We study "classical" bouncing and Genesis models in beyond Horndeski theory. We give an example of spatially flat bouncing solution that is non-singular and stable throughout the whole evolution. We also provide an example of stable geodesically complete Genesis with similar features. The model is arranged in such a way that the scalar field driving the cosmological evolution initially behaves like full-fledged beyond Horndeski, whereas at late times it becomes a massless scalar field minimally coupled to gravity.
We suggest a novel version of a cosmological Genesis model within beyond Horndeski theory. It combines the initial Genesis behavior of Creminelli et al. [1,2] with complete stability property of the previous beyond Horndeski construction [3]. The specific features of the model are that space-time rapidly tends to Minkowski in asymptotic past and that both asymptotic past and future are described by General Relativity (GR). 1 sa.mironov 1@physics.msu.ru 2 rubakov@inr.ac.ru 3 volkova.viktoriya@physics.msu.ru 1 arXiv:1905.06249v1 [hep-th] 15 May 2019Horndeski theories are general scalar-tensor gravities with second order equations of motion. These have been further generalised to theories with higher order equations of motion, dubbed DHOST theories [8,9,10,11,12,13]. The constraint structure of the DHOST theories is such that they propagate only three dynamical degrees of freedom, just like Horndeski theories. Horndeski theories and their generalizations are interesting playground for studying stable NEC/NCC-violating cosmologies (for a review see, e.g., Ref. [14]), and Genesis in particular [15,16,17].One of the main reasons for going beyond Horndeski, at least in the context of the early cosmology, is to construct examples of complete spatially flat, non-singular cosmological scenarios like Genesis. Modulo options that are dangerous from the viewpoint of geodesic completeness and/or strong coupling [18,19,20] (see, however [21]), Horndeski theories are not suitable for this purpose because of inevitable development of gradient or ghost instabilities at some stage of the evolution [18,19,22,23]. However, this no-go theorem does not apply to DHOST theories, as demonstrated in Refs. [24,25,3] for a subclass usually referred to as "beyond Horndeski" (aka GLVP [9]). Indeed, this subclass has been used for constructing non-singular cosmological models of the bouncing Universe and Genesis, which are stable at the linearised level during entire evolution [3,26,27].Previous constructions of complete bouncing and Genesis models in beyond Horndeski theories were limited by overestimating the danger of a phenomenon called γ-crossing (or Θ-crossing). The discussion of this phenomenon is fairly technical, and we postpone it to Section 2. It suffices to point out here that insisting on the absence of γ-crossing prevents one from constructing bounce and Genesis models where linearized gravity agrees with GR both in asymptotic future and in asymptotic past, and, in Genesis case, whose space-time rapidly tends to Minkowski in asymptotic past. An example is a Genesis-like model of Ref. [3] where the scale factor behaves as a(t) ∝ |t| −1/3 as t → −∞.It has been shown, however, that γ-crossing is, in fact, an innocent phenomenon. Originally, this fact has been established in Newtonian gauge [28], and then confirmed in unitary gauge [27]. It opens up a possibility to construct new bouncing and Genesis models 4 . Indeed, an example of fully stable spatially flat bouncing model has been constructed in beyond Horndeski theory [27], whose ...
It is known that Horndeski theories, like many other scalar-tensor gravities, do not support static, spherically symmetric wormholes: they always have either ghosts or gradient instabilities among parity-even linearized perturbations. Here we address the issue of whether or not this no-go theorem is valid in "beyond Horndeski" theories. We derive, in the latter class of theories, the conditions for the absence of ghost and gradient instabilities for non-spherical parity even perturbations propagating in radial direction. We find, in agreement with existing arguments, that the proof of the above no-go theorem does not go through beyond Horndeski. We also obtain conditions ensuring the absence of ghosts and gradient instabilities for all parity odd modes. We give an example of beyond Horndeski Lagrangian which admits a wormhole solution obeying our (incomplete set of) stability conditions. Even though our stability analysis is incomplete, as we do not consider spherically symmetric parity even modes and parity even perturbations propagating in angular directions, as well as "slow" tachyonic instabilities, our findings indicate that beyond Horndeski theories may be viable candidates to support traversable wormholes. 1 sa.mironov 1@physics.msu.ru 2 rubakov@inr.ac.ru 3 volkova.viktoriya@physics.msu.ru 1 arXiv:1812.07022v2 [hep-th] 5 Jun 2019 Bπ XK Xwith
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