Scalar-tensor Research Articles

Recent Developments in Degenerate Higher Order Scalar Tensor Theories

AbstractDegenerate Higher Order Scalar Tensor (DHOST) theories are the most general scalar‐tensor theories whose Lagrangian depends on the metric tensor and a single scalar field and its derivatives up to second order. They propagate only one scalar degree of freedom, without being plagued by Ostrogradsky instabilities. This is achieved through certain degeneracies of the functions forming their Lagrangian. They generalize the Horndeski and beyond‐Horndeski theories. Originally proposed to describe the late‐time acceleration of the expansion of the universe, generalizing the cosmological constant, they can also be used to build models of the early universe, to describe inflation or alternatives to standard inflation. In the late universe, they modify the standard Vainstein screening mechanism from Horndeski theories (which can have observable consequences) and are suited to build black hole models, featuring non‐stealth Kerr black hole solutions. In this work, their phenomenology is reviewed, looking at their basic properties, their parameterizations and classifications, focusing on solutions in the early and the late universe and at cosmological and astrophysical constraints.

Dynamical Casimir effect with screened scalar fields

Understanding the nature of dark energy and dark matter is one of modern physics' greatest open problems. Scalar-tensor theories with screened scalar fields like the chameleon model are among the most popular proposed solutions. In this article, we present the first analysis of the impact of a chameleon field on the dynamical Casimir effect, whose main feature is the particle production associated with a resonant condition of boundary periodic motion in cavities. For this, we employ a recently developed method to compute the evolution of confined quantum scalar fields in a globally hyperbolic spacetime by means of time-dependent Bogoliubov transformations. As a result, we show that particle production is reduced due to the presence of the chameleon field. In addition, our results for the Bogoliubov coefficients and the mean number of created particles agree with known results in the absence of a chameleon field. Our results initiate the discussion of the evolution of quantum fields on screened scalar field backgrounds.

On the stability of electrovacuum space-times in scalar–tensor gravity

We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.

Parametric resonance of gravitational waves in general scalar-tensor theories

Gravitational waves offer a potent mean to test the underlying theory of gravity. In general theories of gravity, such as scalar-tensor theories, one expects modifications in the friction term and the sound speed in the gravitational wave equation. In that case, rapid oscillations in such coefficients, e.g. due to an oscillating scalar field, may lead to narrow parametric resonances in the gravitational wave strain. We perform a general analysis of such possibility within DHOST theories. We use disformal transformations to find the theory space with larger resonances, within an effective field theory approach. We then apply our formalism to a non-minimally coupled ultra-light dark matter scalar field, assuming the presence of a primordial gravitational wave background, e.g., from inflation. We find that the resonant peaks in the spectral density may be detectable by forthcoming detectors such as LISA, Taiji, Einstein Telescope and Cosmic Explorer.

Numerical methods for scalar field dark energy in tabletop experiments and Lunar Laser Ranging

Numerous tabletop experiments have been dedicated to exploring the manifestations of screened scalar field dark energy, such as symmetron or chameleon fields. Precise theoretical predictions require simulating field configurations within the respective experiments. This paper focuses onto the less-explored environment-dependent dilaton field, which emerges in the strong coupling limit of string theory. Due to its exponential self-coupling, this field can exhibit significantly steeper slopes compared to symmetron and chameleon fields, and the equations of motion can be challenging to solve with standard machine precision. We present the first exact solution for the geometry of a vacuum region between two infinitely extended parallel plates. This solution serves as a benchmark for testing the accuracy of numerical solvers. By reparametrizing the model and transforming the equations of motion, we show how to make the model computable across the entire experimentally accessible parameter space. To simulate the dilaton field in one- and two-mirror geometries, as well as spherical configurations, we introduce a non-uniform finite difference method. Additionally, we provide an algorithm for solving the stationary Schrödinger equation for a fermion in one dimension in the presence of a dilaton field. The algorithms developed here are not limited to the dilaton field, but can be applied to similar scalar-tensor theories as well. We demonstrate such applications at hand of the chameleon and symmetron field. Our computational tools have practical applications in a variety of experimental contexts, including gravity resonance spectroscopy (q Bounce), Lunar Laser Ranging (LLR), and the upcoming Casimir and Non-Newtonian Force Experiment (cannex). A Mathematica implementation of all algorithms is provided.

Dark energy with a shift-symmetric scalar field: Obstacles, loophole hunting and dead ends

We discuss the possibility of a scalar field being the fundamental description of dark energy. We focus on shift-symmetric scalar-tensor theories since this symmetry potentially avoids some fine-tuning problems. We also restrict attention to theories satisfying that the propagation speed of gravitational waves is equal to the speed of light. These considerations lead us to investigate shift-symmetric Kinetic Gravity Braiding theories. Analysing the stability of scalar linear perturbations, we discuss the conditions that seems to be necessary to describe (super) accelerated cosmic expansion without introducing instabilities. However, it has been previously established that the linearised analysis does not guarantee the stability of this non-canonical scalar theory, as potentially dangerous interactions between dark energy fluctuations and tensor perturbations (essentially gravitational waves) appear at a higher order in perturbation theory. Indeed, although we shall point out that the standard proof of absence of dark energy stable braiding models due to this interaction has a possible way-out, we find general arguments suggesting that there are no dark energy stable solutions that can exploit this loophole. Thus, we discuss future research directions for finding viable fundamental descriptions of dark energy. We also provide a dictionary between the covariant version of the theory and that of the Effective Field Theory approach, explicitly computing the parameters in the latter formalism in terms of the functions appearing in the covariant version, and its derivatives. To the best of our knowledge, this is the first time these expressions are explicitly obtained up-to arbitrary order in perturbation theory.

Alternative formulations of the thermodynamics of scalar-tensor theories

Alternative formulations of the thermodynamics of scalar-tensor theories

Testing screened modified gravity with SDSS-IV-MaNGA

ABSTRACT Fifth forces are ubiquitous in modified gravity theories and must be screened to evade stringent local tests. This can introduce unusual behaviour in galaxy phenomenology by affecting galaxies’ components differently. Here, we use the SDSS-IV (Sloan Digital Sky Survey IV)-MaNGA (Mapping Nearby Galaxies at Apache Point Observatory) data set to search for a systematic excess of gas circular velocity over stellar circular velocity, expected in thin-shell-screened theories in the partially screened regime. Accounting for asymmetric drift and calibrating our model on screened subsamples, we find no significant evidence for a screened fifth force. We bound the fifth-force strength to $\Delta G/G_\text{N} < 0.1$ for all astrophysical ranges, strengthening to $\sim$0.01 at Compton wavelength of 3 Mpc for the Hu–Sawicki model, for instance. This implies a stringent constraint on scalar–tensor theories, for example $f_{\mathcal {R}0} \lesssim 10^{-8}$ in Hu–Sawicki $f(\mathcal {R})$ gravity.

Dynamical reconstruction of the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model in hybrid metric-Palatini gravity

In this work, we apply the formalism of dynamical systems to analyze the viability of the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model in a generalized form of the hybrid metric-Palatini gravity theory written in terms of its dynamically equivalent scalar–tensor representation. Adopting a matter distribution composed of two relativistic fluids described by the equations of state of radiation and pressureless dust, one verifies that the cosmological phase space features the usual curvature-dominated, radiation-dominated, matter-dominated, and exponentially accelerated fixed points, even in the absence of a dark energy component. A numerical integration of the dynamical equations describing the system, subjected to initial conditions consistent with the cosmographic observations from the Planck satellite and weak-field solar system dynamics, shows that cosmological solutions mimicking the behavior of the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model in General Relativity (GR) are attainable in this theory, with the deviations from GR being exponentially suppressed at early-times and the scalar-field potential effectively playing the role of dark energy at late times.

A simple prediction of the nonlinear matter power spectrum in Brans–Dicke gravity from linear theory

Brans–Dicke (BD), one of the first proposed scalar-tensor theories of gravity, effectively makes the gravitational constant of general relativity (GR) time-dependent. Constraints on the BD parameter ω serve as a benchmark for testing GR, which is recovered in the limit ω → ∞. Current small-scale astrophysical constraints ω ≳ 105 are much tighter than large-scale cosmological constraints ω ≳ 103, but the two decouple if the true theory of gravity features screening. On the largest cosmological scales, BD approximates the most general second-order scalar–tensor (Horndeski) theory, so constraints here have wider implications. These constraints will improve with upcoming large-scale structure and cosmic microwave background surveys. To constrain BD with weak gravitational lensing, one needs its nonlinear matter power spectrum PBD. By comparing the boost B = PBD/PGR from linear theory and nonlinear N-body simulations, we show that the nonlinear boost can simply be predicted from linear theory if the BD and GR universes are parameterized in a way that makes their early cosmological evolution and quasilinear power today similar. In particular, they need the same H0/√Geff(a = 0) and σ8, where Geff is the (effective) gravitational strength. Our prediction is 1% accurate for ω ≥ 100, z ≤ 3, and k ≤ 1 h/Mpc; and 2% up to k ≤ 5 h/Mpc. It also holds for GBD that do not match Newton’s constant today, so one can study GR with different gravitational constants GGR by sending ω → ∞. We provide a code that computes B with the linear Einstein-Boltzmann solver HI_CLASS and multiplies it by the nonlinear PGR from EUCLIDEMULATOR2 to predict PBD.

Thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity

In this study, we examined the thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity (STVG). We calculated some thermodynamic quantities related to the correction of the black hole entropy caused by thermal fluctuations and discussed the effect of the correction parameters on these quantities. By analyzing the changes in the corrected specific heat, we found that thermal fluctuations made the small black hole more stable. It is worth noting that the STVG parameter did not affect the thermodynamic stability of this black hole. Additionally, by utilizing the Gauss–Bonnet theorem, the deflection angle was obtained in the weak field limit, and the effects of the two parameters on the results were visualized. Finally, we calculated the bounds on the greybody factor of a massless scalar field. We observed that as the STVG parameter around the black hole increased, the weak deflection angle became larger, and more scalar particles can reach infinity. However, the spacetime dimension has the opposite effect on the STVG parameter on the weak deflection angle and greybody factor.

Constraining a disformal Schwarzschild black hole in DHOST theories with the orbit of the S2 star

With the observed data of the S2 orbit around the black hole Sgr A∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^*$$\\end{document} and the Markov Chain Monte Carlo method, we make a constraint on parameters of a disformal Schwarzschild black hole in quadratic degenerate higher-order scalar-tensor (DHOST) theories. This black hole belongs to a class of non-stealth solutions and owns an extra disformal parameter described the deviation from general relativity. Our results show that the best fit value of the disformal parameter is positive. However, in the range of 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\sigma $$\\end{document}, we also find that general relativity remains to be consistent with the observation of the S2 orbit.

General analysis of Noether symmetries in Horndeski gravity

We explore Noether symmetries of Horndeski gravity, extending the classification of general scalar–tensor theories. Starting from the minimally coupled scalar field and the first-generation scalar–tensor gravity, the discussion is generalised to kinetic gravity braiding and Horndeski gravity. We highlight the main findings by focusing on the non-minimally coupled Gauss–Bonnet term and the extended cuscuton model. Finally, we discuss how the presence of matter can influence Noether symmetries. It turns out that the selected Horndeski functions are unchanged with respect to the vacuum case.

Phenomenology of Horndeski gravity under positivity bounds

A set of conditions that any effective field theory needs to satisfy in order to allow for the existence of a viable UV completion, has recently gained attention in the cosmological context under the name of positivity bounds. In this paper we revisit the derivation of such bounds for Horndeski gravity, highlighting the limitations that come from applying the traditional methodology to a theory of gravity on a cosmological background. We then translate these bounds into a complete set of viability conditions in the language of effective field theory of dark energy. We implement the latter into EFTCAMB and explore the large scale structure phenomenology of Horndeski gravity under positivity bounds. We build a statistically significant sample of viable Horndeski models, and derive the corresponding predictions for the background evolution, in terms of w DE, and the dynamics of linear perturbations, in terms of the phenomenological functions μ and Σ, associated to clustering and weak lensing, respectively. We find that the addition of positivity bounds to the traditional no-ghost and no-gradient conditions considerably tightens the theoretical constraints on all these functions. The most significant feature is a strengthening of the correlation μ ≃ Σ, and a related tight constraint on the luminal speed of gravitational waves c 2 T ≃ 1. In this work we demonstrate the strong potential of positivity bounds in shaping the viable parameter space of scalar-tensor theories. This is certainly promising, but it also highlights the importance of overcoming all issues that still plague a rigorous formulation of the positivity bounds in the cosmological context.

Galaxy dynamics tracing quantum cosmology beyond [formula omitted]CDM below the de Sitter scale of acceleration

It is proposed that the baryonic Tully–Fisher relation (bTFR) and JWST ’Impossible galaxies’ at cosmic dawn are unified in weak gravity by the trace J of the Schouten tensor below the Sitter scale of acceleration adS=cH, where c is the velocity of light and H is the Hubble parameter. Across adS, J parametrizes short-period galaxy rotation curves and fast gravitational collapse beyond the predictions of ΛCDM. The sensitivity of weak gravitation to J=16R, where R is the Ricci scalar tensor, is derived in infrared gravitation from a consistent limit to quantum gravity, reducing to general relativity in the limit of a small Planck constant. For the first time, it identifies the exact relation a0=c2J/2π of the Milgrom parameter across all redshifts, accounting for the bTFR and early galaxy formation accelerated by a factor ∼J1/8. It predicts a0′(0)<0 at the present epoch.

Scalar induced gravitational waves in chiral scalar–tensor theory of gravity

We study the scalar induced gravitational waves (SIGWs) from a chiral scalar–tensor theory of gravity. The parity-violating (PV) Lagrangian contains the Chern–Simons (CS) term and PV scalar–tensor terms, which are built of the quadratic Riemann tensor term and first-order derivatives of a scalar field. We consider SIGWs in two cases, in which the semi-analytic expression to calculate SIGWs can be obtained. Then, we calculate the fractional energy density of SIGWs with a monochromatic power spectrum for the curvature perturbation. We find that the SIGWs in chiral scalar–tensor gravity behave differently from those in GR before and after the peak frequency, which results in a large degree of circular polarization.

Ward identities under the frame transformations in curved space-time

Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity, as they are used to build feasible models for cosmic inflation. These theories can be formulated both in the Jordan and Einstein frame, which are related by a Weyl transformation with a field transformation, known together as a frame transformation. These theories formulated in the above two frames are often considered to be equivalent from the point of view of classical theory. However, this is no longer true from the quantum field theoretical perspective. In the present article, we show that the Ward identities derived in the above two frames are not connected through the frame transformation. This shows that the quantum field theories formulated in these two frames are not equivalent to each other. Moreover, this inequivalence is also shown by comparing the effective actions derived in these two frames.

Scalarized hybrid neutron stars in scalar tensor gravity

Hybrid neutron stars, the compact objects consisting hadronic matter and strange quark matter, can be considered as the probes for the scalar tensor gravity. In this work, we explore the scalarization of hybrid neutron stars in the scalar tensor gravity. For the hadronic phase, we apply a piecewise polytropic equation of state constrained by the observational data of GW170817 and the data of six low-mass X-ray binaries with thermonuclear burst or the symmetry energy of the nuclear interaction. In addition, to describe the strange quark matter inside the hybrid neutron star, different MIT bag models are employed. We study the effects of the value of bag constant, the mass of s quark, the perturbative quantum chromodynamics correction parameter, and the density jump at the surface of quark-hadronic phase transition on the scalarization of hybrid neutron stars. Our results confirm that the scalarization is more sensitive to the value of bag constant, the mass of s quark, and the density jump compared to the perturbative quantum chromodynamics correction parameter.

Axial perturbations of hairy black holes in generalized scalar-tensor theories

Axial perturbations of hairy black holes in generalized scalar-tensor theories

New scale in the quasi-static limit of aether scalar tensor theory

New scale in the quasi-static limit of aether scalar tensor theory