Imperfect dark energy from kinetic gravity braiding

Abstract

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.1 Similar models were introduced before in another context [17,18]. Also, recently, such models have been extended to vectors and p-forms [19].2 Generic choices of K, G give equations of motion with explicit dependence on the first derivative ∇µφ.Hence, the Lagrangians (1.1) do not have the Galilean symmetry which characterizes the interactions of [7] and [8].We will therefore study the equation of state of the fluid representing the excess over the attractor, with energy density J = − * . Assuming that one can invert J(X, ρ ext ) to find X(J, ρ ext ), we can simply expand the total energy density (J, ρ ext ) =φ(J, ρ ext )J − K(X(J, ρ ext )) for small J to find, at lowest order in Notice that the factor in front of J is a function of ρ ext , implying that J does not dilute like dust as could have been naively expected and as is seen in the case of ghost condensates.

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].…”

“…As observed in [33,34], T (1) µν contains second derivatives (but not higher, by construction) of φ, and as a result Einstein's equations (2.6) (as well as the scalar field equations of motion) contain second derivatives of both the metric g µν and of φ as soon as L (1) is present. There is no conformal transformation that can diagonalise the system of equations, which remain coupled: this phenomenon has been dubbed kinetic braiding [33]. The expressions for T (2,3) µν are rather more involved, again containing second derivatives of φ, but they now also contain second derivatives of g µν .…”

“…For T (2,3) µν the situation is yet more complicated, and from (2.9) and (B.1) they both lead to non-vanishing anisotropic stress π (2,3) µν as well as energy flow. The consequences of this non-perfect fluid picture have been discussed in [33,34,39]. The equation of motion for the scalar field φ is given by…”

“…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.…”

“…Primordial non-Gaussianities [26][27][28][29][30][31] have been studied in G-inflation limit, and it was shown [29] that to leading order in slow-roll parameters there are no new momentum shapes for the bispectrum (beyond the standard ones of k-inflation). Despite that, a distinctive feature of G-inflation is that, though it has only a single scalar field, its energy momentum tensor takes the form of an imperfect fluid [33,34] (contrary to the k-essence models). This fact sheds some light on the understanding of imperfect fluids in cosmology, and furthermore can lead to violations of the null enery condition thus opening up a whole range of possibly exotic phenomena [35].…”