On Robertson Walker Solutions in Noncommutative Gauge Gravity

Abstract

Robertson–Walker solution is presented in terms of gauge fields in a de Sitter gauge theory of gravity (Chamseddine and Mukhanov, J High Energy Phys 3:033, 2010). For a vanishing torsion analogous (Zet et al., Int J Mod Phys C15(7):1031, 2004) we present the field strength tensor and the scalar analogous of the Ricci scalar. Following the noncommutative generalization (Chamseddine, Phys Lett B504:33, 2001) for the de Sitter gauge theory of gravity we study how the noncommutativity of space-time deform, through noncommutative parameters, the homogeneous isotropic solution of the commutative gauge theory of gravity. The study is realized with special conceived analytical procedures under GRTensorII for Maple that we designed for the specific quantities of the gauge theory of gravity (Babeti (Pretorian), Rom J Phys 57(5–6):785, 2012). Noncommutative deformations are obtained using a star product deformation of space time and the Seiberg–Witten map to express the deformed fields in terms of undeformed ones and noncommutative parameter. We analyze a space-time (Fabi et al., Phys Rev D78:065037, 2008) and a space-space noncommutativity. The gauge fields, the field strength tensor and the noncommutative analogue of the metric tensor, the noncommutative scalar analog to Ricci scalar are followed until second order in noncommutative parameter.