Cyclic Cosmic Expansion in Non-Equilibrium Dynamics: Identification of the Initial Velocity v0 as the Contraction Velocity near R = 2ℓp, Turning Points, Return to R = 2ℓp, Cosmic Age, and Repeated Cycles
Abstract
We identify the initial velocity v0 in the exact solution of Non-Equilibrium Dynamics
(NED) as the contraction velocity near R = 2ℓp, and propose the concrete value
v0 = −2.5 × 10130 m/s .
Using the exact solution
2R
3 − 3ℓpR
2 = 3Kt2 + 12ℓ
2
p
v0 t + 4ℓ
3
p
,
we derive and list the following times and radii:
• The time of the turning point (R˙ = 0):
tR˙ =0 ≈ 9.7 × 109
years .
• The radius at the turning point:
RR˙ =0 ≈ 1.69 × 1026 m .
• The time at which the universe returns to R = 2ℓp:
t
future
bounce ≈ 1.94 × 1010 years .
• The cosmic age with v0 included:
tnow ≈ 2.14 × 1010 years .
The cosmic age with v0 included is closer to the observed value 1.38 × 1010 years than the
v0 = 0 result 6.4×109 years. With constant v0, the universe undergoes at most two bounces
(at t = 0 and t = −4ℓ
2
p
v0/K) and does not repeat periodically. However, if v0 or F0 varies in
time, repeated expansion–contraction cycles are possible. Since the speed of light does not
limit the expansion or contraction of space in NED, the large value of v0 is not physically
excluded.
Related
- Cyclic Cosmic Expansion in Non-Equilibrium Dynamics: Identification of the Initial Velocity v0 as the Contraction Velocity near R = 2ℓp, Past Contraction, Future Turning Points, Cosmic Age, and Repeated Cycles
- Parallel Universes in Non-Equilibrium Dynamics: Negative Initial Velocity, Past Contraction, and the Coexistence of Expanding and Contracting Solutions
- Decelerating Expansion in Non-Equilibrium Dynamics: Mass Growth, Negative Acceleration, and the Falsifiable Prediction q0 = 1/2
- Resolution of the Negative Initial Velocity and Parallel Universe Problems in Non-Equilibrium Dynamics: v0 = 0, Reproduction of Radiation and Inflation Eras, Cosmic Age Discrepancy, and the Universal Prediction q0 = 1/2
- Cosmic History from the Big Bang to the Present in Non-Equilibrium Dynamics: Energy Body, Rapid Expansion, Mass Generation, Deceleration, and Planck Particle Formation
BibTeX
@misc{ueda2026cyclic,
title = {{Cyclic Cosmic Expansion in Non-Equilibrium Dynamics: Identification of the Initial Velocity v0 as the Contraction Velocity near R = 2ℓp, Turning Points, Return to R = 2ℓp, Cosmic Age, and Repeated Cycles}},
author = {takashi ueda},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23475063},
url = {https://zenodo.org/records/23475063},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cyclic Cosmic Expansion in Non-Equilibrium Dynamics: Identification of the Initial Velocity v0 as the Contraction Velocity near R = 2ℓp, Turning Points, Return to R = 2ℓp, Cosmic Age, and Repeated Cycles
AU - takashi ueda
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23475063
UR - https://zenodo.org/records/23475063
AB - We identify the initial velocity v0 in the exact solution of Non-Equilibrium Dynamics (NED) as the contraction velocity near R = 2ℓp, and propose the concrete value v0 = −2.5 × 10130 m/s . Using the exact solution 2R 3 − 3ℓpR 2 = 3Kt2 + 12ℓ 2 p v0 t + 4ℓ 3 p , we derive and list the following times and radii: • The time of the turning point (R˙ = 0): tR˙ =0 ≈ 9.7 × 109 years . • The radius at the turning point: RR˙ =0 ≈ 1.69 × 1026 m . • The time at which the universe returns to R = 2ℓp: t future bounce ≈ 1.94 × 1010 years . • The cosmic age with v0 included: tnow ≈ 2.14 × 1010 years . The cosmic age with v0 included is closer to the observed value 1.38 × 1010 years than the v0 = 0 result 6.4×109 years. With constant v0, the universe undergoes at most two bounces (at t = 0 and t = −4ℓ 2 p v0/K) and does not repeat periodically. However, if v0 or F0 varies in time, repeated expansion–contraction cycles are possible. Since the speed of light does not limit the expansion or contraction of space in NED, the large value of v0 is not physically excluded.
ER -