Non-vanishing cosmological constant effect in super-Poincare-invariant Universe

Abstract

In \cite{AminMoc} we defined the Minkowski superspace $SM(4,4\vert \lambda, \mu)$ as the invariant of the Poincare supergroup of supertransformations, which is a solution of Killing superequations. In the present paper we use formulae of super-Riemannian geometry developed by V.~P. Akulov and D.~V. Volkov \cite{AkVolk} for calculating a superconnection and a supercurvature of Minkowski superspace. We show that the curvature of the Minkowski superspace does not vanish, and the Minkowski supermetric is the solution of the Einstein superequations, so the eight-dimensional curved super-Poincare invariant superuniverse $SM(4,4\vert \lambda, \mu)$ is supported by purely fermionic stress-energy supertensor with two real parameters $\lambda$, $\mu$, and, moreover, it has non-vanishing cosmological constant $\Lambda=12/(\lambda^2 -\mu^2)$ defined by these parameters that could mean a new look at the cosmological constant problem.