AN ELASTIC LAGRANGIAN FOR SPACE-TIME

摘要

Space-time is described as a strained four-dimensional elastic continuum. The embedding of a given manifold in a higher dimensional at one allows to extend to four dimensions the usual three-dimensional theory of elastic and plastic deformations. Curvature is then described in terms of strain of the manifold and the strain tensor turns out to be the non-trivial part of the metric tensor. The global behaviour of space-time and its Robertson-Walker symmetry is described as being the consequence of a defect in the manifold. The analogy with the traditional elasticity theory suggests the introduction of an additional term in the Einstein-Hilbert action, representing the potential energy associated with the strained state. The new Lagrangian is then tested on the luminosity curve of type 1a supernovae and the accelerated expansion. The fit turns out to be slightly better than the one obtained by the ΛCDM theory and gives a value for the "bulk modulus" of space-time. The obtained value is consistent with the Newtonian limit of the theory up to the scale of galaxy clusters.