Cosmological implications of a shift symmetric Galileon field

Abstract

A ghost-free metric formulation of the recently proposed covariant Galileon model [31] which retains the internal shift symmetry has been constructed. This presents a new result because the covariant Galileon models introduced so far in the literature lacks the full Galileon symmetry. We demonstrate that the same general procedure is applicable to all the Galileon interaction terms and the resulting ghost-free Galileon action respecting internal shift symmetry cannot predict the late time acceleration of the universe. However, weakly breaking the shift symmetry in the covariant Galileon Lagrangian, allows us to include an appropriate potential term which can explain late time acceleration, in accordance with recent findings in the literature.

Reconstruction of k-essence inflation in Horndeski gravity

“…where we used the condition (44). We should note that whenα =β = 0 we deal with chaotic inflation from canonical scalar field and the reconstruction of the model under the condition (44) leads to the quadratic potential V (φ) = φ 2 /(4c 0 ), while from our Ansatz (30) we easily recover (1 + p/ρ) = φ ′2 /3 = (1/3N ), in agreement with Refs.…”

“…For other works about k-essence and Horndeski gravity see also Ref. [42,43,44] and Ref. [45] for k-essence in the braneworld scenario.…”

Reconstruction of inflation from scalar field non-minimally coupled with the Gauss-Bonnet term

“…By starting from this equations with the Ansatz in (26)- (27), we can find the on-shell potential and the Hubble parameter for different kinds of model. As a consequence, we can derive the spectral index (24) and the tensor-to-scalar ratio (25) in order to study the viable conditions of the theory. Finally, an explicit reconstruction for the coupling function ξ(φ) and for the Lagrangian of the field is possible by inverting the relation (26).…”

“…and we see that, thanks to the non-minimal coupling with the Gauss-Bonnet, it is smaller than one, even if it is extremelly close to one when 1 ≪ N . Now we can derive the spectral index (24) and the tensor-to-scalar ratio (25),…”

Late-time acceleration driven by shift-symmetric Galileon in the presence of torsion

“…Taking a cue from the above, the powerful method of localizing both relativistic symmetry [21,22] as well as non-relativistic symmetry [23,24] was used to obtain the Galileon Lagrangian which respects the full shift symmetry locally [25]. Subsequently, a metric formulation was developed in [26]. Interestingly, the covariant Galileon models formulated so far were obtained in the context of Riemannian manifold and do not involve spacetime torsion.…”