Stephen Perrenod
2 min readOct 6, 2023

--

The problem is people confuse the mathematical model of an open topology universe that is headed toward infinity with the actual physical current state. Assume we are a flat or open topology and converging toward a de Sitter solution, as is the case with dark energy dominant. It's still finite, the scale factor a will be larger tomorrow than today. One can also have a closed topology as a sphere or 3-d torus that nevertheless is expanding indefinitely driven by the same dark energy (really the negative pressure components of dark energy). Ours is a finite age, and the lack of curvature on large scales puts us at a minimum of ~500 times the volume of our particle horizon volume (a 47 billion light year radius sphere) and likely very much larger given an initial inflation epoch. Inflation forces it to be so large such that we see only a very small patch (we are as an ant on a leaf on a raft in the middle of the Pacific seeing only a flat patch around us) and whether it is spherical or toroidal or saddle-shaped we are unable to discriminate. But it could be a sphere or toroid or Euclidian topology or saddle of finite age, growing size, and yet finite as of today. We are approaching infinity, indefinitely, exponential with a ~ exp (H*t) where H is the Hubble parameter. This asymptotes to around 60 km/s/Mpc (present value 70-ish) as dark energy grows to dominate at 99% and above with the next 5 doublings of scale e.g. 55 or 60 billion years from now, assuming a cosmological constant form of dark energy that does not change. If inflation had of order 60 e-fold expansion (factor ~ 10^[26]) we may never be able to discriminate closed vs. open. As long as dark energy retains an equation of state parameter w < -1/3 (currently -1 to within observational uncertainty) it will dominate, there will be no collapse. One can absolutely be finite and open, or a closed topology, finite today, but with no end to the expansion (a sphere that keeps growing, driven by dark energy as long as it does not decay away).

There do not seem to be any repetitive patterns in the COSMIC MICROWAVE BACKGROUND data that would favor a 3-toroidal shape or a slab model of scale less than the distance to the last scattering surface of the cosmic microwave background. https://www.aanda.org/articles/aa/pdf/2016/10/aa25829-15.pdf

--

--

Stephen Perrenod

supercomputing expert, astrophysicist, technology analyst, orionx.net, author of DarkMatter, DarkEnergy, DarkGravity