A maximally symmetric space with torsion

Constraining torsion in maximally symmetric (sub)spaces

“…Moreover, T ABC is a constant since it cannot depend on any of the maximally symmetric bulk coordinates. This is of course a known result, which has been demonstrated in different contexts previously [40,41,42]. We, in this section, have taken the route of [41] in which the authors have made a comprehensive study of maximal symmetry in presence of a completely antisymmetric torsion, i.e.…”

“…What are the constraints otherwise, under the demand that torsion is form-invariant in maximally symmetric spaces? A study of literature reveals that one can in principle resort to two different schemes (from contrasting viewpoints) in order to access the underlying aspects of space-time symmetries (and in particular, of maximal symmetry) in presence of torsion [29,38,39,40,41,42]:…”

“…As such, from the phenomenological point of view the scheme I is generally favoured in spite of the fact that one has to comply with the lack of appropriate covariant generalization of the equations of relevance (the Killing equation inclusive) in presence of torsion [17,18,29,38,39]. Scheme II, on the other hand, gives a clearer geometric picture and wider applicability, but at the same time seems a bit too idealistic as it requires stringent conditions on the torsion tensor for apparently no reason other than to define maximal symmetry in the exact analogy of that in GR * [40,41,42]. Of course, the ambiguity in choosing which * Moreover, a strict enforcement of both the minimal coupling prescription and the principle of general covariance is implied in the scheme II.…”

Torsion, an alternative to dark matter?

“…These results rule out the hypothesis of torsion to replace dark energy. Let us mention the analysis of reference [20], which contains a similar analysis using the parity-odd torsion [21]. They find that this part of torsion can mimic a cosmological constant.…”

Dark matter and torsion

“…As the Weyssenhoff spinning fluid should probably not be a viable model, for whatever reason, we follow another route, having been founded by Tsamparlis ([84,85], see also [86]), and put further in [87][88][89][90][91][92][93][94][95][96] under various different aspects. Since all these works refer to the EC theory, we must adapt the setting to the present case.…”