Kinetic Gravity Braiding Research Articles

Modified natural inflation: A small single field model with a large tensor to scalar ratio

In this paper we explored in detail a phenomenological model of modified single field natural inflation in light of recent cosmological experiments, BICEP2. Our main goal is to construct an inflationary model which not only predicts the important cosmological quantities such as $({n}_{s},r)$ compatible with experimental observation, but also is consistent with the low energy effective theory framework. Therefore, all fundamental scales apart from ${M}_{p}$ and quantities of our interest should be within the sub-Planckian region. In order to achieve our goal, we modify the usual single field natural inflationary model by a specific form of higher derivative kinetic terms called kinetic gravity braiding. One of our guiding principles to construct such a model is the constant shift symmetry of the axion. We have chosen the form of the kinetic gravity braiding term in such a way that it predicts the required value of ${n}_{s}\ensuremath{\simeq}0.96$ and a large tensor to scalar ratio, $r>0.1$. Importantly, for a wide range of parameter space our model has sub-Planckian axion decay constant $f$ and the scale of inflation $\mathrm{\ensuremath{\Lambda}}$. However, the reheating after the end of inflation limits the value of $f$ so that we are unable to get $f$ to be significantly lower than ${M}_{p}$. Furthermore, we find sub-Planckian field excursion for the axion field $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}\ensuremath{\simeq}f$ for the sufficient number of $e$-folding, $\mathcal{N}\ensuremath{\gtrsim}50$. We also discussed in detail about the natural preheating mechanism in our model based on the recently proposed Chern-Simon coupling. We found this gravity mediated preheating is very difficult to achieve in our model. With our general analytic argument, we also would like to emphasize that Chern-Simons mediated preheating is very unlikely to happen in any slow roll inflationary model.

Horndeski theory meets the McVittie solution: A scalar field theory for accretion onto cosmological black holes

We show that the generalized McVittie spacetime, which represents a black hole with time-dependent mass in an expanding universe, is an exact solution of a subclass of the Horndeski family of actions. The heat-flow term responsible for the energy transfer between the black hole and the cosmological background is generated by the higher-order kinetic gravity braiding term, which generalizes the cuscuton action that yields McVittie with constant mass as a solution. Finally, we show that this generalization can be understood in terms of a duality realized by a disformal transformation, connecting the cuscuton field theory to an extension of the Horndeski action which does not propagate any scalar degrees of freedom. Our finding opens a novel window into studies of non-trivial interactions between dark energy/modified gravity theories and astrophysical black holes.

Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity

We present a turnkey solution, ready for implementation in numerical codes, for the study of linear structure formation in general scalar-tensor models involving a single universally coupled scalar field. We show that the totality of cosmological information on the gravitational sector can be compressed — without any redundancy — into five independent and arbitrary functions of time only and one constant. These describe physical properties of the universe: the observable background expansion history, fractional matter density today, and four functions of time describing the properties of the dark energy. We show that two of those dark-energy property functions control the existence of anisotropic stress, the other two — dark-energy clustering, both of which are can be scale-dependent. All these properties can in principle be measured, but no information on the underlying theory of acceleration beyond this can be obtained. We present a translation between popular models of late-time acceleration (e.g. perfect fluids, f(R), kinetic gravity braiding, galileons), as well as the effective field theory framework, and our formulation. In this way, implementing this formulation numerically would give a single tool which could consistently test the majority of models of late-time acceleration heretofore proposed.

Bispectrum of cosmological density perturbations in the most general second-order scalar-tensor theory

We study the bispectrum of matter density perturbations induced by the large-scale structure formation in the most general second-order scalar-tensor theory that may possess the Vainshtein mechanism as a screening mechanism. On the basis of the standard perturbation theory, we derive the bispectrum being expressed by a kernel of the second-order density perturbations. We find that the leading-order kernel is characterized by one parameter, which is determined by the solutions of the linear density perturbations, the Hubble parameter, and the other function specifying nonlinear interactions. This is because our model, which may be equipped with the Vainshtein mechanism, includes only one simple function that describes mode couplings of the nonlinear interactions. This feature does not allow for varied behavior in the bispectrum of the matter density perturbations in the most general second-order scalar-tensor theory equipped with the Vainshtein mechanism. We exemplify the typical behavior of the bispectrum in a kinetic gravity braiding model.

Parametrizing dark sector perturbations via equations of state

The evolution of perturbations is a crucial part of the phenomenology of the dark sector cosmology. We advocate parametrizing these perturbations using equations of state for the entropy perturbation and the anisotropic stress. For small perturbations, these equations of state will be linear in the density, velocity and metric perturbations, and in principle these can be related back to the field content of the underlying model allowing for confrontation with observations. We illustrate our point by constructing gauge-invariant entropy perturbations for theories where the dark sector Lagrangian is a general function of a scalar field, its first and second derivatives, and the metric and its first derivative, $\mathcal{L}=\mathcal{L}(\ensuremath{\phi},{\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\phi},{\ensuremath{\partial}}_{\ensuremath{\mu}}{\ensuremath{\partial}}_{\ensuremath{\nu}}\ensuremath{\phi},{g}_{\ensuremath{\mu}\ensuremath{\nu}},{\ensuremath{\partial}}_{\ensuremath{\alpha}}{g}_{\ensuremath{\mu}\ensuremath{\nu}})$. As an example, we show how to apply this approach to the case of models of kinetic gravity braiding.

Kinetic gravity braiding and axion inflation

We constructed a new class of inflationary model with the higher derivative axion field which obeys constant shift symmetry. In the usual axion (natural) inflation, the axion decay constant is predicted to be in the super-Planckian regime which is believed to be incompatible with an effective field theory framework. With a novel mechanism originating from a higher derivative kinetic gravity braiding (KGB) of an axion field we found that there exists a huge parameter regime in our model where axion decay constant could be naturally sub-Planckian, thanks to the KGB which effectively reduces the Planck constant. This effectively reduced Planck scale provides us the mechanism of further lowering down the speed of an axion field rolling down its potential without introducing super-Planckian axion decay constant. We also find that with that wide range of parameter values, our model induces almost scale invariant power spectrum as observed in CMB experiments.

Consistent perturbations in an imperfect fluid

We present a new prescription for analysing cosmological perturbationsin a more-general class of scalar-field dark-energy models where theenergy-momentum tensor has an imperfect-fluid form. This class includesBrans-Dicke models, f(R) gravity, theories with kinetic gravitybraiding and generalised galileons. We employ the intuitive languageof fluids, allowing us to explicitly maintain a dependence on physicaland potentially measurable properties. We demonstrate that hydrodynamicsis not always a valid description for describing cosmological perturbationsin general scalar-field theories and present a consistent alternativethat nonetheless utilises the fluid language.We apply this approach explicitly to a worked example: k-essencenon-minimally coupled to gravity. This is the simplest case whichcaptures the essential new features of these imperfect-fluid models.We demonstrate the generic existence of a new scale separating regimeswhere the fluid is perfect and imperfect. We obtain the equationsfor the evolution of dark-energy density perturbations in both theseregimes. The model also features two other known scales: the Comptonscale related to the breaking of shift symmetry and the Jeans scalewhich we show is determined by the speed of propagation of small scalar-fieldperturbations, i.e. causality, as opposed to the frequently used definitionof the ratio of the pressure and energy-density perturbations.

Observational constraints on kinetic gravity braiding from the integrated Sachs-Wolfe effect

The cross-correlation between the integrated Sachs-Wolfe (ISW) effect and the large scale structure (LSS) is a powerful tool to constrain dark energy and alternative theories of gravity. In this paper, we obtain observational constraints on kinetic gravity braiding from the ISW-LSS cross-correlation. We find that the late-time ISW effect in the kinetic gravity braiding model anti-correlates with large scale structures in a wide range of parameters, which clearly demonstrates how one can distinguish modified gravity theories from the LCDM model using the ISW effect. In addition to the analysis based on a concrete model, we investigate a future prospect of the ISW-LSS cross-correlation by using a phenomenological parameterization of modified gravity models.

The imperfect fluid behind kinetic gravity braiding

We present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding. In particular, this picture applies to the simplest galileons and k-essence. The fluid variables not only have a clear physical meaning but also drastically simplify the analysis of the system. The fluid carries charges corresponding to shifts in field space. This shift-charge current contains a spatial part responsible for diffusion of the charges. Moreover, in the incompressible limit, the equation of motion becomes the standard diffusion equation. The fluid is indeed imperfect because the energy flows neither along the field gradient nor along the shift current. The fluid has zero vorticity and is not dissipative: there is no entropy production, the energy-momentum is exactly conserved, the temperature vanishes and there is no shear viscosity. Still, in an expansion around a perfect fluid one can identify terms which correct the pressure in the manner of bulk viscosity. We close by formulating the non-trivial conditions for the thermodynamic equilibrium of this imperfect fluid.

G-bounce

We present a wide class of models which realise a bounce in a spatially flat Friedmann universe in standard General Relativity. The key ingredient of the theories we consider is a noncanonical, minimally coupled scalar field belonging to the class of theories with Kinetic Gravity Braiding / Galileon-like self-couplings. In these models, the universe smoothly evolves from contraction to expansion, suffering neither from ghosts nor gradient instabilities around the turning point. The end-point of the evolution can be a standard radiation-domination era or an inflationary phase. We formulate necessary restrictions for Lagrangians needed to obtain a healthy bounce and illustrate our results with phase portraits for simple systems including the recently proposed Galilean Genesis scenario.

Large scale structures in the kinetic gravity braiding model that can be unbraided

We study cosmological consequences of a kinetic gravity braiding model, which is proposed as an alternative to the dark energy model.The kinetic braiding model we study is characterized by a parameter n, which corresponds to the original galileon cosmological model for n = 1. We find that the background expansion of the universe of the kinetic braiding model is the same as the Dvali-Turner's model, which reduces to that of the standard cold dark matter model with a cosmologicalconstant (ΛCDM model) for n equal to infinity. We also find that the evolution of the linear cosmological perturbationin the kinetic braiding model reduces to that of the ΛCDM model for n = ∞.Then, we focus our study on the growth history of the linear density perturbation as well as the spherical collapse in the nonlinear regime of the density perturbations, which might be important in order to distinguish between the kinetic braiding model and the ΛCDM model when n is finite. The theoretical prediction for the large scale structure is confronted with the multipole power spectrum of the luminous red galaxy sample of the Sloan Digital Sky survey. We also discuss future prospects of constraining the kinetic braiding model using a future redshift survey like the WFMOS/SuMIRe PFS survey as well as the cluster redshift distribution in the South Pole Telescope survey.

Imperfect dark energy from kinetic gravity braiding

We introduce a large class of scalar-tensor models with interactions containing the second derivatives of the scalar field but not leading to additional degrees of freedom. These models exhibit peculiar features, such as an essential mixing of scalar and tensor kinetic terms, which we have named kinetic braiding. This braiding causes the scalar stress tensor to deviate from the perfect-fluid form. Cosmology in these models possesses a rich phenomenology, even in the limit where the scalar is an exact Goldstone boson. Generically, there are attractor solutions where the scalar monitors the behaviour of external matter. Because of the kinetic braiding, the position of the attractor depends both on the form of the Lagrangian and on the external energy density. The late-time asymptotic of these cosmologies is a de Sitter state. The scalar can exhibit phantom behaviour and is able to cross the phantom divide with neither ghosts nor gradient instabilities. These features provide a new class of models for Dark Energy. As an example, we study in detail a simple one-parameter model. The possible observational signatures of this model include a sizeable Early Dark Energy and a specific equation of state evolving into the final de-Sitter state from a healthy phantom regime.