Upon building up supersymmetric Supergravity in 4D, is it necessary to modify the Einstein's vacuum field equations (apart from adding the Rarita-Schwinger Lagrangian for the gravitino) in order to obtain Supergravity 4D or can it be built up by simply adding the Hilbert-Einstein Lagrangian and the Rarita-Schwinger Lagrangian  ? I guess, dealing with Einstein's nonlinear equations a modification is necessary. If this is the case, that would suggest that such a modification could be checked by experiments. Are such experiments conceivable  ? Can experiments with this aim give an answer on the search of supersymmetry  ? I am aware that most physicists are more interested in Supergravity in 11D, so perhaps my question is rather academic. I can also make the assumption that Supergravity in 11D upon compactification reduces to Supergravity in 4D, then my question is possibly more interesting. But may be this assumption is wrong and my idea is for this reason (or others) not viable. I would appreciate if somebody could explain it. Thank you.

Upon building up supersymmetric Supergravity in 4D, is it necessary to modify the Einstein's vacuum field equations (apart from adding the Rarita-Schwinger Lagrangian for the gravitino) in order to obtain Supergravity 4D or can it be built up by simply adding the Hilbert-Einstein Lagrangian and the Rarita-Schwinger Lagrangian? I guess, dealing with Einstein's nonlinear equations a modification is necessary. If this is the case, that would suggest that such a modification could be checked by experiments. Are such experiments conceivable? Can experiments with this aim give an answer on the search of supersymmetry? I am aware that most physicists are more interested in Supergravity in 11D, so perhaps my question is rather academic. I can also make the assumption that Supergravity in 11D upon compactification reduces to Supergravity in 4D, then my question is possibly more interesting. But may be this assumption is wrong and my idea is for this reason (or others) not viable. I would appreciate if somebody could explain it.

Upon building up supersymmetric Supergravity in 4D, is it necessary to modify the Einstein's vacuum field equations (apart from adding the Rarita-Schwinger Lagrangian for the gravitino) in order to obtain Supergravity 4D or can it be built up by simply adding the Hilbert-Einstein Lagrangian and the Rarita-Schwinger Lagrangian ? I guess, dealing with Einstein's nonlinear equations a modifiication is necessary. If this is the case, that would suggest that such a modification could be checked by experiments. Are such experiments conceivable ? Can experiments with this aim give an answer on the search of supersymmetry ? I am aware that most physicists are more interested in Supergravity in 11D, so perhaps my question is rather academic. I can also make the assumption that Supergravity in 11D upon compactification reduces to Supergravity in 4D, then my question is possibly more interesting. But may be this assumption is wrong and my idea is for this reason (or others) not viable. I would appreciate if somebody could explain it. Thank you.

Upon building up supersymmetric Supergravity in 4D, is it necessary to modify the Einstein's vacuum field equations (apart from adding the Rarita-Schwinger Lagrangian for the gravitino) in order to obtain Supergravity 4D or can it be built up by simply adding the Hilbert-Einstein Lagrangian and the Rarita-Schwinger Lagrangian ? I guess, dealing with Einstein's nonlinear equations a modification is necessary. If this is the case, that would suggest that such a modification could be checked by experiments. Are such experiments conceivable ? Can experiments with this aim give an answer on the search of supersymmetry ? I am aware that most physicists are more interested in Supergravity in 11D, so perhaps my question is rather academic. I can also make the assumption that Supergravity in 11D upon compactification reduces to Supergravity in 4D, then my question is possibly more interesting. But may be this assumption is wrong and my idea is for this reason (or others) not viable. I would appreciate if somebody could explain it. Thank you.