Inflation Driven by the Galileon Field

Abstract

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 )2φ 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.Inflation in the early universe [1] is now a part of the standard cosmology to solve the horizon and flatness problem as well as to account for the origin of density/curvature fluctuations. It is most commonly driven by a scalar field dubbed as inflaton, and the research on inflationary cosmology has long been focused on the shape of the inflaton potential in the particle physics context. Its underlying physics is now being probed using precision observations of the cosmic microwave background [2] and large scale structure which are sensitive only to the dynamical nature of the inflaton. Reflecting this situation, a number of novel inflation models have been proposed extending the structure of the kinetic function, such as k-inflation [3], ghost condensate [4], and DBI inflation [5].In this Letter, we propose a new class of inflation models, for which the scalar field Lagrangian is of the formwhere K and G are general function of φ and X := −∇ µ φ∇ µ φ/2. The most striking property of this generic Lagrangian (1) is that it gives rise to derivatives no higher than two both in the gravitational-and scalar-field equations. In the simplest form the nonlinear term may be given by G2φ ∝ X2φ, which has recently been discussed in the context of the so-called Galileon field [6,7]. The general form G(φ, X)2φ may be regarded as an extension of the Galileon-type interaction X2φ while maintaining the field equations to be of second-order [8]. So far the phenomenological aspects of the Galileon-type scalar field have been studied mainly in the context of dark energy and modified gravity [9]. In this Letter, we discuss primordial inflation induced by this type of fields. * This paper is the original version of the article published in Phys. Rev. Lett. 105, 231302 (2010) with the title "Inflation driven by the Galileon field."Now let us start investigating our model in detail. Assuming that φ is minimally coupled to gravity, the total action is given byThe energy-momentum tensor T µν derived from the action readsThe equation of motion of the scalar field is equivalent to ∇ ν T ν µ = 0. Here and hereafter we use the notation K X for ∂K/∂X etc.Taking the homogeneous and isotro...

Inflation and primordial non-Gaussianities of “generalized Galileons”

“…In the k-inflation limit, ǫ s = ǫ whereas c 2 s is given by the familiar expression [9]. In G-inflation, our expressions agree with those of [20,33] (on using the background equations of motion), while in the pure Galileon limit they agree with those given [28]. Finally, similar expressions for the general Galileon model can be found in [19].…”

“…Of course the energy fluxes and anisotropic stresses vanish on the background, and (3.6)-(3.13) reduce to the standard expressions [9,14,17,20] in the k-essence (1.3), Galileon (1.4) and G-inflation limits (1.5) respectively. The equation of motion for the scalar field follows from (2.12) (or alternatively as a combination of (3.3) and (3.4)) and is given by…”

“…In the last term in (5.9), we introduced 20) which is proportional to the linear equation of motion for ζ obtained by varying (4.14) with respect to ζ, and…”

“…This prevents the theory from having extra degrees of freedom as well as Ostrogradski instabilities [10], and thus yields a possibly viable higher-order derivative scalar field theory. This general Lagrangian includes, in certain limits, the decoupling limit of DGP model [11] as well as some consistent theories of massive gravity [12,13]; and it also includes the "Galileon" model [14], the conformal Galileon [15], K-mouflage [16], and also "G-" or "KGB" inflation [20,33]. Finally, in a very simple limit (which can be useful to check results) it also reduces to k-inflation.…”

Effective gravitational couplings for cosmological perturbations in the most general scalar–tensor theories with second-order field equations

“…For the covariant Galileon there exists a stable de Sitter solution where X = constant [55] (see also Refs. [56,57] for related works). Since G eff is larger than G before the solution reaches the de Sitter attractor, the growth rate of matter perturbations is larger than that in the ΛCDM model.…”