Dynamical systems analysis of the cubic galileon beyond the exponential potential and the cosmological analogue of the vDVZ discontinuity

Abstract

In this paper we generalize the dynamical systems analysis of the cubic galileon model previously investigated in [1] by including self-interaction potentials beyond the exponential one. It will be shown that, consistently with the results of [1], the cubic self-interaction of the galileon vacuum appreciably modifies the late-time cosmic dynamics by the existence of a phantom-like attractor (among other super-accelerated solutions that do not modify in any appreciable way the late-time dynamics and hence are not of interest in the present investigation). In contrast, in the presence of background matter the late-time cosmic dynamics remains practically the same as in the standard quintessence scenario. This means that we can not recover the cubic galileon vacuum continuously from the more general cubic quintessence with background matter, by setting to zero the matter energy density (and the pressure). This happens to be a kind of cosmological vDVZ discontinuity that can be evaded by means of the cosmological version of the Vainshtein screening mechanism. PACS numbers: 02.30.Hq, 04.20.Ha, 04.50.Kd, 05.45.-a, 98.80.-k I. INTRODUCTIONAccording to the increasing set of independent cosmological observations [2-8] the universe today is experiencing an accelerated expansion era. An unknown component dubbed as dark energy has been proposed to explain this recent acceleration in the context of the general relativity. The cosmological constant with equation of state ω = −1, is the simplest and the most accurate candidate according the observations [9]. However, it is plagued by serious theoretical issues such as the vacuum energy problem, the cosmic coincidence problem, the particle nature of dark matter, the validity of general relativity on large scales, and the age problem [10,11]. Since the observations allow the variation in time of the dark energy component, another possibility is to consider the existence of light scalar fields known as "quintessence" [12].Modified gravity represents an alternative approach for addressing the unusual cosmological dynamics at large scales. It is based on the modification of general relativity. We can observe two main streams in this context: introducing a Lagrangian built up of a Ricci, Riemann or another metric tensors as in the case of f (R, G) theories [13] and Brans-Dicke (BD) theories [14], or assuming the existence of additional dimensions that realize cosmic acceleration through the leakage of gravity into the extra-space at cosmological scales as in the Dvali-Gabadadze-Porrati (DGP) braneworld [15,16]. This latter model, however, is plagued by ghost instabilities that cast doubts on its validity. 1 Inspired by the DGP model, in [17] the authors proposed an infrared modification of gravity which is a generalization of the 4D effective theory in the DGP braneworld. The theory is invariant under the Galilean shift symmetry ∂ µ φ → ∂ µ φ + b µ in the Minkowski space-time, which keeps the equations of motion at second order. The scalar field that respects the Galilean symmetry is...

Selected topics in scalar–tensor theories and beyond

“…Here we summarize the result of Ref. 573. The solutions that arise only in the vacuum case, but that are not found when background matter is considered, are the following:…”

“…482 for the exponential potential, and then in Ref. 573 for potentials beyond the exponential one. It was shown that a kind of vDVZ discontinuity arises: It is not possible to recover all of the vacuum solutions of the theory by going to the continuous limit when the matter density vanishes.…”

“…It was shown that a kind of vDVZ discontinuity arises: It is not possible to recover all of the vacuum solutions of the theory by going to the continuous limit when the matter density vanishes. It was then conjectured that the non-linear (cubic derivative) interactions of the Galileon with the background matter "screens" the relevant vacuum solutions, 573 which seems like another cosmological version of the Vainshtein mechanism. Below we shall briefly discuss on the above mentioned cosmological realizations of this screening mechanism.…”

“…482 for a particular choice of the self-interaction potential: the exponential potential, while in Ref. 573 it was shown that the above kind of cosmological vDVZ discontinuity, and its resolution through the cosmological version of the Vainshtein screening effect, is independent of the specific form of the potential V . Here we summarize the result of Ref.…”

An issue with the classification of the scalar–tensor theories of gravity

“…where the constant σ is the self-coupling parameter, we get the cubic galileon action in the Einstein's frame (EF) [83,84]:…”