Scalar-tensor Gravity Research Articles

Stealth metastable state of scalar-tensor thermodynamics

We investigate a puzzle in the recent thermodynamics of scalar-tensor gravity, in which general relativity is a zero-temperature state of equilibrium and scalar-tensor gravity is the non-equilibrium configuration of an effective dissipative fluid. A stealth solution of Brans-Dicke gravity with constant positive temperature is shown to be analogous to a metastable state for the effective fluid and to suffer from an instability. The stability analysis employs a version of the Bardeen-Ellis-Bruni-Hwang gauge-invariant formalism for cosmological perturbations adapted to modified gravity. The metastable state is destroyed by tensor perturbations.

Bifurcated symmetry breaking in scalar-tensor gravity

We present models that simultaneously predict the presence of dark energy and cold dark matter along with slow-roll inflation. The dark energy density is found to be of order $(\text{a few meV}{)}^{4}$, and the mass of dark matter constituent is $\ensuremath{\approx}1\text{ }\text{ }\mathrm{meV}$. These numbers are given in terms of the present value of Hubble constant ${H}_{0}$ and the Plank energy ${M}_{\mathrm{P}}\text{ }=\text{ }1/\sqrt{16\ensuremath{\pi}{G}_{N}}$: they are $({H}_{0}{M}_{\mathrm{P}}{)}^{2}$ for the dark energy density and $({H}_{0}{M}_{\mathrm{P}}{)}^{1/2}$ for the dark matter constituent mass. The basic theoretical framework we work in is a multiscalar tensor gravity with nontrivial conformal coupling to the Ricci scalar curvature in the Lagrangian density. The key for a right amount of dark energy is to incorporate in a novel way the spatially homogeneous kinetic contribution of Nambu-Goldstone modes in a spontaneously broken multiscalar field sector. Proposed theories are made consistent with general relativity tests at small cosmological distances, yet are different from general relativity at cosmological scales. Dark matter is generated as a spatially inhomogeneous component of the scalar system, with a roughly comparable amount to the dark energy. In some presented models a cosmological bifurcation of symmetry breaking of the scalar sector is triggered by the spontaneous breaking of electroweak $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge symmetry, hence the separation occurring simultaneously at the electroweak phase transition. The best experimental method to test presented models is to search for the fifth-force type of scalar exchange interaction with a force range, $O({10}^{\ensuremath{-}2})\text{ }\text{ }\mathrm{cm}$, whose coupling to matter is basically of gravitational strength.

First-order thermodynamics of scalar-tensor cosmology

A new thermodynamics of scalar-tensor gravity is applied to spatiallyhomogeneous and isotropic cosmologies in thisclass of theories and testedon analytical solutions. A forever-expanding universe approaches theEinstein “state of equilibrium” with zero effective temperature at latetimes and departs from it near spacetime singularities. “Cooling” byexpansion and “heating” by singularities compete near the Big Rip, whereit is found that the effective temperature diverges in the case ofa conformally coupled scalar field.

Black hole thermodynamics in (2+1)-dimensional scalar–tensor-Born–Infeld theory

The action of scalar–tensor (ST) gravity theory can be written in both of the Jordan and Einstein frames, which are related via conformal transformations. Here, by introducing a suitable conformal transformation (CT), the action of three-dimensional Einstein-dilaton-Born–Infeld (EdBI) gravity has been obtained from that of scalar–tensor-Born–Infeld (STBI) theory. Despite the field equations of ST gravity, the exact solutions of Einstein-dilaton (Ed) theory can be obtained, easily. The exact solutions of STBI theory have been obtained from those of EdBI gravity by applying the inverse CTs. As the result, two novel classes of ST black hole (BH) solutions have been introduced in the presence of Born–Infeld (BI) nonlinear electrodynamics. The BHs’ conserved and thermodynamic quantities have been calculated under the influence of nonlinear electrodynamics. Then, through a Smarr-type mass formula, it has been shown that these quantities satisfy the standard form of the thermodynamical first law, in both of the Jordan and Einstein frames. Thermal stability or phase transition of the BHs have been investigate by use of the canonical ensemble method and regarding the signature of specific heat (SH). The points of first- and second-order phase transitions, and the size of those BHs which remain locally stable have been determined.

Neutron stars in scalar–tensor gravity with quartic order scalar potential

In this work we investigate the effects of a non-minimally coupled quartic order scalar model on static neutron stars, with the non-minimal coupling in the Jordan frame being of the form f(ϕ)=1+ξϕ2. Particularly we derive the Einstein frame Tolman–Oppenheimer–Volkoff equations, and by numerically integrating them for both the interior and the exterior of the neutron star, using a double shooting python 3 based numerical code, we extract the masses and radii of the neutron stars evaluated finally in the Jordan frame, along with several other related physical quantities of interest. With regard to the equation of state for the neutron star, we use a piecewise polytropic equation of state with the central part being Skyrme-Lyon (SLy), Akmal–Pandharipande–Ravenhall (APR) or the Wiringa–Fiks–Fabrocini (WFF1) equations of state. The resulting M–R graphs are compatible with the observational bounds imposed by the GW170817 event which require the radius of a static M∼1.6M⊙ neutron star to be larger than R=10.68−0.04+15km and the radius of a static neutron star corresponding to the maximum mass of the star to be larger than R=9.6−0.03+0.14km. Moreover, the WFF1 EoS, which was excluded for static neutron stars in the context of general relativity, for the quartic order scalar model neutron star model provides realistic results compatible with the GW170817 event.

Constructions of entropy and modified Friedmann equations in gravity theories

The FRW universe is considered a thermodynamical system. We assume that the universe filled in a perfect fluid. So, we obtain apparent horizon radius, surface gravity, and temperature. Using the unified first law as well as the first law of thermodynamics and Friedmann equations, we obtain the entropy-area relation on the apparent horizon in Einstein’s gravity. In Horava–Lifshitz gravity, scalar–tensor gravity, f(R) gravity and f(T) gravity theories, using corresponding Friedmann equations, we obtain the corresponding entropies in integration forms. Next, for a power law, future singularity, and de Sitter expansions, we obtain the general entropy function F(A) in terms of horizon area A on different IR cutoffs like Hubble, apparent, particle, event, (m, n)-type event, conformal age, and Ricci horizons. Moreover, by considering general entropy, we determine the modified Friedmann equations for Horava–Lifshitz gravity, scalar–tensor gravity, f(R) gravity and f(T) gravity theories.

Absorption cross section of regular black holes in scalar-tensor conformal gravity

In terms of the complex angular momentum method, we compute the absorption cross section by analyzing a massless test scalar field around conformally related black holes. At first, we investigate circular null geodesics and thereby prove a precondition for calculating the absorption cross section in the context of conformally related black holes. Then we use the WKB approximation method to derive the analytic expression of Regge frequency and the oscillation part of absorption cross sections. We find that this oscillation part depends on the scale factor of conformal transformations. By taking the conformally related Schwarzschild-Tangherlini black hole as an example, we show that this regular black hole has substantially distinctive absorption behavior compared with singular black holes. Our result provides a new approach to distinguish a regular black hole from a singular one.

Effective potential of scalar-tensor gravity with quartic self-interaction of scalar field

One-loop effective potential of scalar-tensor gravity with a quartic scalar field self-interaction is evaluated up to first post-Minkowskian order. The potential develops an instability in the strong field regime which is expected from an effective theory. Depending on model parameters the instability region can be exponentially far in a strong field region. Possible applications of the model for inflationary scenarios are highlighted. It is shown that the model can enter the slow-roll regime with a certain set of parameters.

Imprints of interacting dark energy on cosmological perturbations

We investigate the characteristic modifications in the evolving cosmological perturbations when dark energy interacts with dust-like matter, causing the latter’s background energy density fall off with time faster than usual. Focusing in particular to the late-time cosmic evolution, we show that such an interaction (of a specific form, arising naturally in a scalar-tensor formulation, or a wide range of modified gravity equivalents thereof), can have a rather significant effect on the perturbative spectrum, than on the background configuration which is not expected to get distorted much from [Formula: see text]CDM. Specifically, the matter density contrast, which is by and large scale-invariant in the deep sub-horizon limit, not only gets dragged as the interaction affects the background Hubble expansion rate, but also receives a contribution from the perturbation in the (scalar field induced) dark energy, which oscillates about a nonzero mean value. As such, the standard parametrization ansatz for the matter density growth factor becomes inadequate. So we modify it suitably, and also find a numerical fit of the growth index in terms of the background parameters, in order to alleviate the problems that arise otherwise. Such a fit enables direct estimations of the background parameters, as well as the growth parameter and the reduced Hubble parameter, which we duly carry out using a redshift space distortion (RSD) subsample and its combination with the observational Hubble data. On the whole, the parametric estimates show consistency with the general observational constraints on the background level cosmology, as well as the constraints on scalar-tensor gravity from astrophysical observations, apart from having significance in the domain of cosmological perturbations.

Bouncing cosmological isotropic solutions in scalar-tensor gravity

Bouncing non-singular isotropic cosmological solutions are investigated in a simple model of scalar-tensor gravity. New families of such solutions are found and their properties are presented and analyzedusing an effective potential as the main tool.Bouncing solutions are shown to exist for a Higgs-like self-interactionpotential which is bounded from below, in contrast to previous solutions that appeared in the literature based on potentials which were unbounded from below. In the simplest version of a scalar field with the quartic potential and conformal coupling to gravity, bouncing spatially flat solutions either have the Hubble function diverging in the past beforethe bounce, but with a well-behaved future, or are globally regular but unstable with respect to anisotropic or inhomogeneousperturbations at some finite values of the scalar field and curvature. Regular solutions can only exist in the part of the parameter space where the maximum ofthe effective potential is larger than the first zero of the potential, and gravity becomesrepulsive at the bounce.

Gravitational decoupling of generalized Horndeski hybrid stars

Gravitational decoupled compact polytropic hybrid stars are here addressed in generalized Horndeski scalar-tensor gravity. Additional physical properties of hybrid stars are scrutinized and discussed in the gravitational decoupling setup. The asymptotic value of the mass function, the compactness, and the effective radius of gravitational decoupled hybrid stars are studied for both cases of a bosonic and a fermionic prevalent core. These quantities are presented and discussed as functions of Horndeski parameters, the decoupling parameter, the adiabatic index, and the polytropic constant. Important corrections to general relativity and generalized Horndeski scalar-tensor gravity, induced by the gravitational decoupling, comply with available observational data. Particular cases involving white dwarfs, boson stellar configurations, neutron stars, and Einstein–Klein–Gordon solutions, formulated in the gravitational decoupling context, are also scrutinized.

New approach to the thermodynamics of scalar-tensor gravity

We discuss and expand a new approach to the thermodynamics of scalar-tensor gravity and its diffusion toward general relativity (seen as an equilibrium state) proposed in a previous paper [Phys. Rev. D 103, L121501 (2021), upon which we build. We describe scalar-tensor gravity as an effective dissipative fluid and apply Eckart's first order thermodynamics to it, obtaining explicitly effective quantities such as heat flux, ``temperature of gravity,'' viscosities, entropy density, plus an equation describing the ``diffusion'' to Einstein gravity. These quantities, still missing in the usual thermodynamics of spacetime, are obtained with minimal assumptions. Furthermore, we examine certain exact solutions of scalar-tensor gravity to test the proposed formalism and gain some physical insight on the ``approach to equilibrium'' for this class of theories.

Well-tempered Minkowski solutions in teleparallel Horndeski theory

Well-tempering stands among the few classical methods of screening vacuum energy to deliver a late-time, low energy vacuum state. We build on the class of Horndeski models that admit a Minkowski vacuum state despite the presence of an arbitrarily large vacuum energy to obtain a much larger family of models in teleparallel Horndeski theory. We set up the routine for obtaining these models and present a variety of cases, all of which are able to screen a natural particle physics scale vacuum energy using degeneracy in the field equations. We establish that well-tempering is the unique method of utilizing degeneracy in Horndeski scalar-tensor gravity—and its teleparallel generalisation—that can accommodate self-tuned flat Minkowski solutions, when the explicit scalar field dependence in the action is minimal (a tadpole and a conformal coupling to the Ricci scalar). Finally, we study the dynamics of the well-tempered teleparallel Galileon. We generate its phase portraits and assess the attractor nature of the Minkowski vacuum under linear perturbations and through a phase transition of vacuum energy. ‘The effort to understand the Universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy.’-Steven Weinberg

Extended reduced-order surrogate models for scalar-tensor gravity in the strong field and applications to binary pulsars and gravitational waves

Statistically sound tests of scalar-tensor gravity theories in the strong-field regime usually involves computationally intensive calculations. In this study, we construct a reduced order surrogate model for the scalar-tensor gravity of Damour and Esposito-Far\`ese (DEF) with spontaneous scalarization phenomena developed for neutron stars (NSs). This model allows us to perform a rapid and comprehensive prediction of NS properties, including mass, radius, moment of inertia, effective scalar coupling, and two extra coupling parameters. We code the model in the pySTGROMX package, as an extension of our previous work, that speeds up the calculations at two and even three orders of magnitude and yet still keeps accuracy of $\sim1\%$. Using the model, we can calculate all the post-Keplerian parameters in the timing of binary pulsars conveniently, which provides a quick approach for us to place comprehensive constraints on the DEF theory. We perform Markov-chain Monte Carlo simulations with the model to constrain the parameters of the DEF theory with well-timed binary pulsars. Utilizing five NS-white dwarf and three NS-NS binaries, we obtain the most stringent constraints on the DEF theory up to now. Our work provides a public tool for quick evaluation of NSs' derived parameters to test gravity in the strong-field regime.

Quasinormal modes of the Kerr-Newman black hole: GW150914 and fundamental physics implications

We develop an analytical ringdown waveform model, including both the fundamental and the overtone quasinormal modes, for charged black holes and show that it is precise enough to analyze current gravitational wave data. Applying this waveform model to GW150914, the charge to mass ratio of the remnant black hole (${\ensuremath{\lambda}}_{f}$) has been constrained with the sole ringdown gravitational wave data for the first time and the 90% upper limit is ${\ensuremath{\lambda}}_{f}\ensuremath{\le}0.38$. Correspondingly, the deviation parameter of the scalar-tensor vector gravity (${\ensuremath{\alpha}}_{\mathrm{s}}$) is limited to be ${\ensuremath{\alpha}}_{\mathrm{s}}\ensuremath{\le}0.17$. Our approach can be directly applied to other binary black hole mergers with loud ringdown radiation.

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.

Relic gravitational waves in cosmological models based on the modified gravity theories

We consider cosmological models based on the generalized scalar-tensor gravity, which correspond to the observational constraints on the parameters of cosmological perturbations for any model’s parameters. The estimates of the energy density of relic gravitational waves for such a cosmological models were made. The possibility of direct detection of such a gravitational waves using modern and prospective methods was discussed as well.

Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star

After giving a short overview of previous results on constraining of Extended Gravity by stellar orbits, we discuss the Schwarzschild orbital precession of S2 star assuming the congruence with predictions of General Relativity (GR). At the moment, the S2 star trajectory is remarkably fitted with the first post-Newtonian approximation of GR. In particular, both Keck and VLT (GRAVITY) teams declared that the gravitational redshift near its pericenter passage for the S2 star orbit corresponds to theoretical estimates found with the first post-Newtonian (pN) approximation. In 2020, the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center and showed that it is close to the GR prediction. Based on this observational fact, we evaluated parameters of the Extended Gravity theories with the Schwarzschild precession of the S2 star. Using the mentioned method, we estimate the orbital precession angles for some Extended Gravity models including power-law f(R), general Yukawa-like corrections, scalar–tensor gravity, and non-local gravity theories formulated in both metric and Palatini formalism. In this consideration, we assume that a gravitational field is spherically symmetric, therefore, alternative theories of gravity could be described only with a few parameters. Specifically, considering the orbital precession, we estimate the range of parameters of these Extended Gravity models for which the orbital precession is like in GR. Then we compare these results with our previous results, which were obtained by fitting the simulated orbits of S2 star to its observed astrometric positions. In case of power-law f(R), generic Yukawa-like correction, scalar–tensor gravity and non-local gravity theories, we were able to obtain a prograde orbital precession, like in GR. According to these results, the method is a useful tool to evaluate parameters of the gravitational potential at the Galactic Center.

Spin-orbit effects for compact binaries in scalar-tensor gravity

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 0.5 PN or 1.5 PN order, while those that arise from a disformal coupling start at either 3.5 PN or 4.5 PN 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.