Scalar-tensor Gravity Model Research Articles

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.

Cosmological test of an extended quintessence model

We investigate the cosmological observational test of the extended quintessence model, i.e. a scalar-tensor gravity model with a scalar field potential serving as dark energy, by using the Planck 2018 cosmic microwave background (CMB) data, together with the baryon acoustic oscillations (BAO) and redshift-space distortion (RSD) data. As an example, we consider the model with a Brans-Dicke kinetic term $\frac{\omega(\phi)}{\phi} \phi_{;\mu} \phi^{;\mu} $ and a quadratic scalar potential $V (\phi) = A + B (\phi - \phi_0) + \frac{C}{2} (\phi - \phi_0)^2$, which reduces to general relativity (GR) in the limit $\omega(\phi) \to \infty$, and the cosmological constant in the limit $B=C=0$. In such a model the scalar field typically rolls down the potential and oscillates around the minimum of $V (\phi)$. We find that the model parameter estimate for the CMB+BAO+RSD data set is given by $\lg \alpha = -3.6 _{-0.54}^{+0.66}~ (68\%)$, corresponding to $ 3.8 \times 10^5 < \omega_0 < 9.5 \times 10^7~ (68\%)$, and $\lg C = 4.9 \pm 1.4~ (68\%) $. However, the GR $\Lambda$CDM model can fit the data almost as good as this extended quintessence model, and is favored by the Akaike information criterion (AIC). The variation of the gravitational constant since the epoch of Recombination is constrained to be $0.97 < G_{\rm rec}/G_0 < 1.03~ (1 \sigma)$. In light of recent report that the CMB data favors a closed universe, we consider the case with non-flat geometry in our fit, and find that the mean value of $\Omega_k$ shifts a little bit from $-0.049$ to $-0.036$, and the parameters in our model are not degenerate with $\Omega_k$.

Boson and neutron stars with increased density

We discuss boson stars and neutron stars, respectively, in a scalar-tensor gravity model with an explicitly time-dependent real scalar field. While the boson stars in our model – in contrast to the neutron stars – do not possess a hard core, we find that the qualitative effects of the formation of scalar hair are similar in both cases: the presence of the gravity scalar allows both type of stars to exist for larger central density as well as larger mass at given radius than their General Relativity counterparts. In particular, we find new types of neutron stars with scalar hair which have radii very close to the corresponding Schwarzschild radius and hence are comparable in density to black holes. This new branch of solutions is stable with respect to the decay into individual baryons.

One-loop effective scalar-tensor gravity

Non-minimal interactions are proven to be generated at the one-loop level in simple scalar-tensor gravity models. The John interaction from the Fab Four class is generated. The interaction affects the speed of gravitational waves in the contemporary Universe. Its role in low-energy phenomenology is discussed. Brans-Dicke-like interaction is generated in a non-minimal model. An opportunity to generate a dynamic low-energy Newton constant is addressed.

Scalarization of asymptotically anti–de Sitter black holes with applications to holographic phase transitions

We study the spontaneous scalarization of spherically symmetric, static and asymptotically Anti-de Sitter (aAdS) black holes in a scalar-tensor gravity model with non-mininal coupling of the form $\phi^2\left(\alpha{\cal R} + \gamma {\cal G}\right)$, where $\alpha$ and $\gamma$ are constants, while ${\cal R}$ and ${\cal G}$ are the Ricci scalar and Gauss-Bonnet term, respectively. Since these terms act as an effective ``mass'' for the scalar field, non-trivial values of the scalar field in the black hole space-time are possible for {\it a priori} vanishing scalar field mass. In particular, we demonstrate that the scalarization of an aAdS black hole requires the curvature invariant $-\left(\alpha{\cal R} + \gamma {\cal G}\right)$ to drop below the Breitenlohner-Freedman bound close to the black hole horizon, while it asymptotes to a value well above the bound. The dimension of the dual operator on the AdS boundary depends on the parameters $\alpha$ and $\gamma$ and we demonstrate that -- for fixed operator dimension -- the expectation value of this dual operator increases with decreasing temperature of the black hole, i.e. of the dual field theory. When taking backreaction of the space-time into account, we find that the scalarization of the black hole is the dual description of a phase transition in a strongly coupled quantum system, i.e. corresponds to a holographic phase transition. A possible application are liquid-gas quantum phase transitions, e.g. in $^4$He. Finally, we demonstrate that extremal black holes with $AdS_2\times S^2$ near-horizon geometry {\it cannot support regular scalar fields on the horizon} in the scalar-tensor model studied here.

Revisiting the coincidence problem in f(R) gravitation

The energy densities of dark matter (DM) and dark energy (DE) are of the same order at the present epoch despite the fact that both these quantities have contrasting characteristics and are presumed to have evolved distinctively with cosmic evolution. This is a major issue in standard ΛCDM cosmology and is termed “The Coincidence Problem” which hitherto cannot be explained by any fundamental theory. In this spirit, Bisabr (2010) reported a cosmological scenario in f(R) gravity where DM and DE interact and exchange energy with each other and therefore evolve dependently. We investigate the efficiency and model independancy of the technique reported in Bisabr (2010) in addressing the Coincidence problem with the help of two f(R) gravity models with model parameters constrained from various observations. Our result confirm the idea that not all scalar-tensor gravity theories and models can circumvent the Coincidence Problem and any cosmological scenario with interacting fluids is highly model dependent and hence alternate model independent theories and ideas should be nominated to solve this mystery.

Spontaneous scalarization of boson stars

We study the spontaneous scalarization of spherically symmetric, asymptoically flat boson stars in the (αℛ + γ mathcal{G} )ϕ2 scalar-tensor gravity model. These compact objects are made of a complex valued scalar field that has harmonic time dependence, while their space-time is static and they can reach densities and masses similar to that of supermassive black holes. We find that boson stars can be scalarized for both signs of the scalar-tensor coupling α and γ, respectively. This is, in particular, true for boson stars that are a priori stable with respect to decay into individual bosonic particles. A fundamental difference between the α- and γ-scalarization exists, though: while we find an interval in α > 0 for which boson stars can never be scalarized when γ = 0, there is no restriction on γ ≠ 0 when α = 0. Typically, two branches of solutions exist that differ in the way the boson star gets scalarized: either the scalar field is maximal at the center of the star, or on a shell with finite radius which roughly corresponds to the outer radius of the boson star. We also demonstrate that the former solutions can be radially excited.

Conformal Frame Dependence on Cosmological Observations in Scalar-Tensor Theories of Gravity

Cosmological observations provide more accurate values both for background evolution of the Universe and for the structure formation. These values are given by the so-called dark energy equation of state, $\omega$ and the growth index parameter, $\gamma$. From these observed parameters, one can reconstruct the model functions in scalar tensor gravity theories. However, there is a long standing debate about the (in)equality between conformally transformed frames in scalar tensor gravity models. We show that cosmological observables are frame dependent when they are described by frame independent parameter, redshift. Thus, if the cosmological observables are interpreted in one frame, then all of the observables should also be interpreted in that frame. This explicitly shows the conformal inequality of cosmological observables. Also, our method provides the model independent analysis for STG models about various observables in both frames.

Constraining scalar-tensor gravity models by S2 star orbits around the galactic center

The aim of our investigation is to derive a particular theory among the class of scalar-tensor(ST) theories of gravity, and then to test it by studying kinematics and dynamics of S-stars around a supermassive black hole (BH) at Galactic Center (GC). We also discuss the Newtonian limit of this class of ST theories of gravity, as well as its parameters. We compare the observed orbit of S2 star with our simulated orbit which we obtained theoretically with the derived ST potential and constrained parameters. Using the obtained best-fit parameters we calculated orbital precession of S2 star in ST gravity and found that it has the same direction as in General Relativity (GR) but causes much larger pericenter shift.

Charged scalar-tensor solitons and black holes with (approximate) Anti-de Sitter asymptotics

We discuss charged and static solutions in a shift-symmetric scalar-tensor gravity model including a negative cosmological constant. The solutions are only approximately Anti-de Sitter (AdS) asymptotically. While spherically symmetric black holes with scalar-tensor hair do exist in our model, the uncharged spherically symmetric scalar-tensor solitons constructed recently cannot be generalised to include charge. We point out that this is due to the divergence of the electric monopole at the origin of the coordinate system, while higher order multipoles are well-behaved. We also demonstrate that black holes with scalar hair exist only for horizon value larger than that of the corresponding extremal Reissner-Nordström-AdS (RNAdS) solution, i.e. that we cannot construct solutions with arbitrarily small horizon radius. We demonstrate that for fixed Q a horizon radius exists at which the specific heat CQ diverges — signalling a transition from thermodynamically unstable to stable black holes. In contrast to the RNAdS case, however, we have only been able to construct a stable phase of large horizon black holes, while a stable phase of small horizon black holes does not (seem to) exist.

Nutty black holes in Galileon scalar-tensor gravity

Einstein gravity supplemented by a scalar field nonminimally coupled to a Gauss–Bonnet term provides an example of model of scalar-tensor gravity where hairy black holes do exist. We consider the classical equations within a metric endowed with a NUT-charge and obtain a two-parameter family of nutty-hairy black holes. The pattern of these solutions in the exterior and the interior of their horizon is studied in some details. The influence of both — the hairs and the NUT-charge — on the lightlike and timelike geodesics is emphasized.

Comment on “Cosmic evolution in Brans-Dicke chameleon cosmology” by Mubasher Jamil et al.

The authors of Ref. \cite{1-2}, investigated cosmic evolution in an external interacting model of scalar tensor gravity namely Brans Dicke chameleon scenario. The procedure of this work contains novelties but, it shall be observed from this comment, their report faces three fundamental drawbacks. One of them concerns the energy conservation equation, and the other two flaws are about mathematical mistakes. In the scalar tensor gravity models, a well-known method, in order to obtain conservation equation one must combine Friedmann equations with modified Klein-Gordon equation. But in Ref. \cite{1-2}, by virtue of the mentioned approach one would not be able to achieve a correct result for conservation equation. In addition, one can readily realize that their mathematical mistakes lead to different results compared to the present report.

Compact objects in scalar-tensor theories after GW170817

The recent observations of neutron star mergers have changed our perspective on scalar-tensor theories of gravity, favouring models where gravitational waves travel at the speed of light. In this work we consider a scalar-tensor set-up with such a property, belonging to a beyond Horndeski system, and we numerically investigate the physics of locally asymptotically flat black holes and relativistic stars. We first determine regular black hole solutions equipped with horizons: they are characterized by a deficit angle at infinity, and by large contributions of the scalar to the geometry in the near horizon region. We then study configurations of incompressible relativistic stars. We show that their compactness can be much higher than stars with the same energy density in General Relativity, and the scalar field profile imposes stringent constraints on the star properties. These results can suggest new ways to probe the efficiency of screening mechanisms in strong gravity regimes, and can help to build specific observational tests for scalar-tensor gravity models with unit speed for gravitational waves.

Solitons and black hole in shift symmetric scalar-tensor gravity with cosmological constant

We demonstrate the existence of static, spherically symmetric globally regular, i.e. solitonic solutions of a shift-symmetric scalar-tensor gravity model with negative cosmological constant. The norm of the Noether current associated to the shift symmetry is finite in the full space-time. We also discuss the corresponding black hole solutions and demonstrate that the interplay between the scalar-tensor coupling and the cosmological constant leads to the existence of new branches of solutions. To linear order in the scalartensor coupling, the asymptotic space-time corresponds to an Anti-de Sitter space-time with a non-trivial scalar field on its conformal boundary. This allows the interpretation of our solutions in the context of the AdS/CFT correspondence. Finally, we demonstrate that — for physically relevant, small values of the scalar-tensor coupling — solutions with positive cosmological constant do not exist in our model.

General theories of linear gravitational perturbations to a Schwarzschild black hole

We use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes of perturbed black holes may be affected by modifications to General Relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyse odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.

Scalar-Tensor Black Holes Embedded in an Expanding Universe

In this review, we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on black holes, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the issues that are not fully investigated.

Charged black holes in a generalized scalar–tensor gravity model

We study 4-dimensional charged and static black holes in a generalized scalar–tensor gravity model, in which a shift symmetry for the scalar field exists. For vanishing scalar field the solution corresponds to the Reissner–Nordström (RN) solution, while solutions of the full scalar-gravity model have to be constructed numerically. We demonstrate that these black holes support Galilean scalar hair up to a maximal value of the scalar–tensor coupling that depends on the value of the charge and can be up to roughly twice as large as that for uncharged solutions. The Hawking temperature TH of the hairy black holes at maximal scalar–tensor coupling decreases continuously with the increase of the charge and reaches TH=0 for the highest possible charge that these solutions can carry. However, in this limit, the scalar–tensor coupling needs to vanish. The limiting solution hence corresponds to the extremal RN solution, which does not support regular Galilean scalar hair due to its AdS2×S2 near-horizon geometry.

Gauge invariant fluctuations of the metric during inflation from a new scalar-tensor Weyl-integrable gravity model

We investigate gauge invariant scalar fluctuations of the metric during inflation in a non-perturbative formalism in the framework of a recently introduced scalar-tensor theory of gravity formulated on a Weyl-Integrable geometry. We found that the Weyl scalar field can play the role of the inflaton field in this theory. As an application we study the case of a power law inflation. In this case the quasi-scale invariance of the spectrum for scalar fluctuations of the metric is achieved for determined values of the $\omega$ parameter of the scalar-tensor theory. In our formalism the physical inflaton field has a geometrical origin.

Dynamical stability of Minkowski space in higher order gravity

We discuss the Minkowski stability problem in modified gravity by using dynamical system approach. The method to investigate dynamical stability of Minkowski space is proposed. This method was applied for some modified gravity theories, such as f(R) gravity, f(R)+αR□R gravity and scalar–tensor gravity models with non-minimal kinetic coupling. It was shown that in the case of f(R) gravity Minkowski solution is asymptotically stable in ghost-free (f′ &gt; 0) and tachyon-free (f″ &gt; 0) theories in expanding Universe with respect to isotropic and basic anisotropic perturbations. In the case of higher order gravity with αR□R correction conditions of Minkowski stability with respect to isotropic perturbations are significantly different: f′(0) &lt; 0, f″(0) &lt; 0 and 3f′(0) + f″(0)2/α &gt; 0. And in the case of scalar-tensor gravity with non-minimal kinetic coupling Minkowski solution is asymptotically stable in expanding Universe with respect to isotropic perturbations of metric. Moreover, the developed method may be used for finding additional restrictions on parameters of different modified gravity theories.

Scalar field cosmologies with inverted potentials

Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of the model in the Jordan frame (JF) are either of the Big Bang or of the Big Crunch type in the EF. As a result we obtain integrable scalar field cosmological models in general relativity (GR) with inverted double-well potentials unbounded from below which possess solutions regular in the future, tending to a de Sitter space, and starting with a Big Bang. The existence of the two fixed points for the field dynamics at late times found earlier in the JF becomes transparent in the EF.