Galileon Field Research Articles

Galileons on cosmological backgrounds

We construct four-dimensional effective field theories of a generalized DBI galileon field, the dynamics of which naturally takeplace on a Friedmann-Robertson-Walker spacetime. The theories are invariantunder non-linear symmetry transformations, which can be thought of as being inherited from five-dimensional bulk Killing symmetries via theprobe brane technique through which they are constructed. The resulting model provides a framework in which to explore the cosmological role that galileons may play as the universe evolves.

Defrosting in an emergent Galileon cosmology

We study the transition from an Emergent Galileon condensate phase of the early universe to a later expanding radiation phase. This "defrosting" or "preheating" transition is a consequence of the excitation of matter fluctuations by the coherent Galileon condensate, in analogy to how preheating in inflationary cosmology occurs via the excitation of matter fluctuations through coupling of matter with the coherent inflaton condensate. We show that the "minimal" coupling of matter (modeled as a massless scalar field) to the Galileon field introduced by Creminelli, Nicolis and Trincherini in order to generate a scale-invariant spectrum of matter fluctuations is sufficient to lead to efficient defrosting, provided that the effects of the non-vanishing expansion rate of the universe are taken into account. If we neglect the effects of expansion, an additional coupling of matter to the Galileon condensate is required. We study the efficiency of the defrosting mechanism in both cases.

Classical stability of the Galileon

We consider the classical equations of motion for a single Galileon field with generic parameters in the presence of non-relativistic sources. We introduce the concept of absolute stability of a theory: if one can show that a field at a single point---like infinity for instance---in spacetime is stable, then stability of the field over the rest of spacetime is guaranteed for any positive energy source configuration. The Dvali-Gabadadze-Porrati (DGP) model is stable in this manner, and previous studies of spherically symmetric solutions suggest that certain classes of the single field Galileon (of which the DGP model is a subclass) may have this property as well. We find, however, that when general solutions are considered this is not the case. In fact, when considering generic solutions there are no choices of free parameters in the Galileon theory that will lead to absolute stability except the DGP choice. Our analysis indicates that the DGP model is an exceptional choice among the large class of possible single field Galileon theories. This implies that if general solutions (non-spherically symmetric) exist they may be unstable. Given astrophysical motivation for the Galileon, further investigation into these unstable solutions may prove fruitful.

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.

Galileon hairs of Dyson spheres, Vainshtein’s coiffure and hirsute bubbles

We study the fields of spherically symmetric thin shell sources, a.k.a. Dyson spheres, in a fully nonlinear covariant theory of gravity with the simplest galileon field. We integrate exactly all the field equations once, reducing them to first order nonlinear equations. For the simplest galileon, static solutions come on six distinct branches. On one, a Dyson sphere surrounds itself with a galileon hair, which far away looks like a hair of any Brans-Dicke field. The hair changes below the Vainshtein scale, where the extra galileon terms dominate the minimal gradients of the field. Their hair looks more like a fuzz, because the galileon terms are suppressed by the derivative of the volume determinant. It shuts off the ‘hair bunching’ over the ‘angular’ 2-sphere. Hence the fuzz remains dilute even close to the source. This is really why the Vainshtein’s suppression of the modifications of gravity works close to the source. On the other five branches, the static solutions are all singular far from the source, and shuttered off from asymptotic infinity. One of them, however, is really the self-accelerating branch, and the singularity is removed by turning on time dependence. We give examples of regulated solutions, where the Dyson sphere explodes outward, and its self-accelerating side is nonsingular. These constructions may open channels for nonperturbative transitions between branches, which need to be addressed further to determine phenomenological viability of multi-branch gravities.

Decoding the bispectrum of single-field inflation

Galileon fields arise naturally from the decoupling limit of massive gravities, and possess special self-interactions which are protected by a spacetime generalization of Galilean symmetry. We briefly revisit the inflationary phenomenology of Galileon theories. Working from recent computations of the fluctuation Lagrangian to cubic order in the most general model with second-order equations of motion, we show that a distinct shape is present but with suppressed amplitude. A similar shape has been found in other higher-derivative models. It may be visible in a theory tuned to suppress the leading-order shapes, or if the overall bispectrum has large amplitude. Using a partial-wave expansion of the bispectrum, we suggest a possible origin for the frequent appearance of this shape. It follows that models with very disparate microphysics can produce very similar bispectra. We argue that it may be more profitable to distinguish these models by searching for relations between the amplitudes of these common shapes. We illustrate this method using the examples of DBI and k-inflation.

Galileon design of slow expansion

We show a model of the slow expansion, in which the scale invariant spectrum of curvature perturbation is adiabatically induced by its increasing mode, by applying a generalized Galileon field. In this model, initially \epsilon << -1, which then is rapidly increasing, during this period the universe is slowly expanding. There is not the ghost instability, the perturbation theory is healthy. When \epsilon \sim -1, the slow expansion phase ends, and the available energy of field can be released and the universe reheats. This scenario might be a viable design of the early universe.

Instabilities of spherical solutions with multiple Galileons andSO(N)symmetry

The 4-dimensional effective theory arising from an induced gravity action for a codimension greater than one brane consists of multiple Galileon fields ${\ensuremath{\pi}}^{I}$, $I=1,\dots{},N$, invariant under separate Galilean transformations for each scalar, and under an internal $SO(N)$ symmetry. We study the viability of such models by examining spherically symmetric solutions. We find that for general, nonderivative couplings to matter invariant under the internal symmetry, such solutions exist and exhibit a Vainshtein screening effect. By studying perturbations about such solutions, we find both an inevitable gradient instability and fluctuations propagating at superluminal speeds. These findings suggest that more general, derivative couplings to matter are required for the viability of $SO(N)$ Galileon theories.

Galileon accretion

We study steady-state spherically symmetric accretion of a galileon field onto a Schwarzschild black hole in the test fluid approximation. The galileon is assumed to undergo a stage of cosmological evolution, thus setting a non-trivial boundary condition at spatial infinity. The critical flow is found for some parameters of the theory. There is a range of parameters when the critical flow exists, but the solution is unstable. It is also shown that for a certain range of parameters the critical flow solution does not exist. Depending on the model the sound horizon of the flow can be either outside or inside of the Schwarzschild horizon. The latter property may make it problematic to embed the galileon theory in the standard black hole thermodynamics.

Observational constraints on Galileon cosmology

We study the cosmology of a covariant Galileon field with five covariant Lagrangians and confront this theory with the most recent cosmological probes: the type Ia supernovae data (Constitution and Union2 sets), cosmic microwave background (WMAP7) and the baryon acoustic oscillations (SDSS7). In the Galileon cosmology with a late-time de Sitter attractor, there is a tracker that attracts solutions with different initial conditions to a common trajectory. Including the cosmic curvature K, we place observational constraints on two distinct cases: (i) the tracker, and (ii) the generic solutions to the equations of motion. We find that the tracker solution can be consistent with the individual observational data, but it is disfavored by the combined data analysis. The generic solutions fare quite well when a non-zero curvature parameter is taken into account, but the Akaike and Bayesian information criteria show that they are not particularly favored over the LCDM model.

Multifield Galileons and higher codimension branes

In the decoupling limit, the Dvali-Gabadadze-Porrati model reduces to the theory of a scalar field $\ensuremath{\pi}$, with interactions including a specific cubic self-interaction---the Galileon term. This term, and its quartic and quintic generalizations, can be thought of as arising from a probe 3-brane in a five-dimensional bulk with Lovelock terms on the brane and in the bulk. We study multifield generalizations of the Galileon and extend this probe-brane view to higher codimensions. We derive an extremely restrictive theory of multiple Galileon fields, interacting through a quartic term controlled by a single coupling, and trace its origin to the induced brane terms coming from Lovelock invariants in the higher codimension bulk. We explore some properties of this theory, finding de Sitter like self-accelerating solutions. These solutions have ghosts if and only if the flat space theory does not have ghosts. Finally, we prove a general nonrenormalization theorem: multifield Galileons are not renormalized quantum mechanically to any loop in perturbation theory.

Inflation Driven by the Galileon Field

We propose a new class of inflation model, G inflation, which has a Galileon-like nonlinear derivative interaction of the form G(ϕ,(∇ϕ)(2))□ϕ in the Lagrangian with the resultant equations of motion being of second order. It is shown that (almost) scale-invariant curvature fluctuations can be generated even in the exactly de Sitter background and that the tensor-to-scalar ratio can take a significantly larger value than in the standard inflation models, violating the standard consistency relation. Furthermore, violation of the null energy condition can occur without any instabilities. As a result, the spectral index of tensor modes can be blue, which makes it easier to observe quantum gravitational waves from inflation by the planned gravitational-wave experiments such as LISA and DECIGO as well as by the upcoming CMB experiments such as Planck and CMBpol.

Modified gravityà laGalileon: Late time cosmic acceleration and observational constraints

In this paper we examine the cosmological consequences of fourth order Galileon gravity. We carry out detailed investigations of the underlying dynamics and demonstrate the stability of one de Sitter phase. The stable de Sitter phase contains a Galileon field $\ensuremath{\pi}$ which is an increasing function of time ($\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\pi}}&gt;0$). Using the required suppression of the fifth force, supernovae, Baryon acoustic oscillations, and CMB data, we constrain parameters of the model. We find that the $\ensuremath{\pi}$ matter coupling parameter $\ensuremath{\beta}$ is constrained to small numerical values such that $\ensuremath{\beta}&lt;0.02$. We also show that the parameters of the third and fourth order in the action $({c}_{3},{c}_{4})$ are not independent and with reasonable assumptions, we obtain constraints on them. We investigate the growth history of the model and find that the subhorizon approximation is not allowed for this model. We demonstrate strong scale dependence of linear perturbations in the fourth order Galileon gravity.

Galilean genesis: an alternative to inflation

We propose a novel cosmological scenario, in which standard inflation is replaced by an expanding phase with a drastic violation of the Null Energy Condition (NEC): Ḣ >> H2. The model is based on the recently introduced Galileon theories, which allow NEC violating solutions without instabilities. The unperturbed solution describes a Universe that is asymptotically Minkowski in the past, expands with increasing energy density until it exits the regime of validity of the effective field theory and reheats. This solution is a dynamical attractor and the Universe is driven to it, even if it is initially contracting. The study of perturbations of the Galileon field reveals some subtleties, related to the gross violation of the NEC and it shows that adiabatic perturbations are cosmologically irrelevant. The model, however, suggests a new way to produce a scale invariant spectrum of isocurvature perturbations, which can later be converted to adiabatic: the Galileon is forced by symmetry to couple to the other fields as a dilaton; the effective metric it yields on the NEC violating solution is that of de Sitter space, so that all light scalars will automatically acquire a nearly scale-invariant spectrum of perturbations.

Cosmology of a Covariant Galileon Field

We study the cosmology of a covariant scalar field respecting a Galilean symmetry in flat space-time. We show the existence of a tracker solution that finally approaches a deSitter fixed point responsible for cosmic acceleration today. The viable region of model parameters is clarified by deriving conditions under which ghosts and Laplacian instabilities of scalar and tensor perturbations are absent. The field equation of state exhibits a peculiar phantomlike behavior along the tracker, which allows a possibility to observationally distinguish the Galileon gravity from the cold dark matter model with a cosmological constant.

Revisiting fifth forces in the Galileon model

A Galileon field is one which obeys a spacetime generalization of the non-relativistic Galilean invariance. Such a field may possess non-canonical kinetic terms, but ghost-free theories with a well-defined Cauchy problem exist, constructed using a finite number of relevant operators. The interactions of this scalar with matter are hidden by the Vainshtein effect, causing the Galileon to become weakly coupled near heavy sources. We revisit estimates of the fifth force mediated by a Galileon field, and show that the parameters of the model are less constrained by experiment that previously supposed.

Galileon gravity and its relevance to late time cosmic acceleration

We consider the covariant Galileon gravity taking into account the third order and fourth order scalar field Lagrangians ${L}_{3}(\ensuremath{\pi})$ and ${L}_{4}(\ensuremath{\pi})$, consisting of three and four $\ensuremath{\pi}$'s with four and five derivatives acting on them, respectively. The background dynamical equations are set up for the system under consideration and the stability of the self-accelerating solution is demonstrated in a general setting. We extended this study to the general case of the fifth order theory. For the spherically symmetric static background, we spell out conditions for the suppression of fifth force effects mediated by the Galileon field $\ensuremath{\pi}$. We study field perturbations in the fixed background and investigate the conditions for their causal propagation. We also briefly discuss metric fluctuations and derive an evolution equation for matter perturbations in Galileon gravity.