Noncommutative accelerated multidimensional universe dominated by quintessence

Abstract

Noncommutative Geometry recently attracted growing interest of cosmologists, mainly after the greatest success of unifying the forces of nature into a single gravitational spectral action in a purely algebraic way, rather than as being an entirely new formalism. In the present work, we discuss a multidimensional Friedmann–Robertson–Walker flat universe in which the perfect fluid has a Gaussian profile in time and depends on a fundamental minimal length \(\sqrt{\theta}\) like ρ=ρ(0)exp (−t2/4θ) for some positive constant ρ(0). This special form is motivated by a more recent noncommutative inflationary cosmological model, which was found to be able to drive the universe through a bounce without the need of any scalar field. Furthermore, we conjecture that the generalized equation of state has the special form p=ωamρ−ρ,(ω,m)∈ℝ where a(t) is the scale factor. It was found that the expansion of the multidimensional universe accelerates in time and is dominated for very large time by quintessence. Many additional consequences are revealed and discussed in some detail.