Galileon Field Research Articles

G-bounce inflation: towards nonsingular inflation cosmology with galileon field

We study a nonsingular bounce inflation model, which can drive the early universe from a contracting phase, bounce into an ordinary inflationary phase, followed by the reheating process. Besides the bounce that avoided the Big-Bang singularity which appears in the standard cosmological scenario, we make use of the Horndesky theory and design the kinetic and potential forms of the lagrangian, so that neither of the two big problems in bouncing cosmology, namely the ghost and the anisotropy problems, will appear. The cosmological perturbations can be generated either in the contracting phase or in the inflationary phase, where in the latter the power spectrum will be scale-invariant and fit the observational data, while in the former the perturbations will have nontrivial features that will be tested by the large scale structure experiments. We also fit our model to the CMB TT power spectrum.

Black holes in bi-scalar extensions of Horndeski theories

We study certain bi-scalar-tensor theories emanating from conformal symmetry requirements of Horndeski’s four-dimensional action. The former scalar is a Galileon with shift symmetry whereas the latter scalar is adjusted to have a higher order conformal coupling. Employing techniques from local Weyl geometry certain Galileon higher order terms are thus constructed to be conformally invariant. The combined shift and partial conformal symmetry of the action, allow us to construct exact black hole solutions. The black holes initially found are of planar horizon geometry embedded in anti de Sitter space and can accommodate electric charge. The conformally coupled scalar comes with an additional independent charge and it is well-defined on the horizon whereas additional regularity of the Galileon field is achieved allowing for time dependence. Guided by our results in adS space-time we then consider a higher order version of the BBMB action and construct asymptotically flat, regular, hairy black holes. The addition of the Galileon field is seen to cure the BBMB scalar horizon singularity while allowing for the presence of primary scalar hair seen as an independent integration constant along-side the mass of the black hole.

Galileon bounce after ekpyrotic contraction

We consider a simple cosmological model that includes a long ekpyrotic contraction stage and smooth bounce after it. Ekpyrotic behavior is due to a scalar field with a negative exponential potential, whereas the Galileon field produces bounce. We give an analytical picture of how the bounce occurs within the weak gravity regime, and then perform numerical analysis to extend our results to a non-perturbative regime.

Simulating the quartic Galileon gravity model on adaptively refined meshes

We develop a numerical algorithm to solve the high-order nonlinear derivative-coupling equation associated with the quartic Galileon model, and implement it in a modified version of the ramses N-body code to study the effect of the Galileon field on the large-scale matter clustering. The algorithm is tested for several matter field configurations with different symmetries, and works very well. This enables us to perform the first simulations for a quartic Galileon model which provides a good fit to the cosmic microwave background (CMB) anisotropy, supernovae and baryonic acoustic oscillations (BAO) data. Our result shows that the Vainshtein mechanism in this model is very efficient in suppressing the spatial variations of the scalar field. However, the time variation of the effective Newtonian constant caused by the curvature coupling of the Galileon field cannot be suppressed by the Vainshtein mechanism. This leads to a significant weakening of the strength of gravity in high-density regions at late times, and therefore a weaker matter clustering on small scales. We also find that without the Vainshtein mechanism the model would have behaved in a completely different way, which shows the crucial role played by nonlinearities in modified gravity theories and the importance of performing self-consistent N-body simulations for these theories.

Towards anisotropy-free and nonsingular bounce cosmology with scale-invariant perturbations

We investigate nonsingular bounce realizations in the framework of ghost-free generalized Galileon cosmology, which furthermore can be free of the anisotropy problem. Considering an ekpyroticlike potential we can obtain a total equation of state larger than 1 in the contracting phase, which is necessary for the evolution to be stable against small anisotropic fluctuations. Since such a large equation of state forbids the Galileon field to generate the desired form of perturbations, we additionally introduce the curvaton field which can in general produce the observed nearly scale-invariant spectrum. In particular, we provide approximate analytical and exact semianalytical expressions under which the bouncing scenario is consistent with observations. Finally, the combined Galileon-curvaton system is free of the big rip after the bounce.

Late-time acceleration in a slow-moving Galileon field

In this paper, we examine the cosmological viability of a slow moving galileon field in a potential. The Lagrangian $\cal{L}$ $ =-\frac{1}{2}g^{\mu\nu}\pi_{;\mu}\pi_{;\nu} +\frac{G^{\mu\nu}}{2M^2}\pi_{;\mu}\pi_{;\nu}$ respects the galileon symmetry in curved space time. We carry out detailed investigations of the underlying dynamics of this Lagrangian with Einstein-Hilbert term and a potential. We demonstrate that the model can give rise to a viable ghost free late time acceleration of universe. Furthermore we study the cosmological perturbation of the model and see that the model gives different BBN constraints at early times. We also carry out the observational analysis of the model and use observational data from growth, Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO) and Cosmic Microwave Background (CMB) to constrain the parameters of the theory.

Experimental constraints on the uncoupled Galileon model from SNLS3 data and other cosmological probes

The Galileon model is a modified gravity theory that may provide an explanation for the accelerated expansion of the Universe. This model does not suffer from instabilities or ghost problems (normally associated with higher-order derivative theories), restores local General Relativity -- thanks to the Vainshtein screening effect -- and predicts late time acceleration of the expansion. In this paper, we derive a new definition of the Galileon parameters that allows us to avoid having to choose initial conditions for the Galileon field, and then test this model against precise measurements of the cosmological distances and the rate of growth of cosmic structures. We observe a small tension between the constraints set by growth data and those from distances. However, we find that the Galileon model remains consistent with current observations and is still competitive with the \Lambda CDM model, contrary to what was concluded in recent publications.

No-hair theorem for the Galileon.

We consider a Galileon field coupled to gravity. The standard no-hair theorems do not apply because of the Galileon's peculiar derivative interactions. We prove that, nonetheless, static spherically symmetric black holes cannot sustain nontrivial Galileon profiles. Our theorem holds for trivial boundary conditions and for cosmological ones, and regardless of whether there are nonminimal couplings between the Galileon and gravity of the covariant Galileon type.

Parameter space in Galileon gravity models

We present the first constraints on the full parameter space of the Galileon modified gravity model, considering both the cosmological parameters and the coefficients which specify the additional terms in the Lagrangian due to the Galileon field, which we call the Galileon parameters. We use the latest cosmic microwave background measurements, along with distance measurements from supernovae and baryonic acoustic oscillations, performing a Monte Carlo Markov Chain exploration of the 9-dimensional parameter space. The integrated Sachs-Wolfe signal can be very different in Galileon models compared to standard gravity, making it essential to use the full CMB data rather than the CMB distance priors. We demonstrate that meaningful constraints are only possible in the Galileon parameter space after taking advantage of a scaling degeneracy. We find that the Galileon model can fit the WMAP 9-year results better than the standard \Lambda-Cold Dark Matter model, but gives a slightly worse fit overall once lower redshift distance measurements are included. The best-fitting cosmological parameters (e.g. matter density, scalar spectral index, fluctuation amplitude) can differ by more than 2\sigma\ in the Galileon model compared with \Lambda CDM. We highlight other potential constraints of the Galileon model using galaxy clustering and weak lensing measurements.

Time-dependent spherically symmetric covariant Galileons

We study spherically symmetric solutions of the cubic covariant Galileon model in curved spacetime in presence of a matter source, in the test scalar field approximation. We show that a cosmological time evolution of the Galileon field gives rise to an induced matter-scalar coupling, due to the Galileon-graviton kinetic braiding, therefore the solution for the Galileon field is non trivial even if the bare matter-scalar coupling constant is set to zero. The local solution crucially depends on the asymptotic boundary conditions, and in particular, Minkowski and de Sitter asymptotics correspond to different branches of the solution. We study the stability of these solutions, namely, the well-posedness of the Cauchy problem and the positivity of energy for scalar and tensor perturbations, by diagonalizing the kinetic terms of the spin-2 and spin-0 degrees of freedom. In addition, we find that in presence of a cosmological time evolution of the Galileon field, its kinetic mixing with the graviton leads to a friction force, resulting to efficient damping of scalar perturbations within matter.

Retarded Green’s function of a Vainshtein system and Galileon waves

Motivated by the desire to test modified gravity theories exhibiting the Vainshtein mechanism, we solve in various physically relevant limits, the retarded Galileon Green's function (for the cubic theory) about a background sourced by a massive spherically symmetric static body. The static limit of our result will aid us, in a forthcoming paper, in understanding the impact of Galileon fields on the problem of motion in the solar system. In this paper, we employ this retarded Green's function to investigate the emission of Galileon radiation generated by the motion of matter lying deep within the Vainshtein radius ${r}_{v}$ of the central object: acoustic waves vibrating on its surface, and the motion of compact bodies gravitationally bound to it. If $\ensuremath{\lambda}$ is the typical wavelength of the emitted radiation, and ${r}_{0}$ is the typical distance of the source from the central mass, with ${r}_{0}\ensuremath{\ll}{r}_{v}$, then, compared to its noninteracting massless scalar counterpart, we find that the Galileon radiation rate is suppressed by the ratio $({r}_{v}/\ensuremath{\lambda}{)}^{\ensuremath{-}3/2}$ at the monopole and dipole orders at high frequencies ${r}_{v}/\ensuremath{\lambda}\ensuremath{\gg}1$. However, at high enough multipole order, the radiation rate is enhanced by powers of ${r}_{v}/{r}_{0}$. At low frequencies ${r}_{v}/\ensuremath{\lambda}\ensuremath{\ll}1$, and when the motion is nonrelativistic, Galileon waves yield a comparable rate for the monopole and dipole terms, and are amplified by powers of the ratio ${r}_{v}/{r}_{0}$ for the higher multipoles.

Linear perturbations in Galileon gravity models

We study the cosmology of Galileon modified gravity models in the linear perturbation regime. We derive the fully covariant and gauge invariant perturbed field equations using two different methods, which give consistent results, and solve them using a modified version of the {\tt CAMB} code. We find that, in addition to modifying the background expansion history and therefore shifting the positions of the acoustic peaks in the cosmic microwave background (CMB) power spectrum, the Galileon field can cluster strongly from early times, and causes the Weyl gravitational potential to grow, rather than decay, at late times. This leaves clear signatures in the low-$l$ CMB power spectrum through the modified integrated Sachs-Wolfe effect, strongly enhances the linear growth of matter density perturbations and makes distinctive predictions for other cosmological signals such as weak lensing and the power spectrum of density fluctuations. The quasi-static approximation is shown to work quite well from small to the near-horizon scales. We demonstrate that Galileon models display a rich phenomenology due to the large parameter space and the sensitive dependence of the model predictions on the Galileon parameters. Our results show that some Galileon models are already ruled out by present data and that future higher significance galaxy clustering, ISW and lensing measurements will place strong constraints on Galileon gravity.

Covariant master theory for novel Galilean invariant models and massive gravity

Coupling the galileons to a curved background has been a tradeoff between maintaining second order equations of motion, maintaining the galilean shift symmetries, and allowing the background metric to be dynamical. We propose a construction which can achieve all three for a novel class of galilean invariant models, by coupling a scalar with the galilean symmetry to a massive graviton. This generalizes the brane construction for galileons, by adding to the brane a dynamical metric, (non-universally) interacting with the galileon field. Alternatively, it can be thought of as an extension of the ghost-free massive gravity, or as a massive graviton-galileon scalar-tensor theory. In the decoupling limit of these theories, new kinds of galileon invariant interactions arise between the scalar and the longitudinal mode of the graviton. These have higher order equations of motion and infinite powers of the field, yet are ghost-free.

Light mass galileons: Cosmological dynamics, mass screening and observational constraints

In this Letter, we examine the cosmological viability of a light mass galileon field consistent with local gravity constraints. The minimal, L3=□ϕ(∂μϕ)2, massless galileon field requires an additional term in order to give rise to a viable ghost free late time acceleration of Universe. The desired cosmological dynamics can either be achieved by incorporating an additional terms in the action such as (L4,L5) – the higher order galileon Lagrangians or by considering a light mass field à la galileon field potential. We analyze the second possibility and find that: (1) The model produces a viable cosmology in the regime where the non-linear galileon field is subdominant, (2) the Vainshtein mechanism operates at small scales where the non-linear effects become important and contribution of the field potential ceases to be significant. Also the small mass of the field under consideration is protected against strong quantum corrections thereby providing quantum stability to the system.

Symmetrically reduced Galileon equations and solutions

The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional Monge-Ampere equation, axial symmetry to its cubic extension etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, but highly implicit, lower-D solutions.

Chronology protection in Galileon models and massive gravity

Galileon models are a class of effective field theories that have recently received much attention. They arise in the decoupling limit of theories of massive gravity, and in some cases they have been treated in their own right as scalar field theories with a specific nonlinearly realized global symmetry (Galilean transformation). It is well known that in the presence of a source, these Galileon theories admit superluminal propagating solutions, implying that as quantum field theories they must admit a different notion of causality than standard local Lorentz invariant theories. We show that in these theories it is easy to construct closed timelike curves (CTCs) within the naive regime of validity of the effective field theory. However, on closer inspection we see that the CTCs could never arise since the Galileon inevitably becomes infinitely strongly coupled at the onset of the formation of a CTC. This implies an infinite amount of backreaction, first on the background for the Galileon field, signaling the break down of the effective field theory, and subsequently on the spacetime geometry, forbidding the formation of the CTC.Furthermore the background solution required to create CTCs becomes unstable with an arbitrarily fast decay time.Thus Galileon theories satisfy a direct analogue of Hawking's chronology protection conjecture.

Spherical collapse in covariant Galileon theory

In this paper we study the evolution of a spherical matter overdensity in the context of the recently introduced Galileon field theory. Our analysis considers the complete covariant Lagrangian in four dimensions. This theory is composed by a potential and a standard kinetic term, a cubic kinetic term and two additional terms that include the coupling between the Galileon and the metric, to preserve the original properties of Galileons also in curved space-times. Here we extend previous studies, which considered both the quintessence and the cubic terms, by focussing on the role of the last two terms. The background evolution we consider is driven by a tracker solution. Studying scalar perturbations in the non-linear regime, we find constraints on the parameter of the model. We will show how the new terms contribute to the collapse phase and how they modify physical parameters, such as the linearized density contrast and the virial overdensity. The results show that the Galileon modifies substantially the dynamics of the collapse, thus making it possible to observationally constrain the parameters of this theory.

Hamiltonian of Galileon field theory

We give a detailed calculation for the Hamiltonian of single Galileon field theory, keeping track of all the surface terms. We calculate the energy of static, spherically symmetric configuration of the single Galileon field at cubic order coupled to a point source and show that the 2-branches of the solution possess energy of equal magnitude and opposite sign, the sign of which is determined by the coefficient of the kinetic term ${\ensuremath{\alpha}}_{2}$. Moreover, the energy is regularized in the short distance (ultraviolet) regime by the dominant cubic term even though the source is divergent at the origin. We argue that the origin of the negativity is due to the ghostlike modes in the corresponding branch in the presence of the point source. This seems to be a nonlinear manifestation of the ghost instability.

Generalized Galileon cosmology

We study the cosmology of a generalized Galileon field $\phi$ with five covariant Lagrangians in which $\phi$ is replaced by general scalar functions $f_{i}(\phi)$ (i=1,...,5). For these theories, the equations of motion remain at second-order in time derivatives. We restrict the functional forms of $f_{i}(\phi)$ from the demand to obtain de Sitter solutions responsible for dark energy. There are two possible choices for power-law functions $f_{i}(\phi)$, depending on whether the coupling $F(\phi)$ with the Ricci scalar $R$ is independent of $\phi$ or depends on $\phi$. The former corresponds to the covariant Galileon theory that respects the Galilean symmetry in the Minkowski space-time. For generalized Galileon theories we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar and tensor perturbations as well as the condition for the stability of de Sitter solutions. We also carry out detailed analytic and numerical study for the cosmological dynamics in those theories.

G-Curvaton

In this Letter, we study a curvaton model where the curvaton is acted by Galileon field. We calculate the power spectrum of fluctuation of G-Curvaton during inflation and discuss how it converts to the curvature perturbation after the end of inflation. We estimate the bispectrum of curvature perturbation induced, and show the dependence of non-Gaussianity on the parameters of model. It is found that our model can have sizable local and equilateral non-Gaussianities to up to O(102), which is illustrated by an explicit example.