Author:
Awwad Yassir,Prokopec Tomislav
Abstract
Abstract
The large scale geometry of the late Universe can be decomposed
as ℝ × Σ3, where ℝ
stands for cosmic time and Σ3 is the three dimensional
spatial manifold.
We conjecture that the geometry of the Universe's spatial
section Σ3
conforms with the Thurston-Perelman theorem,
according to which the geometry of Σ3 is either one of the
eight geometries from the Thurston geometrization conjecture,
or a combination of Thurston geometries smoothly sewn together.
We assume that topology of individual geometries plays
no observational role, i.e. the size of individual
geometries is much larger than the Hubble radius today.
We investigate the dynamics of each of the individual
geometries by making use of the simplifying assumption
that our local Hubble patch consists of only one such geometry,
which is approximately homogeneous on very large scales,
but spatial isotropy is generally violated.
Spatial anisotropies grow in time in decelerating universes, but they
decay in accelerating universes. The thus-created anisotropy problem can be solved
by a period of primordial inflation, akin to how the flatness problem is solved.
Therefore, as regards Universe's large scale geometry,
any of the Thurston's geometries should be considered on a par with
Friedmann's geometries.
We consider two observational methods that can be used to test our conjecture: one based on
luminosity distance and one on angular diameter
distance measurements,
but leave for the future their detailed forecasting implementations.