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We study the variational principle on a Hilbert-Einstein action in anextended geometry with torsion taking into account non-trivial boundaryconditions. We obtain an effective energy-momentum tensor that has its sourcein the torsion, which represents the matter geometrically induced. We exploreabout the existence of magnetic monopoles and gravitational waves in thistorsional geometry. We conclude that the boundary terms can be identified aspossible sources for the cosmological constant and torsion as the source ofmagnetic monopoles. We examine an example in which gravitational waves areproduced during a de Sitter inflationary expansion of the universe.

Gravitational waves and magnetic monopoles during inflation with Weitzenb\"ock torsion