SPACE, TIME AND FUNDAMENTAL INTERACTIONS

NON-VANISHING COSMOLOGICAL CONSTANT EFFECT IN SUPER-POINCARE-INVARIANT UNIVERSE

Aminova A.V., Lyulinsky M.Kh.

In [1] we defined the Minkowski superspace \(SM(4,4|\lambda,\mu)\) 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 [2] 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 \(SM(4,4|\lambda,\mu)\) is supported by purely fermionic stress-energy supertensor with two free 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.