Accelerating cosmologies and the phase structure ofF(R)gravity with Lagrange multiplier constraints: A mimetic approach

Abstract

We study mimetic F (R) gravity with potential and Lagrange multiplier constraint. In the context of these theories, we introduce a reconstruction technique which enables us to realize arbitrary cosmologies, given the Hubble rate and an arbitrarily chosen F (R) gravity. We exemplify our method by realizing cosmologies that are in concordance with current observations (Planck data) and also well known bouncing cosmologies. The attribute of our method is that the F (R) gravity can be arbitrarily chosen, so we can have the appealing features of the mimetic approach combined with the known features of some F (R) gravities, which unify early-time with late-time acceleration. Moreover, we study the existence and the stability of de Sitter points in the context of mimetic F (R) gravity. In the case of unstable de Sitter points, it is demonstrated that graceful exit from inflation occurs. We also study the Einstein frame counterpart theory of the Jordan frame mimetic F (R) gravity, we discuss the general properties of the theory and exemplify our analysis by studying a quite interesting from a phenomenological point of view, model with two scalar fields. We also calculate the observational indices of the two scalar field model, by using the two scalar field formalism. Furthermore, we extensively study the dynamical system that corresponds to the mimetic F (R) gravity, by finding the fixed points and studying their stability. Finally, we modify our reconstruction method to function in the inverse way and thus yielding which F (R) gravity can realize a specific cosmological evolution, given the mimetic potential and the Lagrange multiplier.PACS numbers: 95.35.+d, 98.80.Cq, 95.36.+x

Inflation in Mimetic f(G) Gravity

“…Other equivalent formulations introduce a constraint directly in the gravitational action through a Lagrange multiplier [62] or analyse the lack of invariance under "disformations" for the mimetic case [63]. Some extensions of original mimetic gravity have been discussed, for which the conformal degree of freedom is also isolated in theories as f (R) or f (G) gravities; this provides a complete solution to the dark matter and dark energy problems, as shown in [64][65][66][67][68][69]. As commented on above, some modified gravities have been shown to provide a consistent explanation for dark energy and inflation, such that the mimetic version of such theories may also give a correct description of dark matter (for a review on modified mimetic gravities, see [70]).…”

Thick branes with inner structure in mimetic gravity

“…For more recent work concerning mimetic gravity see Refs. [5][6][7][8][11][12][13][17][18][19][20][21][22][23][24][25][26] or Ref.…”

The Mimetic Born-Infeld Gravity: The Primordial Cosmos and Spherically Symmetric Solutions

“…On the other hand, the recently proposed mimetic formulation is found to be able to generate non-trivial vacuum solutions [25]. When applied to Einstein-Hilbert action, the theory can explain the mysterious dark matter at the cosmological scale [25][26][27][28]. The vacuum, static, and spherically symmetric solutions of mimetic GR were also found in references [29][30][31].…”