I'm exploring whether the Friedmann equation, typically used to describe the large-scale structure of the universe, can be reframed as a nested oscillatory system when considered within a quantum cosmological framework.
Recent works, such as those by Matone & Dimakis (2024), suggest that a linearized form of the Friedmann equations reduces to a WKB-like expansion of a quantum cosmological wave equation. This brings up the possibility that the quantum scale factor itself behaves as a standing wave, whose dynamics may recursively couple across temporal and curvature scales.
From the perspective of the Oscillatory Dynamics Transductive-Bridging Theorem (ODTBT), I am particularly interested in modeling this structure as a transductive sine-cosine field, where curvature, time, and mass evolve through nested phase dynamics. The TWIST (Threshold Waveform Interaction for State Transformation) provides a boundary framework for state changes between classical expansion, quantum collapse, and informational decoherence.
Has anyone formally modeled or considered the Friedmann equation as a recursive oscillatory structure—either mathematically, numerically, or ontologically—within quantum gravity, loop quantum cosmology, or field-theoretic formulations?
I'm especially interested in:
- Quantum Friedmann equations expressed through WKB approximations
- Recursive or self-referential curvature waveforms
- Oscillatory modeling of scale factor dynamics (e.g., phase-shifted transitions between geometries)
Any insights, citations, or collaborative leads would be greatly appreciated.
John Surmont
Check following article.
In this wave equation, f(t) is like a scale factor. Separated solution of f(t) has an exponential term as well as Hubble parameter which causes inflation. Solution of single wave equation generates entire table of standard model particles.
- In book: The Wave Equation: An Overview
- Lionel S. Price (Ed.)
- Edition: April 2020
- Chapter: 1
- Periodic quantum gravity and cosmology
- Publisher: Nova Science Publishers, New York.
- https://www.researchgate.net/publication/338621845
Dear Vikram Zaveri
Thank you very much for sharing your paper "Periodic Quantum Gravity and Cosmology". It is a fascinating and highly relevant work.
Your approach of modeling the scale factor f(t) as an emergent oscillatory field, embedding inflationary dynamics within standing wave solutions, resonates deeply with the direction I am pursuing through the Oscillatory Dynamics Transductive-Bridging Theorem (ODTBT). In particular, the structure of f(t) aligns naturally with the idea of nested phase strain (ΔΦ) accumulation and TWIST transitions as boundary conditions governing systemic reorganization.
Please see the following papers.
Preprint From Entropy to Coherence: A Transductive Reframing of Therm...
Preprint Recursive Thermodynamic Structures: Bridging Ψ Phase Transit...
I see strong potential in extending this framework by explicitly modeling the critical saturation points within f(t) evolution as TWIST-induced bifurcations, with RCR and SRI metrics capturing system stability and realignment capacity across recursive scales.
I am currently outlining a short preprint proposing a unified view of Friedmann-like cosmological dynamics as a nested oscillatory architecture under the ODTBT lens. I would be happy to share it once complete and would warmly welcome any future discussion or collaboration around these ideas.
Thank you again for the thoughtful and insightful connection.
Warm regards,
John Surmont
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