📝 SummarXiv

Abstract

There have been persistent suggestions, based on several diverse data sets, that the cosmic expansion is not exactly isotropic. It is not easy to develop a coherent theoretical account of such a ``Hubble anisotropy'', for, in standard General Relativity, intuition suggests that it contradicts the predictions of the very successful Inflationary hypothesis. We put this intuition on a firm basis, by proving that if we [a] make use of an Inflationary theory in which Inflation isotropises spatial geometry -- $\,$ this, of course, includes the vast majority of such theories -- $\,$ and if [b] we insist on assuming that spacetime has a strictly metric geometry (one in which the geometry is completely determined by a metric tensor), then indeed all aspects of the ``Hubble field'' must be isotropic. Conversely, should a Hubble anisotropy be confirmed, then either we must contrive to build anisotropy into Inflation (and into the geometry of space) from the outset, or we will have to accept that spacetime geometry is not strictly metric. We argue that the second option, implemented by allowing spacetime torsion to be non-zero, would be by far the most natural way to accommodate such observations. Such theories can reconcile non-isotropic matter distributions with a perfectly isotropic spatial geometry, and thus are able to reconcile Inflation with possibly observed anisotropies. They also allow us to reconcile the absence of anisotropy in one era (say, that of the CMB) with its presence in another.