Supersymetric Taub model, the micro-superspace sector

Abstract

Since there are reasons for expecting supersymmetry in an underlying quantum theory of gravity, one is led to study quantum and classical cosmology with supergravity. In particular, classical solutions corresponding to these models could also be used to generate the quantization of supersymmetric minisuperspaces. In generating these solutions, the solution to the Rarita-Schwinger field in the cosmological background is also obtained. In this paper the supercosmological equations of Einstein-Rarita-Schwinger are solved for the micro-superspace sector of the Taub model, under the assumption Ψμ=e1Ψμ1*e2Ψμ2 and\(g_{\mu v} = \mathop {g_{\mu v} }\limits^0 + \varepsilon _1 \varepsilon _2 \mathop {g_{\mu v} }\limits^2 \). The solution for the parameters of the metric Ω and β are proportional to each other in each order, the zeroth-order and also the second-order terms. The zeroth-order terms correspond to the solution in general relativity and are logarithmic in time, the ɛ1ɛ2 terms have an hyperbolic time-dependence. The Rarita-Schwinger field has the form ∼cos((2/D3)ln |t−t0|) and oscillates an infinite number of times ast→t0. This oscillating behaviour of the solution for Ψμ is not only present when spinor fields are treated in a curved background, but also some cosmological wave functions behave in this manner. This solution is at the same time the supercosmological solution for the microsuperspace sector of the Taub model and also the Rarita-Schwinger field in this background.