Showing papers on "Scalar field published in 2016"

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

Abstract: Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering ``degenerate'' Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degenerate cases. We also identify new families of scalar-tensor theories with the property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.

Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order

Abstract: We present all scalar-tensor Lagrangians that are cubic in second derivatives of a scalar field, and that are degenerate, hence avoiding Ostrogradsky instabilities. Thanks to the existence of constraints, they propagate no more than three degrees of freedom, despite having higher order equations of motion. We also determine the viable combinations of previously identified quadratic degenerate Lagrangians and the newly established cubic ones. Finally, we study whether the new theories are connected to known scalar-tensor theories such as Horndeski and beyond Horndeski, through conformal or disformal transformations.

Extended scalar-tensor theories of gravity

Abstract: We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators in the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.

Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations

Abstract: We consider all degenerate scalar-tensor theories that depend quadratically on second-order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy, in general, ensures the absence of Ostrogradsky’s instability, include the quartic Horndeski Lagrangian and its quartic extension beyond Horndeski, as well as other Lagrangians. We study how all these theories transform under general disformal transformations and find that they can be separated into three main classes that are stable under these transformations. This leads to a complete classification modulo disformal transformations. Finally, we show that these higher order theories include mimetic gravity and some particular khronometric theories. They also contain theories that do not correspond, to our knowledge, to already studied theories, even up to disformal transformations.

Hamiltonian analysis of higher derivative scalar-tensor theories

Abstract: We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.

Phenomenology of a 750 GeV singlet

Abstract: We study the recently reported excess in the diphoton resonance search by ATLAS and CMS. We investigate the available parameter space in the combined run-1 and run-2 diphoton data and study its interpretation in terms of a singlet scalar field which possibly mixes with the Standard Model Higgs boson. We show that the mixing angle is already strongly constrained by high-mass Higgs searches in the diboson channel, and by Higgs coupling measurements. While a broad resonance is slightly favored, we argue that the signal is consistent with a narrow-width singlet which couples to colored and electromagnetically-charged vector-like fermions. Dijet signals are predicted and may be visible in upcoming analyses. Allowing for additional decay modes could explain a broader resonance, however, we show that monojet searches disfavor a large invisible width. Finally, we comment on the possible relation of this scenario to the naturalness problem.

Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M

Abstract: This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I{II: the cases jaj M or axisymmetry, arXiv:1010.5132], providing the complete proof of denitive boundedness and decay results for the scalar wave equation on Kerr backgrounds in the general subextremal jaj < M case without symmetry assumptions. The essential ideas of the proof (together with explicit constructions of the most dicult mul

Black hole collapse in the 1 /c expansion

Abstract: We present a first-principles CFT calculation corresponding to the spherical collapse of a shell of matter in three dimensional quantum gravity. In field theory terms, we describe the equilibration process, from early times to thermalization, of a CFT following a sudden injection of energy at time t = 0. By formulating a continuum version of Zamolodchikov’s monodromy method to calculate conformal blocks at large central charge c, we give a framework to compute a general class of probe observables in the collapse state, incorporating the full backreaction of matter fields on the dual geometry. This is illustrated by calculating a scalar field two-point function at time-like separation and the time-dependent entanglement entropy of an interval, both showing thermalization at late times. The results are in perfect agreement with previous gravity calculations in the AdS3-Vaidya geometry. Information loss appears in the CFT as an explicit violation of unitarity in the 1/c expansion, restored by nonperturbative corrections.

Explosion and Final State of an Unstable Reissner-Nordström Black Hole.

Abstract: A Reissner-Nordstrom black hole (BH) is superradiantly unstable against spherical perturbations of a charged scalar field enclosed in a cavity, with a frequency lower than a critical value. We use numerical relativity techniques to follow the development of this unstable system-dubbed a charged BH bomb-into the nonlinear regime, solving the full Einstein-Maxwell-Klein-Gordon equations, in spherical symmetry. We show that (i) the process stops before all the charge is extracted from the BH, and (ii) the system settles down into a hairy BH: a charged horizon in equilibrium with a scalar field condensate, whose phase is oscillating at the (final) critical frequency. For a low scalar field charge q, the final state is approached smoothly and monotonically. For large q, however, the energy extraction overshoots, and an explosive phenomenon, akin to a bosenova, pushes some energy back into the BH. The charge extraction, by contrast, does not reverse.

Beginning inflation in an inhomogeneous universe

Abstract: Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially expanding, highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the inhomogeneities is comparable to the initial Hubble length, and overdense regions collapse and form black holes, because underdense regions continue expanding, allowing inflation to eventually begin. This establishes that inflation can arise from highly inhomogeneous initial conditions and solve the horizon and flatness problems, at least as long as the variations in the scalar field do not include values that exceed the inflationary plateau.

Searching for an Oscillating Massive Scalar Field as a Dark Matter Candidate Using Atomic Hyperfine Frequency Comparisons.

Abstract: We use 6 yrs of accurate hyperfine frequency comparison data of the dual rubidium and caesium cold atom fountain FO2 at LNE-SYRTE to search for a massive scalar dark matter candidate. Such a scalar field can induce harmonic variations of the fine structure constant, of the mass of fermions, and of the quantum chromodynamic mass scale, which will directly impact the rubidium/caesium hyperfine transition frequency ratio. We find no signal consistent with a scalar dark matter candidate but provide improved constraints on the coupling of the putative scalar field to standard matter. Our limits are complementary to previous results that were only sensitive to the fine structure constant and improve them by more than an order of magnitude when only a coupling to electromagnetism is assumed.

Super-Planckian Spatial Field Variations and Quantum Gravity

Abstract: We study scenarios where a scalar field has a spatially varying vacuum expectation value such that the total field variation is super-Planckian. We focus on the case where the scalar field controls the coupling of a U(1) gauge field, which allows us to apply the Weak Gravity Conjecture to such configurations. We show that this leads to evidence for a conjectured property of quantum gravity that as a scalar field variation in field space asymptotes to infinity there must exist an infinite tower of states whose mass decreases as an exponential function of the scalar field variation. We determine the rate at which the mass of the states reaches this exponential behaviour showing that it occurs quickly after the field variation passes the Planck scale.

Spontaneous scalarization with massive fields

Abstract: We study the effect of a mass term in the spontaneous scalarization of neutron stars, for a wide range of scalar field parameters and neutron star equations of state. Even though massless scalars have been the focus of interest in spontaneous scalarization so far, recent observations of binary systems rule out most of their interesting parameter space. We point out that adding a mass term to the scalar field potential is a natural extension to the model that avoids these observational bounds if the Compton wavelength of the scalar is small compared to the binary separation. Our model is formally similar to the asymmetron scenario recently introduced in application to cosmology, though here we are interested in consequences for neutron stars and thus consider a mass term that does not modify the geometry on cosmological scales. We review the allowed values for the mass and scalarization parameters in the theory given current binary system observations and black hole spin measurements. We show that within the allowed ranges, spontaneous scalarization can have nonperturbative, strong effects that may lead to observable signatures in binary neutron star or black hole–neutron star mergers, or even in isolated neutron stars.

Generalized Galileons: instabilities of bouncing and Genesis cosmologies and modified Genesis

Abstract: We study spatially flat bouncing cosmologies and models with the early-time Genesis epoch in a popular class of generalized Galileon theories. We ask whether there exist solutions of these types which are free of gradient and ghost instabilities. We find that irrespectively of the forms of the Lagrangian functions, the bouncing models either are plagued with these instabilities or have singularities. The same result holds for the original Genesis model and its variants in which the scale factor tends to a constant as t → −∞. The result remains valid in theories with additional matter that obeys the Null Energy Condition and interacts with the Galileon only gravitationally. We propose a modified Genesis model which evades our no-go argument and give an explicit example of healthy cosmology that connects the modified Genesis epoch with kination (the epoch still driven by the Galileon field, which is a conventional massless scalar field at that stage).

Geometry of the scalar sector

Abstract: The S-matrix of a quantum field theory is unchanged by field redefinitions, and so it only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold $$ \mathrm{\mathcal{M}} $$ is flat. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved $$ \mathrm{\mathcal{M}} $$ , since they parametrize deviations from the flat SM case. We show that the HEFT Lagrangian can be written in SMEFT form if and only if $$ \mathrm{\mathcal{M}} $$ has a SU(2) L × U(1) Y invariant fixed point. Experimental observables in HEFT depend on local geometric invariants of $$ \mathrm{\mathcal{M}} $$ such as sectional curvatures, which are of order 1/Λ 2 , where Λ is the EFT scale. We give explicit expressions for these quantities in terms of the structure constants for a general $$ \mathcal{G}\to \mathrm{\mathscr{H}} $$ symmetry breaking pattern. The one-loop radiative correction in HEFT is determined using a covariant expansion which preserves manifest invariance of $$ \mathrm{\mathcal{M}} $$ under coordinate redefinitions. The formula for the radiative correction is simple when written in terms of the curvature of $$ \mathrm{\mathcal{M}} $$ and the gauge curvature field strengths. We also extend the CCWZ formalism to non-compact groups, and generalize the HEFT curvature computation to the case of multiple singlet scalar fields.

Evading the Vainshtein Mechanism with Anomalous Gravitational Wave Speed: Constraints on Modified Gravity from Binary Pulsars.

Abstract: By using observations of the Hulse-Taylor pulsar, we constrain the gravitational wave (GW) speed to the level of 10(-2). We apply this result to scalar-tensor theories that generalize Galileon 4 and 5 models, which display anomalous propagation speed and coupling to matter for GWs. We argue that this effect survives conventional screening due to the persistence of a scalar field gradient inside virialized overdensities, which effectively "pierces" the Vainshtein screening. In specific branches of solutions, our result allows us to directly constrain the cosmological couplings in the effective field theory of dark energy formalism.

Black holes and stars in Horndeski theory

Abstract: We review black hole and star solutions for Horndeski theory. For non-shift symmetric theories, black holes involve a Kaluza-Klein reduction of higher dimensional Lovelock solutions. On the other hand, for shift symmetric theories of Horndeski and beyond Horndeski, black holes involve two classes of solutions: those that include, at the level of the action, a linear coupling to the Gauss-Bonnet term and those that involve time dependence in the galileon field. We analyze the latter class in detail for a specific subclass of Horndeski theory, discussing the general solution of a static and spherically symmetric spacetime. We then discuss stability issues, slowly rotating solutions as well as black holes coupled to matter. The latter case involves a conformally coupled scalar field as well as an electromagnetic field and the (primary) hair black holes thus obtained. We review and discuss the recent results on neutron stars in Horndeski theories.

Challenging the presence of scalar charge and dipolar radiation in binary pulsars

Abstract: Corrections to general relativity that introduce long-ranged scalar fields which are nonminimally coupled to curvature typically predict that neutron stars possess a nontrivial scalar field profile anchored to the star. An observer far from a star is most sensitive to the spherically symmetric piece of this profile that decays linearly with the inverse of the distance to the source, the so-called scalar monopole charge, which is related to the emission of dipolar radiation from compact binary systems. The presence of dipolar radiation has the potential to rule out or very strongly constrain extended theories of gravity. These facts may lead people to believe that gravitational theories that introduce long-ranged scalar fields have already been constrained strongly from binary pulsar observations. Here we challenge this “lore” by investigating the decoupling limit of Gauss-Bonnet gravity as an example, in which the scalar field couples linearly to the Gauss-Bonnet density in the action. We prove a theorem that neutron stars in this theory cannot possess a scalar charge, due to the topological nature of the Gauss-Bonnet density. Thus Gauss-Bonnet gravity evades the strong binary pulsar constraints on dipole radiation. We discuss the astrophysical systems which will yield the best constraints on Gauss-Bonnet gravity and related quadratic gravity theories. To achieve this we compute the scalar charge in quadratic gravity theories by performing explicit analytic and numerical matching calculations for slowly rotating neutron stars. In generic quadratic gravity theories, either neutron star–binary or neutron star–black hole systems can be used to constrain the theory, but because of the vanishing charge, Gauss-Bonnet gravity evades the neutron star–binary constraints. However, in contrast to neutron stars, black holes in Gauss-Bonnet gravity do anchor scalar charge, because of the difference in topology. The best constraints on Gauss-Bonnet gravity will thus come from accurate black hole observations, for example through gravitational waves from inspiraling binaries or the timing of pulsar–black hole binaries with radio telescopes. We estimate these constraints to be a factor of 10 better than the current estimated bound, and also include estimated constraints on generic quadratic gravity theories from pulsar timing.

Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates

Abstract: We study the effective cosmological dynamics, emerging as the hydrodynamics of simple condensate states, of a group field theory model for quantum gravity coupled to a massless scalar field and reduced to its isotropic sector. The quantum equations of motion for these group field theory condensate states are given in relational terms with respect to the scalar field, from which effective dynamics for spatially flat, homogeneous and isotropic space-times can be extracted. The result is a generalization of the Friedmann equations, including quantum gravity modifications, in a specific regime of the theory. The classical Friedmann equations of general relativity are recovered in a suitable semi-classical limit for some range of parameters of the microscopic dynamics. An important result is that the quantum geometries associated with these GFT condensate states are non-singular: a bounce generically occurs in the Planck regime. For some choices of condensate states, these modified Friedmann equations are very similar to those of loop quantum cosmology.

Passive scalars in turbulent channel flow at high Reynolds number

Abstract: We study passive scalars in turbulent plane channels at computationally high Reynolds number, thus allowing us to observe previously unnoticed effects. The mean scalar profiles are found to obey a generalized logarithmic law which includes a linear correction term in the whole lower half-channel, and they follow a universal parabolic defect profile in the core region. This is consistent with recent findings regarding the mean velocity profiles in channel flow. The scalar variances also exhibit a near universal parabolic distribution in the core flow and hints of a sizeable log layer, unlike the velocity variances. The energy spectra highlight the formation of large scalar-bearing eddies with size proportional to the channel height which are caused by a local production excess over dissipation, and which are clearly visible in the flow visualizations. Close correspondence of the momentum and scalar eddies is observed, with the main difference being that the latter tend to form sharper gradients, which translates into higher scalar dissipation. Another notable Reynolds number effect is the decreased correlation of the passive scalar field with the vertical velocity field, which is traced to the reduced effectiveness of ejection events.

Bounce inflation in $f(T)$ Cosmology: A unified inflaton-quintessence field

Abstract: We investigate a bounce inflation model with a graceful exit into the Friedmann-Robertson-Walker (FRW) decelerated Universe within $f(T)$-gravity framework, where $T$ is the torsion scalar in the teleparallelism. We study the cosmic thermal evolution, the model predicts a supercold universe during the precontraction phase, which is consistent with the requirements of the slow-roll models, while it performs a reheating period by the end of the contraction with a maximum temperature just below the grand unified theory (GUT) temperature. However, it matches the radiation temperature of the hot big bang at later stages. The equation-of-state due to the effective gravitational sector suggests that our Universe is self-accelerated by teleparallel gravity. We assume the matter component to be a canonical scalar field. We obtain the scalar field potential that is induced by the $f(T)$ theory. The power spectrum of the model is nearly scale invariant. In addition, we show that the model unifies inflaton and quintessence fields in a single model. Also, we revisited the primordial fluctuations in $f(T)$ bounce cosmology, to study the fluctuations that are produced at the precontraction phase.

Astrophysical imaging of Kerr black holes with scalar hair

Abstract: We address the astrophysical imaging of a family of deformed Kerr black holes (BHs). These are stationary, asymptotically flat BH spacetimes that are solutions of general relativity minimally coupled to a massive, complex scalar field: Kerr BHs with scalar hair (KBHsSH). Such BHs bifurcate from the vacuum Kerr solution and can be regarded as a horizon within a rotating boson star. In a recent letter [P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. R\'unarsson, Phys. Rev. Lett. 115, 211102 (2015).], it was shown that KBHsSH can exhibit very distinct shadows from the ones of their vacuum counterparts. The setup therein, however, considers the light source to be a celestial sphere sufficiently far away from the BH. Here, we analyze KBHsSH surrounded by an emitting torus of matter simulating a more realistic astrophysical environment, and study the corresponding lensing of light as seen by a very faraway observer, to appropriately model ground-based observations of Sgr ${\mathrm{A}}^{*}$. We find that the differences in imaging between KBHsSH and comparable vacuum Kerr BHs remain, albeit less dramatic than those observed for the corresponding shadows in the previous setup. In particular, we highlight two observables that might allow differentiating KBHsSH and Kerr BHs. The first is the angular size of the photon ring (in a Kerr spacetime) or lensing ring (in a KBHSH spacetime), the latter being significantly smaller for sufficiently non-Kerr-like spacetimes. The second is the existence of an edge in the intensity distribution (the photon ring in Kerr spacetime). This edge can disappear for very non-Kerr-like KBHsSH. It is plausible, therefore, that sufficiently precise very long baseline interferometric observations of BH candidates can constrain this model.

Spinning black holes in Einstein–Gauss-Bonnet–dilaton theory: Nonperturbative solutions

Abstract: We present an investigation of spinning black holes in Einstein--Gauss-Bonnet--dilaton (EGBd) theory. The solutions are found within a nonperturbative approach, by directly solving the field equations. These stationary axially symmetric black holes are asymptotically flat. They possess a nontrivial scalar field outside their regular event horizon. We present an overview of the parameter space of the solutions together with a study of their basic properties. We point out that the EGBd black holes can exhibit some physical differences when compared to the Kerr solution. For example, their mass is always bounded from below, while their angular momentum can exceed the Kerr bound. Also, in contrast to the Kerr case, the extremal solutions are singular, with the scalar field diverging on the horizon.

Black holes and stars in Horndeski theory

Abstract: We review black hole and star solutions for Horndeski theory. For non-shift symmetric theories, black holes involve a Kaluza-Klein reduction of higher dimensional Lovelock solutions. On the other hand, for shift symmetric theories of Horndeski and beyond Horndeski, black holes involve two classes of solutions: those that include, at the level of the action, a linear coupling to the Gauss-Bonnet term and those that involve time dependence in the galileon field. We analyze the latter class in detail for a specific subclass of Horndeski theory, discussing the general solution of a static and spherically symmetric spacetime. We then discuss stability issues, slowly rotating solutions as well as black holes coupled to matter. The latter case involves a conformally coupled scalar field as well as an electromagnetic field and the (primary) hair black holes thus obtained. We review and discuss the recent results on neutron stars in Horndeski theories.

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

Abstract: 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 latter 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.

Solving higher curvature gravity theories

Abstract: Solving field equations in the context of higher curvature gravity theories is a formidable task. However, in many situations, e.g., in the context of f(R) theories, the higher curvature gravity action can be written as an Einstein–Hilbert action plus a scalar field action. We show that not only the action but the field equations derived from the action are also equivalent, provided the spacetime is regular. We also demonstrate that such an equivalence continues to hold even when the gravitational field equations are projected on a lower-dimensional hypersurface. We have further addressed explicit examples in which the solutions for Einstein–Hilbert and a scalar field system lead to solutions of the equivalent higher curvature theory. The same, but on the lower-dimensional hypersurface, has been illustrated in the reverse order as well. We conclude with a brief discussion on this technique of solving higher curvature field equations.

Conformal transformations in modified teleparallel theories of gravity revisited

Abstract: It is well known that one cannot apply a conformal transformation to $f(T)$ gravity to obtain a minimally coupled scalar field model, and thus no Einstein frame exists for $f(T)$ gravity. Furthermore nonminimally coupled "teleparallel dark energy models" are not conformally equivalent to $f(T)$ gravity. However, it can be shown that $f(T)$ gravity is conformally equivalent to a teleparallel phantom scalar field model with a nonminimal coupling to a boundary term only. In this work, we extend this analysis by considering a recently studied extended class of models, known as $f(T,B)$ gravity, where $B$ is a boundary term related to the divergence of a contraction of the torsion tensor. We find that nonminimally coupled "teleparallel dark energy models" are conformally equivalent to either an $f(T,B)$ or $f(B)$ gravity model. Finally conditions on the functional form of $f(T,B)$ gravity are derived to allow it to be transformed to particular nonminimally coupled scalar field models.