Non-vanishing cosmological constant effect in super-Poincare-invariant Universe
In \cite{AminMoc} we defined the Minkowski superspace $SM(4,4\vert λ, μ)$ 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 $SM(4,4\vert λ, μ)$ is supported by purely fermionic stress-energy supertensor with two real parameters $λ$, $μ$, and, moreover, it has non-vanishing cosmological constant $Λ=12/(λ^2 -μ^2)$ defined by these parameters that could mean a new look at the cosmological constant problem.