  A conjectured finite M-theory based on eleven-dimensional supergravity
formulated in a superspace with a non-anticommutative <>-product of field
operators is proposed. Supermembranes are incorporated in the superspace
<>-product formalism. When the deformed supersymmetry invariant action of
eleven-dimensional supergravity theory is expanded about the standard
supersymmetry invariant action, the spontaneously compactified M-theory can
yield a four-dimensional de Sitter spacetime inflationary solution with dark
energy described by the four-form F-fields. A fit to the present cosmological
data for an accelerating universe is obtained from matter fields describing the
dominant dark matter and the four-form F-field dark energy. Chiral fermions are
obtained from the M-theory by allowing singularities in the compact internal
seven-dimensional space. The possibility of obtaining a realistic M-theory
containing the standard model is discussed.
