Non-commutative multi-dimensional cosmology

Abstract

A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these problems find natural solutions in a universe described by an increasing time parameter. PACS: 04.50.+h, 02.40.Gh, 11.25.Mj IntroductionNon-commutativity between space-time coordinates, first introduced in [1], has been attracting considerable attention in the recent past [2,3,4]. This renewed interest has its roots in the development of string and M-theories, [5,6]. However, in all fairness, investigation of non-commutative theories may also be justified in its own right because of the interesting predictions regarding, for example, the IR/UV mixing and non-locality [7], Lorentz violation [8] and new physics at very short distance scales [9,10,11]. The impact of non-commutativity in cosmology has also been considerable and has been addressed in different works [12]. Hopefully, non-commutative cosmology would lead us to the formulation of semiclassical approximations of quantum gravity and tackles the cosmological constant problem [13]. Of particular interest would be the application of non-commutativity to multi-dimensional cosmology.Multi-dimensional spaces were introduced for the geometric unification of interactions by Kaluza and Klein and have since been a source of inspiration for numerous authors [14]. Also, the introduction of extra dimensions suggests possible solutions to some of the important problems that cosmology has been facing, namely, the mass hierarchy and cosmological constant problem, to name but a few. That said, it should also be mentioned that the question of compactification and the stabilization of the extra dimensions is a challenge one cannot avoid. In this paper, we have considered a multidimensional cosmology with a cosmological constant and introduced non-commutativity between the scale factors of our ordinary space and the extra dimensions. We have shown that the classical cosmology of this model can be solved exactly. These solutions offer an explanation for the cosmological constant problem and show how the extra dimensions can be compactified. *

Cosmological and solar system consequences off(R,T)gravity models

“…, we obtain 33) and by applying the conservation of the energy-momentum tensor and equation (2.33), for any perfect fluid, we geṫ…”

“…These models have 33) where c R and c T are two coupling constants. The potential Ψ, for these models, is 34) which, by comparing it with the Newtonian potential, we reach at the following result…”

“…In addition, there are higher-order gravities including the special case f (R) gravity [13][14][15][16][17][18][19], the induced gravity [20,21], the scalar-tensor theories with the special case of Brans-Dicke theory [22][23][24][25][26][27][28], higher-dimensional theories, e.g., the Kaluza-Klein theories [29] and the braneworld scenarios [30]. Also, there are theories that introduce some modifications in the matter component [31,32] or change the geometrical structure, e.g., the non-commutative theories [33][34][35][36][37][38].…”

Stabilization of Internal Space in Noncommutative Multidimensional Cosmology

“…These commutation relations are the same as those in (18). Thus, for introducing noncommutativity, it is more convenient to work with Poisson brackets (20) than the α-star deformed Poisson brackets (18). In the noncommutative case we only assume that the scale factor associated with the internal dimensions does not commute with the matter field and keep other commutation relations unchanged as in the previous section.…”

“…Noncommutative cosmology [17,18] is an example of such an approach and has benefited from it greatly in that it can offer a view of the semiclassical approximation of quantum gravity and may be used in tackling the cosmological constant problem [19]. Also, this kind of noncommutativity is used in [20] to address the stabilization of internal dimensions and the cosmological constant problem.…”