike matter in a spatially flat, homogeneous isotropic universe, we reduce the equations of motion to a system of two differential equations of first order which can be exactly solved. We obtain simple and explicit expressions for $\frac{\ensuremath{\Phi}(z)}{\ensuremath{\Phi}(0)}$ and $\frac{H(z)}{{H}_{0}}$ that depend only on two parameters, ${K}^{2}$ and ${\ensuremath{\Omega}}_{m,0}$. For $K\ensuremath{\le}1/400$, the expansion rate $H(z)$ can be practically superposed on the $\ensuremath{\Lambda}\mathrm{CDM}$ solution ${H}_{\ensuremath{\Lambda}}(z)$, up to high redshift $z$, but the equation of state ${w}_{\mathrm{DE}}(z)$ of the dark energy is not constant: it presents a very slight crossing of the phantom divide line $w=\ensuremath{-}1$ in the neighborhood of $z=0$ and becomes very slightly positive at high redshifts.