Kinetic Gravity Braiding Research Articles

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.

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.

Perturbations and stability conditions of k-essence and kinetic gravity braiding models in two-field measure theory

We study cosmological perturbations for k-essence and kinetic gravity braiding models in the context of the two-field measure theory (TMT). Considering scalar perturbations and the uniform field gauge, we obtain the sound speed of the fields and present a stability analysis by means of the kinetic matrix and the mass eigenvalues. For k-essence models, in the two-field measure theory, the speed of propagation of the field is modified completely due to the new measure field and it gives rise to crucial differences with respect to the case without new measure. The stability analysis gives a physical viable model for the Universe. For the kinetic gravity braiding models in the two-field measure theory we get that, in general, the speed of perturbations is equal to the speed of light which is a consequence of the properties of the new measure field. In the latter case, there is always a ghost field. Furthermore, we calculate general expressions for the mass eigenvalues and find, for an explicit example, the existence of tachyonic instabilities.

Phantom attractors in kinetic gravity braiding theories: a dynamical system approach

We revise the expansion history of the scalar field theories known as Kinetic Gravity Braiding. These theories are well-known for the possibility of driving the expansion of the cosmos towards a future self-tuning de Sitter state when the corresponding Lagrangian is invariant under constant shifts in the scalar field. Nevertheless, this is not the only possible future fate of these shift-symmetric models. Using a dynamical system formulation we show that future cosmological singularities can also appear in this framework. Moreover, we present explicit examples where the future attractor in the configuration space of the theory corresponds to a big rip singularity.

A forecast for large-scale structure constraints on Horndeski gravity with CO line intensity mapping

ABSTRACT We consider the potential for line intensity mapping (LIM) of the rotational CO(1-0), CO(2-1), and CO(3-2) transitions to detect deviations from General Relativity from 0 < z < 3 within the framework of a very general class of modified gravity models, called Horndeski’s theories. Our forecast assumes a multitracer analysis separately obtaining information from the matter power spectrum and the first two multipoles of the redshift space distortion power spectrum. To achieve ±0.1 level constraints on the slope of the kinetic gravity braiding and Planck mass evolution parameters, a mm-wave LIM experiment would need to accumulate ≈108–109 spectrometre-hours, feasible with instruments that could be deployed in the 2030s. Such a measurement would constrain the parameters of Horndeski’s theory at a level at worst competitive to and at best an order of magnitude tighter than existing constraints from the CMB and LSS. Our modelling code is publicly available.

Symmetric teleparallel Horndeski gravity

Horndeski gravity is the most general scalar-tensor theory with one scalar field leading to second-order Euler-Lagrange field equations for the metric and scalar field, and it is based on Riemannian geometry. In this paper, we formulate an analog version of Horndeski gravity in a symmetric teleparallel geometry which assumes that both the curvature (general) and torsion are vanishing and gravity is only related to nonmetricity. Our setup requires that the Euler-Lagrange equations for not only metric and scalar field but also connection should be at most second order. We find that the theory can be always recast as a sum of the Riemannian-Horndeski theory and new terms that are purely teleparallel. Due to the nature of nonmetricity, there are many more possible ways of constructing second-order theories of gravity. In this regard, up to some assumptions, we find the most general $k$-essence extension of symmetric teleparallel Horndeski gravity. We also formulate a novel theory containing higher-order derivatives acting on nonmetricity while still respecting the second-order conditions, which can be recast as an extension of kinetic gravity braiding. We finish our study by presenting the FLRW cosmological equations for our model.

Big rip in shift-symmetric Kinetic Gravity Braiding theories

We revise the future fate of a group of scalar-tensor theories known as kinetic gravity braiding models. As it is well-known, these theories can safely drive the expansion of the universe towards a future de Sitter state if the corresponding Lagrangian is invariant under constant shifts in the scalar field. However, this is not the only possible future state of these shift-symmetric models as we show in this letter. In fact, future cosmic singularities characterized by a divergence of the energy density can also appear in this framework. We present an explicit example where a big rip singularity is the only possible future fate of the cosmos.

Neutrino mass and kinetic gravity braiding degeneracies

Modified theories of gravity yield an effective dark energy in the background dynamics that achieves an accelerated expansion of the universe. In addition, they present a fifth force that induces gravitational signatures in structure formation, and therefore in the matter power spectrum and related statistics. On the other hand, massive neutrinos suppress the power spectrum at scales that also modified gravity enhances it, so a degeneration of these effects has been recognized for some gravity models. In the present work, we study both effects using kinetic gravity braiding (nKGB) models to find that in spite of some degeneracies, the role of the fifth force at very large scales imprints a bump in the matter power spectrum as a distinctive signature of this model and, therefore, acts as a smoking gun that seems difficult to match within the present knowledge of power spectra. These models result interesting, however, since the n = 1 presents no H 0 tension, and all nKGB studied here present no σ 8 tension and, in addition, a null neutrino mass is excluded.

Is local H 0 at odds with dark energy EFT?

Local H_0 determinations currently fall in a window between H 0 ∼ 70 km/s/Mpc (TRGB) and H 0 ∼ 76 km/s/Mpc (Tully-Fisher). In contrast, BAO data calibrated in an early ΛCDM universe are largely consistent with Planck-ΛCDM, H 0 ∼ 67.5 km/s/Mpc. Employing a generic two parameter family of evolving equations of state (EoS) for dark energy (DE) w DE(z) and mock BAO data, we demonstrate that if i) w DE(z = 0) < -1 and ii) integrated DE density less than ΛCDM, then H 0 increases. EoS that violate these conditions at best lead to modest H 0 increases within 1σ. Tellingly, Quintessence and K-essence satisfy neither condition, whereas coupled Quintessence can only satisfy ii). Beyond these seminal DE Effective Field Theories (EFTs), we turn to explicit examples. Working model agnostically in an expansion in powers of redshift z, we show that Brans-Dicke/f(R) and Kinetic Gravity Braiding models within the Horndeski class can lead to marginal and modest increases in H 0, respectively. We confirm that as far as increasing H 0 is concerned, no DE EFT model can outperform the phenomenological two parameter family of the DE models. Evidently, the late universe may no longer be large enough to accommodate H 0, BAO and DE described by EFT.

Stealth black hole perturbations in kinetic gravity braiding

We study stealth black hole perturbations in shift symmetric kinetic gravity braiding and obtain its analogous Regge–Wheeler and Zerilli master equations for the odd and even parity sectors. We show that the nontrivial hair of static and spherically symmetric stealth black holes contributes only an additional source term to the even parity master equation. Furthermore, we derive exact solutions to the monopolar and dipolar perturbations and show that they are generally pathological non-gauge modes or else reduce to the pure-gauge low-order multipoles of general relativity.

Anisotropic cosmological models in Horndeski gravity

It was found recently that the anisotropies in the homogeneous Bianchi I cosmology considered within the context of a specific Horndeski theory are damped near the initial singularity instead of being amplified. In this work we extend the analysis of this phenomenon to cover the whole of the Horndeski family. We find that the phenomenon is absent in the K-essence and/or Kinetic Gravity Braiding theories, where the anisotropies grow as one approaches the singularity. The anisotropies are damped at early times only in more general Horndeski models whose Lagrangian includes terms quadratic and cubic in second derivatives of the scalar field. Such theories are often considered as being inconsistent with the observations because they predict a non-constant speed of gravitational waves. However, the predicted value of the speed at present can be close to the speed of light with any required precision, hence the theories actually agree with the present time observations. We consider two different examples of such theories, both characterized by a late self-acceleration and an early inflation driven by the non-minimal coupling. Their anisotropies show a maximum at intermediate times and approach zero at early and late times. The early inflationary stage exhibits an instability with respect to inhomogeneous perturbations, suggesting that the initial state of the universe should be inhomogeneous. However, more general Horndeski models may probably be stable.

Reconstruction method in the kinetic gravity braiding theory with shift-symmetric

We present a reconstruction method for flat Friedman-Robertson-Walker (FRW) spacetime in a subclass of Horndeski theory -- specifically shiftsymmetric, the kinetic gravity braiding (KGB) theory with a non-vanishing conserved current. Choosing the form of the Hubble parameter and kinetic density $X$, we restore the functions $G_2$, $G_3$ of the KGB model. In order to determine whether the model is free of ghosts and Laplacian instabilities and thus cosmologically viable, two conditions related to scalar perturbations are checked. Initially, the Lagrangian does not include the term that describes, for example, the perfect fluid with the EoS parameter $w\neq -1$. This fluid can provide a dynamic solution $H(t)$, $X(t)$. In the presented method, dynamic solutions are provided by a nonzero scalar charge associated with the shift symmetry $\phi\rightarrow\phi+\phi_0$. Reconstruction examples are given for models: an perfect fluid, a unified description dark energy-dark matter, a post-inflationary transition to the radiation-dominated phase.

Self-tuning kinetic gravity braiding: cosmological dynamics, shift symmetry, and the tadpole

We study the self-tuning subclass of kinetic gravity braiding and obtain robust predictions on self-tuning and dynamics in the tadpole-free shift symmetric sector of the theory. In particular, we show inevitability of cosmic acceleration, prove the dynamical stability of this late-time asymptotic state, and derive ghost and gradient stability constraints on the self-tuning vacuum. We discuss the results concretely in the context of generalized cubic covariant Galileon theory and an exponential kinetic gravity braiding.

Kinetic gravity braiding wormhole geometries

An interesting class of scalar-tensor models, denoted by kinetic gravity braiding (KGB), has recently been proposed. These models contain interactions of the second derivatives of the scalar field that do not lead to additional degrees of freedom and exhibit peculiar features, such as an essential mixing of the scalar $\phi$ and tensor kinetic $X$ terms. In this work, we consider the possibility that wormhole geometries are sustained by the KGB theory. More specifically, we present the full gravitational field equations in a static and spherically symmetric traversable wormhole background, and outline the general constraints at the wormhole throat, imposed by the flaring-out conditions. Furthermore, we present a plethora of analytical and numerical wormhole solutions by considering particular choices of the KGB factors. The analysis explicitly demonstrates that the KGB theory exhibits a rich structure of wormhole geometries, ranging from asymptotically flat solutions to asymptotically anti-de Sitter spacetimes.

General constraints on Horndeski wormhole throats

In this work, we consider the full Horndeski Lagrangian applied to wormhole geometries and present the full gravitational field equations. We analyse the general constraints imposed by the flaring-out conditions at the wormhole throat and consider a plethora of specific subclasses of the Horndeski Lagrangian, namely, quintessence/phantom fields, $k$-essence, scalar-tensor theories, covariant galileons, nonminimal kinetic coupling, kinetic gravity braiding, and the scalar-tensor representation of Gauss-Bonnet couplings, amongst others. The generic constraints analysed in this work serve as a consistency check of the main solutions obtained in the literature and draws out new avenues of research in considering applications of specific subclasses of the Horndeski theory to wormhole physics.

Stealth black holes in shift symmetric kinetic gravity braiding

We derive all hairy stealth black holes in the most general second-order, shift symmetric, scalar-tensor theory with luminally propagating gravitational waves, often called kinetic gravity braiding. Our approach exploits an overlooked loophole in a recently obtained no-go statement which claims shift symmetry breaking to be necessary for stealth solutions to exist in kinetic gravity braiding. We highlight the essential role played by a covariantly constant kinetic density in obtaining these solutions. Lastly, we propose a parametrization of the theories based on the asymptotics of its stealth solutions and comment on the intriguing singular effective metric for scalar perturbations in stealth black holes.

K-essence and kinetic gravity braiding models in two-field measure theory

We show that, in the context of the two-field measure theory, any k-essence model leads to the existence of a fluid made of non-relativistic matter and cosmological constant that would explain the dark matter and dark energy problem at the same time. On the other hand, kinetic gravity braiding models can lead to different behaviors, such as phantom dark energy, stiff matter, and a cosmological constant. For stiff matter, there even exists the case where the scalar field does not have any effect in the dynamics of the Universe.

The Lanczos Equation on Light-Like Hypersurfaces in a Cosmologically Viable Class of Kinetic Gravity Braiding Theories

We discuss junction conditions across null hypersurfaces in a class of scalar–tensor gravity theories (i) with second-order dynamics, (ii) obeying the recent constraints imposed by gravitational wave propagation, and (iii) allowing for a cosmologically viable evolution. These requirements select kinetic gravity braiding models with linear kinetic term dependence and scalar field-dependent coupling to curvature. We explore a pseudo-orthonormal tetrad and its allowed gauge fixing with one null vector standing as the normal and the other being transversal to the hypersurface. We derive a generalization of the Lanczos equation in a 2 + 1 decomposed form, relating the energy density, current, and isotropic pressure of a distributional source to the jumps in the transverse curvature and transverse derivative of the scalar. Additionally, we discuss a scalar junction condition and its implications for the distributional source.

Generalized 2D dilaton gravity and kinetic gravity braiding

We show explicitly that the nonminimal coupling between the scalar field and the Ricci scalar in 2D dilaton gravity can be recast in the form of kinetic gravity braiding (KGB). This is as it should be, because KGB is the 2D version of the Horndeski theory. We also determine all the static solutions with a linearly time-dependent scalar configuration in the shift-symmetric KGB theories in 2D.

Third order solutions of cosmological density perturbations in Horndeski’s most general scalar-tensor theory with the Vainshtein mechanism

We study the third order solutions of the cosmological density perturbations in Horndeski's most general scalar-tensor theory under the condition that the Vainshtein mechanism is at work. In this work, we thoroughly investigate the independence property of the functions describing the nonlinear mode couplings, which is also useful for models within general relativity. Then, we find that the solutions of the density contrast and the velocity divergence up to third order are characterized by six parameters. Furthermore, the one-loop order power spectra obtained with third order solutions are described by four parameters. We exemplify the behavior of the one-loop order power spectra assuming the kinetic gravity braiding model, which demonstrates that the effect of modified gravity appears more significantly in the power spectrum of the velocity divergence than the density contrast.