PI, cosmological expansion and observation

[dbl...@bulldoghome.com]

As I understand things; PI indicates the curvature of local space, the
value 3.14..... is for a flat, euclidian, space.

I assume that: As the cosmos / universe expands it curvature is slowly
decreasing to its current value, which may well NOT be exactly
consistant with the 3.14... above.

Now:
Various 'constants' involve PI in their evaluation, e.g. the Fine
Structure Constant, so beloved by spectroscopists.

Might it no be the case that, in some cases at least, disparities of
observation between the earliest ( >12 Bn years ago) and 'modern'
spectral sources, might be due to a variation in PI, indicating a
change in curvature, over the intervening period.

David N Laine
(engineer, retired)