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
Abstract
We identify the initial velocity v0 in the exact solution of Non-Equilibrium Dynamics
(NED) as the contraction velocity near R = 2ℓp, and we propose the concrete value
v0 = −2.5 × 10130 m/s .
This identification implies that the universe was contracting in the past. Using the exact
solution
2R
3 − 3ℓpR
2 = 3Kt2 + 12ℓ
2
p
v0 t + 4ℓ
3
p
,
we derive the time at which the expansion velocity vanishes,
tR˙ =0 = −
2ℓ
2
p
v0
K
≈ 9.7 × 109
years,
the corresponding radius,
RR˙ =0 ≈ 1.69 × 1026 m,
and the time required for the universe to return to R = 2ℓp,
t
future
bounce = −
4ℓ
2
p
v0
K
≈ 1.94 × 1010 years.
We also compute the cosmic age with v0 included:
tnow =
−2ℓ
2
p
v0 +
√
4ℓ
4
p
v
2
0 −
Kc
3
K
,
where c = 4ℓ
3
p − 2R3
now + 3ℓpR2
now. For v0 = −2.5 × 10130 m/s, we obtain
tnow ≈ 2.14 × 1010 years ,
which is closer to the observed value 1.38 × 1010 years than the v0 = 0 result 6.4 × 109
years. With constant v0, the equation admits only two times at which R = 2ℓp: t = 0
and t = −4ℓ
2
p
v0/K. This means that the universe undergoes at most two bounces and does
not repeat periodically. However, if v0 (or F0) varies in time, the universe can undergo
repeated expansion–contraction cycles. 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, Turning Points, Return to R = 2ℓp, 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, Past Contraction, Future Turning Points, Cosmic Age, and Repeated Cycles}},
author = {takashi ueda},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23474906},
url = {https://zenodo.org/records/23474906},
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, Past Contraction, Future Turning Points, Cosmic Age, and Repeated Cycles
AU - takashi ueda
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23474906
UR - https://zenodo.org/records/23474906
AB - We identify the initial velocity v0 in the exact solution of Non-Equilibrium Dynamics (NED) as the contraction velocity near R = 2ℓp, and we propose the concrete value v0 = −2.5 × 10130 m/s . This identification implies that the universe was contracting in the past. Using the exact solution 2R 3 − 3ℓpR 2 = 3Kt2 + 12ℓ 2 p v0 t + 4ℓ 3 p , we derive the time at which the expansion velocity vanishes, tR˙ =0 = − 2ℓ 2 p v0 K ≈ 9.7 × 109 years, the corresponding radius, RR˙ =0 ≈ 1.69 × 1026 m, and the time required for the universe to return to R = 2ℓp, t future bounce = − 4ℓ 2 p v0 K ≈ 1.94 × 1010 years. We also compute the cosmic age with v0 included: tnow = −2ℓ 2 p v0 + √ 4ℓ 4 p v 2 0 − Kc 3 K , where c = 4ℓ 3 p − 2R3 now + 3ℓpR2 now. For v0 = −2.5 × 10130 m/s, we obtain tnow ≈ 2.14 × 1010 years , which is closer to the observed value 1.38 × 1010 years than the v0 = 0 result 6.4 × 109 years. With constant v0, the equation admits only two times at which R = 2ℓp: t = 0 and t = −4ℓ 2 p v0/K. This means that the universe undergoes at most two bounces and does not repeat periodically. However, if v0 (or F0) varies in time, the universe can undergo repeated expansion–contraction cycles. 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 -