Dear Zhang (or Rone),
I found your ideas on curvature continuity, redshift/blueshift, and the holistic dynamics of spacetime very interesting. I’m working on a related line of thought through a different framework.
My model is based on a 4-dimensional spherical surface expanding at the speed of light (r = ct). I assume that the Cosmic Microwave Background (CMB) is the continuous field responsible for maintaining the global shape of the universe. Matter, on the other hand, is treated as a discontinuity and does not contribute to the preservation of the 4D geometry.
This idea is developed in my post here:
https://forums.fqxi.org/d/961-alternative-models-of-cosmology/385
The theme of shape preservation is, in my opinion, fundamental. Mathematically, I was able to reach consistent results by focusing solely on the CMB and neglecting matter. However, I eventually had to introduce an additional conjecture: that the expansion of the universe is governed by the CMB and that matter is dragged along with it.
This conjecture is a limitation, but it led to some results I consider meaningful, even if not confirmed. Among them:
• A derivation of special relativity from a geometric principle (without assuming it).
• A reinterpretation of redshift in terms of 4D expansion.
• A consistent energy balance in radiation consistent with blackbody evolution.
• A possible link between gravity and entropy through equilibrium in the expanding hypersurface.
I also find your approach equally valid and would be happy to exchange ideas.
I expect a common objection might be that matter’s mass-energy today dominates over the CMB, so it cannot be neglected. My reply is that, in my model, it is not the total energy content but the geometric continuity that preserves the 4d-sphere’s shape. The CMB, being a continuous and isotropic field, defines a coherent equilibrium surface, while matter, being discontinuous and localized, cannot maintain global curvature but only causes local deformations.
Best regards,
Claudio Marchesan