2019, no. 3

### 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.

Keywords: supersymmetry, Minkowski superspace $$SM(4,4|\lambda,\mu)$$, Einstein superequations, cosmological constant.

UDC: 53: 52: 514.8

PACS: 11.30.Pb, 12.60.Jv

DOI: 10.17238/issn2226-8812.2019.3.11-19