Absolute parallelism, modified gravity, and suppression of gravitational short waves

Abstract

There is a unique variant of Absolute Parallelism, which is very simple as it has no free parameters: nothing (nor D=5) can be changed if to keep the theory safe from emerging singularities of solutions. On the contrary, eternal solutions of this theory, due to the linear instability of the trivial solution, should be of great complexity which can in some scenarios (with a set of slowly varying parameters of solutions) provide a few phenomenological models including a modified (better to say, new or another) gravity and an expanding-shell cosmology (the longitudinal polarization gives the anti-Milne model). The former looks (mostly) like a variant of tensor-Ricci-squared gravity on a brane of a huge scale L along the extra-dimension. The correction to Newton's law of gravity, which depends in this theory on two parameters (bi-Laplace equation) and behaves as 1/r on large scales, r>L (kpc>L>pc), can start from zero (the Rindler term vanishes) if a constraint is imposed on these parameters. On further consideration, one can conclude that generation of gravitational `short' waves, \lambda<L, is inhibited in this new gravity.