Galileon Model Research Articles

Constraints on general second-order scalar-tensor models from gravitational Cherenkov radiation

We demonstrate that the general second-order scalar-tensor theories, which have attracted attention as possible modified gravity models to explain the late time cosmic acceleration, could be strongly constrained from the argument of the gravitational Cherenkov radiation. To this end, we consider the purely kinetic coupled gravity and the extended galileon model on a cosmological background. In these models, the propagation speed of tensor mode could be less than the speed of light, which puts very strong constraints from the gravitational Cherenkov radiation.

Do observations favour Galileon over quintessence?

We study the Galileon scalar field model arising as a decoupling limit of the Dvali–Gababdaze–Porrati (DGP) construction for the late time acceleration of the universe. The model has one extra Galileon correction term over and above the standard kinetic and potential energy terms for a canonical quintessence field. We aim to study whether the current observational data can distinguish between the Galileon and the quintessence field. Our study shows the remarkable result that for linear and ϕ2 potentials, the data prefers the Galileon model over quintessence with significant Bayesian evidence. It confirms that the observable universe indeed prefers the inclusion of higher derivative Galileon correction in the standard scalar field Lagrangian.

Constraining Galileon Gravity from Observational Data with Growth Rate

We studied the cosmological constraints on the Galileon gravity obtained from observational data of the growth rate of matter density perturbations, the supernovae Ia (SN Ia), the cosmic microwave background (CMB), and baryon acoustic oscillations (BAO). For the same value of the energy density parameter of matter $\Omega_{m,0}$, the growth rate $f$ in Galileon models is enhanced, relative to the $\Lambda$CDM case, because of an increase in Newton's constant. The smaller $\Omega_{m,0}$ is, the more growth rate is suppressed. Therefore, the best fit value of $\Omega_{m,0}$ in the Galileon model, based only the growth rate data, is quite small. This is incompatible with the value of $\Omega_{m,0}$ obtained from the combination of SN Ia, CMB, and BAO data. On the other hand, in the $\Lambda$CDM model, the values of $\Omega_{m,0}$ obtained from different observational data sets are consistent. In the analysis of this paper, we found that the Galileon model is less compatible with observations than the $\Lambda$CDM model. This result seems to be qualitatively the same in most of the generalized Galileon models in which Newton's constant is enhanced.

Testing gravity with halo density profiles observed through gravitational lensing

We present a new test of the modified gravity endowed with the Vainshteinmechanism with the density profile of a galaxy cluster halo observed through gravitational lensing.A scalar degree of freedom in the galileon modified gravity is screened by the Vainshtein mechanism to recover Newtonian gravity in high-density regions, however it might not be completely hidden on the outer side of a cluster of galaxies. Then the modified gravity might yield an observational signature in a surface mass density of a cluster of galaxies measured through gravitational lensing, since the scalar field could contribute to the lensing potential. We investigate how the transition in the Vainshtein mechanism affects the surface mass density observed through gravitational lensing, assuming that the density profile of a cluster of galaxies follows the original Navarro-Frenk-White (NFW) profile, the generalized NFW profile and the Einasto profile. We compare the theoretical predictions with observational resultsof the surface mass density reported recently by other researchers. We obtain constraints on the amplitude and the typical scale of the transition in the Vainshtein mechanism in a subclass of the generalized galileon model.

Galileons with Gauge Symmetries

Galileon models arise in certain braneworld scenarios as modifications to General Relativity, and are also interesting as field theories in their own right. We show how the galileon model can be naturally generalized to include local gauge symmetries, by allowing for couplings to Yang-Mills fields. The resulting theories have at most second order spacetime derivatives in any representation of the gauge group, thereby avoiding Ostrogradski ghosts. We also extend the models to include curved space, and show how in that case we need to include non-minimal couplings between the galileons and the curvature tensors for the theory to retain its second order nature.

Stability of closed timelike curves in a Galileon model

Recently Burrage, de Rham, Heisenberg and Tolley have constructed eternal, classical solutions with closed timelike curves (CTCs) in a Galileon model coupled to an auxiliary scalar field. These theories contain at least two distinct metrics and, in configurations with CTCs, two distinct notions of locality. As usual, globally CTCs lead to pathologies including nonlocal constraints on the initial Cauchy data. Locally, with respect to the gravitational metric, we use an eikonal approximation to explicitly construct small, short-wavelength perturbations without imposing the nonlocal constraints and observe that these perturbations do not grow and so do not lead to an instability.

The paths of gravity in galileon cosmology

Galileon gravity offers a robust gravitational theory for explaining cosmic acceleration, having a rich phenomenology of testable behaviors. We explore three classes of Galileon models — standard uncoupled, and linearly or derivatively coupled to matter — investigating the expansion history with particular attention to early time and late time attractors, as well as the linear perturbations. From the relativistic and nonrelativistic Poisson equations we calculate the generalizations of the gravitational strength (Newton's constant), deriving its early and late time behavior. By scanning through the parameters we derive distributions of the gravitational strength at various epochs and trace the paths of gravity in its evolution. Using ghost-free and stability criteria we restrict the allowed parameter space, finding in particular that the linear and derivative coupled models are severely constrained by classical instabilities in the early universe.

Cosmological constraints on extended Galileon models

The extended Galileon models possess tracker solutions with de Sitterattractors along which the dark energy equation of state is constantduring the matter-dominated epoch, i.e. wDE = −1−s, wheres is a positive constant. Even with this phantom equation of statethere are viable parameter spaces in which the ghosts and Laplacianinstabilities are absent. Using the observational data of the supernovaetype Ia, the cosmic microwave background (CMB), and baryon acousticoscillations, we place constraints on the tracker solutions at thebackground level and find that the parameter s is constrained tobe s = 0.034−0.034+0.327 (95 % CL) in the flat Universe. Inorder to break the degeneracy between the models we also study theevolution of cosmological density perturbations relevant to the large-scalestructure (LSS) and the Integrated-Sachs-Wolfe (ISW) effect in CMB.We show that, depending on the model parameters, the LSS and the ISWeffect is either positively or negatively correlated. It is then possibleto constrain viable parameter spaces further from the observationaldata of the ISW-LSS cross-correlation as well as from the matter powerspectrum.

Conditions for the cosmological viability of the most general scalar-tensortheories and their applications to extended Galileon dark energy models

In the Horndeski's most general scalar-tensor theories with second-orderfield equations, we derive the conditions for the avoidance of ghostsand Laplacian instabilities associated with scalar, tensor, and vectorperturbations in the presence of two perfect fluids on the flat Friedmann-Lemaître-Robertson-Walker(FLRW) background. Our general results are useful for the constructionof theoretically consistent models of dark energy. We apply our formulasto extended Galileon models in which a tracker solution with an equationof state smaller than -1 is present. We clarify the allowed parameterspace in which the ghosts and Laplacian instabilities are absent andwe numerically confirm that such models are indeed cosmologicallyviable.

Vainshtein screening in a cosmological background in the most general second-order scalar-tensor theory

A generic second-order scalar-tensor theory contains a nonlinear derivative self-interaction of the scalar degree of freedom $\ensuremath{\phi}$ \`a la Galileon models, which allows for the Vainshtein screening mechanism. We investigate this effect on subhorizon scales in a cosmological background, based on the most general second-order scalar-tensor theory. Our analysis takes into account all the relevant nonlinear terms and the effect of metric perturbations consistently. We derive an explicit form of Newton's constant, which in general is time-dependent and hence is constrained from observations, as suggested earlier. It is argued that in the most general case the inverse-square law cannot be reproduced on the smallest scales. Some applications of our results are also presented.

Fab Four: When John and George Play Gravitation and Cosmology

Scalar-tensor theories of gravitation attract again a great interest since the discovery of the Chameleon mechanism and of the Galileon models. The former allows reconciling the presence of a scalar field with the constraints from Solar System experiments. The latter leads to inflationary models that do not need ad hoc potentials. Further generalizations lead to a tensor-scalar theory, dubbed the “Fab Four,” with only first and second order derivatives of the fields in the equations of motion that self-tune to a vanishing cosmological constant. This model needs to be confronted with experimental data in order to constrain its large parameter space. We present some results regarding a subset of this theory named “John,” which corresponds to a nonminimal derivative coupling between the scalar field and the Einstein tensor in the action. We show that this coupling gives rise to an inflationary model with very unnatural initial conditions. Thus, we include the term named “George,” namely, a nonminimal, but nonderivative, coupling between the scalar field and Ricci scalar. We find a more natural inflationary model, and, by performing a post-Newtonian analysis, we derive the set of equations that constrain the parameter space with data from experiments in the Solar System.

HALO MODELS IN MODIFIED GRAVITY THEORIES WITH SELF-ACCELERATED EXPANSION

We investigate the structure of halos in the sDGP (self-accelerating branch of the Dvali–Gavadadze–Porrati braneworld gravity) model and the Galileon modified gravity model on the basis of the static and spherically symmetric solutions of the collisionless Boltzmann equation, which reduce to the singular isothermal sphere model and the King model in the limit of Newtonian gravity. The common feature of these halos is that the density of a halo in the outer region is larger (smaller) in the sDGP (Galileon) model, respectively, in comparison with Newtonian gravity. This comes from the suppression (enhancement) of the effective gravity at large distance in the sDGP (Galileon) model, respectively. However, the difference between these modified gravity models and Newtonian gravity only appears outside the halo due to the Vainshtein mechanism, which makes it difficult to distinguish between them. We also discuss the case in which the halo density profile is fixed independently of the gravity model for comparison between our results and previous work.

Closed timelike curves in the Galileon model

It has long been known that generic solutions to the nonlinear DGP and Galileon models admit superluminal propagation. In this note we present a solution of these models which also admits closed timelike curves (CTCs). We observe that these CTCs only arise when, according to each observer, there exists some region in which the higher derivative terms are larger than the 2-derivative kinetic term.

Conserved cosmological perturbation in Galileon models

We prove the existence of a fully nonlinear conserved curvature perturbation on large scales in Galileon-type scalar field models in two approaches. The first approach is based on the conservation of energy-momentum tensor of the Galileon field, which is also the familiar approach in understanding the conservation in k-essence or perfect fluid models. We show that the fluid corresponding to the Galileon field becomes perfect and barotropic on large scales, which is responsible to the conservation. The difference from k-essence model is that, besides the energy-momentum conservation, the Einstein equation must be employed in order to complete the proof of barotropy. In the second approach, we derive the fully non-perturbative action for the curvature perturbation ζ in Galileon models on large scales, and argue that ζ = const is indeed an exact solution on large scales. This conservation of curvature perturbation is important since it relates the later and the primordial universe.

Bouncing Galileon cosmologies

We present nonsingular, homogeneous and isotropic bouncingsolutions of the conformal Galileon model. We show that suchsolutions necessarily begin with a radiation-dominated contractingphase. This is followed by a quintom scenario in which thebackground equation of state crosses the cosmological constantboundary allowing for a nonsingular bounce which in turn is followedby Galilean Genesis. We analyze the spectrum of cosmologicalperturbations in this background. Our results show that thefluctuations evolve smoothly and without any pathology, but theadiabatic modes form a blue tilted spectrum. In order to achieve ascale-invariant primordial power spectrum as required by currentobservations, we introduce a light scalar field coupling to theGalileon kinetically. We find two couplings which yield ascale-invariant spectrum, one of which requires a fine tuning of theinitial conditions. This model also predicts a blue tilted spectrumof gravitational waves stemming from quantum vacuum fluctuations inthe contracting phase.

Laboratory tests of the Galileon

The Galileon model is a ghost free scalar effective field theory containing higher derivative terms that are protected by the Galileon symmetry. The presence of a Vainshtein screening mechanism allows the scalar field to couple to matter without mediating unacceptably large fifth forces in the solar system. We describe how laboratory measurements of the Casimir effect and possible deviations from Newtonian gravity can be used to search for Galileon scalar fields. Current experimental measurements are used to bound a previously unconstrained combination of Galileon parameters.

Some adventures in the search for a modified gravity explanation of cosmic acceleration

The discovery of cosmic acceleration has raised the intriguing possibility that we are witnessing the first breakdown of General Relativity on cosmological scales. In this article I will briefly review current attempts to construct a theoretically consistent and observationally viable modification of gravity that is capable of describing the accelerating universe. I will discuss f(R) models, and their obvious extensions, and the DGP model as an example of extra-dimensional implementations. I will then briefly describe the Galileon models and their very recent multifield and curved space extensions - a class of four-dimensional effective field theories encoding extra dimensional modifications to gravity. This article is dedicated to the career of my friend and former colleague, Joshua Goldberg, and is written to appear in his festschrift.

Large slow-roll corrections to the bispectrum of noncanonical inflation

Nongaussian statistics are a powerful discriminant between inflationary models, particularly those with noncanonical kinetic terms. Focusing on theories where the Lagrangian is an arbitrary Lorentz-invariant function of a scalar field and its first derivatives, we review and extend the calculation of the observable three-point function. We compute the ``next-order'' slow-roll corrections to the bispectrum in closed form, and obtain quantitative estimates of their magnitude in DBI and power-law k-inflation. In the DBI case our results enable us to estimate corrections from the shape of the potential and the warp factor: these can be of order several tens of percent. We track the possible sources of large logarithms which can spoil ordinary perturbation theory, and use them to obtain a general formula for the scale dependence of the bispectrum. Our result satisfies the next-order version of Maldacena's consistency condition and an equivalent consistency condition for the scale dependence. We identify a new bispectrum shape available at next-order, which is similar to a shape encountered in Galileon models. If fNL is sufficiently large this shape may be independently detectable.

Goldstone’s theorem and Hamiltonian of multi-Galileon modified gravity

The galileon model was recently proposed to locally describe a class of modified gravity theories, including the braneworld DGP model. We discuss spontaneous symmetry breaking of the self-accelerating branch in a multi-galileon theory with internal global symmetries. We show a modified version of Goldstone's theorem is applicable to the symmetry breaking pattern and discuss its implications. We also derive the Hamiltonian of a general multi-galileon theory and discuss its implications.

Matter perturbations in Galileon cosmology

We study the evolution of matter density perturbations in Galileon cosmology where the late-time cosmic acceleration can be realized by a field kinetic energy. We obtain full perturbation equations at linear order in the presence of five covariant Lagrangians ${cal L}_i$ ($i=1,...,5$) satisfying a Galilean symmetry in the flat space-time. The equations for a matter perturbation as well as an effective gravitational potential are derived under a quasi-static approximation on sub-horizon scales. This approximation can reproduce full numerical solutions with high accuracy for the wavelengths relevant to large-scale structures. For the model parameters constrained by the background expansion history of the Universe the growth rate of matter perturbations is larger than that in the LCDM model, with the growth index $gamma$ today typically smaller than 0.4. We also find that, even on very large scales associated with the Integrated-Sachs-Wolfe (ISW) effect in Cosmic Microwave Background (CMB) temperature anisotropies, the effective gravitational potential exhibits a temporal growth during the transition from the matter era to the epoch of cosmic acceleration. These properties are useful to distinguish the Galileon model from the LCDM in future high-precision observations.