Hořava–Lifshitz cosmological models with noncommutative phase space variables

Abstract

In this work, we will analyze a noncommutative (NC) version of the Friedmann-Robert-Walker cosmological models within the gravitational Hořava-Lifshitz theory. The matter content of the models is described by a perfect fluid and the constant curvature of the spatial sections may be positive, negative or zero. In order to obtain this theory, we will use the Faddeev-Jackiw symplectic formalism to introduce, naturally, space-time noncommutativity inside the equations that provide the dynamics of the theory. We will investigate, in details, the classical field equations of a particular version of the NC models. The equations will be modified, with respect to the commutative ones, by the introduction of a NC parameter. We will demonstrate that various NC models, with different types of matter and spatial constant curvatures, show several interesting and new results relative to the corresponding commutative ones. We will pay special attention to some cases, where the NC model predicts a scale factor accelerated expansion, which may describe the current state of our Universe.

Extended phase-space analysis of the Hořava–Lifshitz cosmology

“…In [66] it is analyzed the electromagnetic-gravity interaction in a pure HL framework formulated in 4+1 dimensions and it is performed a Kaluza-Klein reduction to 3+1 dimensions. In [67] it was studied a noncommutative version of the Friedmann-Robertson-Walker (FRW) cosmological models within the gravitational HL theory. The matter content of the models is described by a perfect fluid and the constant curvature of the spatial sections may be positive, negative or zero.…”

Global dynamics of the Hořava–Lifshitz cosmological system

“…Moreover, all points on the w-axis, i.e. u = 0, are singularities of system (13). Thus the local phase portraits of system ( 12) is shown in Figure 4(c), and then the local phase portrait at the origins of U 2 and V 2 for y 2 = 0 can be found in Figure 4(d).…”

“…In recent years Lepe and Saavedra [12] discussed some aspects of Hořava-Lifshitz cosmology with emphasis on some cosmological solutions that exist in general relativity (Friedmann cosmology), especially in the flat case that dust-driven evolution is the same in both cosmological theories. For Hořava-Lifshitz theory of gravitation Abreu et al [13] explored a non-commutative version of the Friedmann-Robertson-Walker cosmological model, in which material content is described by ideal fluids, and the constant curvature of the spatial sections can be positive, negative or zero. Under the background spacetime of Friedmann-Lemaître-Robertson-Walker, Paliathanasis and Leon [14] divided the integrability of Hořava-Lifshitz scalar field into four cases according to the existence of cosmological constant term and the disappearance of space curvature.…”

Global dynamics of the Horava-Lifshitz cosmology in the presence of non-zero cosmological constant in a flat space

“…A decade ago Hořava [1] brought forward a new theory on spacetime asymmetric gravitation, called Hořava-Lifshitz gravity, together with the scalar field theory of Lifshitz. This theory's applications in cosmology, dark energy, and black hole have stimulated many studies (See review papers [20], [21] or regular literature [2]- [19]).…”