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
Abstract
We show that setting the initial velocity to zero, v0 = 0, resolves two problems in Non-
Equilibrium Dynamics (NED): the negative initial velocity problem and the parallel universe
problem. With v0 = 0, the exact solution reduces to
2R
3 − 3ℓpR
2 = 3Kt2 + 4ℓ
3
p
,
which has only one branch and one bounce at t = 0. This eliminates the need for v0 <
0 and the associated parallel universe interpretation. We then show that this equation
may reproduce the radiation and inflation eras without invoking R ∝ t
1/2 or exponential
expansion:
• At the end of inflation (t ∼ 10−32 s), R ≈ 1.79 × 10−7 m, giving R/(2ℓp) ≈ 5.5 × 1027
,
comparable to or larger than the standard inflation factor e
60 ≈ 1026
.
• At the end of the radiation era (t ∼ 5 × 104 years), R ≈ 5.2 × 1022 m, comparable to
the standard value.
We discuss the cosmic age discrepancy: the NED prediction with v0 = 0 is tnow ≈ 6.74 ×
109 years, whereas the standard Friedman cosmology gives tnow ≈ 1.38 × 1010 years. We
propose that this discrepancy may arise from the different theoretical frameworks: NED
predicts decelerating expansion and a finite asymptotic future, while Friedman cosmology
with dark energy predicts accelerating expansion and an infinite future. Finally, we derive
the deceleration parameter
q0 =
1
2
,
which is independent of v0. This is a universal prediction of NED, in direct conflict with
the observed value q0 ≈ −0.55. The prediction q0 = +1/2 provides a decisive falsifiable test
of NED.
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BibTeX
@misc{ueda2026resolution,
title = {{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}},
author = {takashi ueda},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23528795},
url = {https://zenodo.org/records/23528795},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - 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
AU - takashi ueda
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23528795
UR - https://zenodo.org/records/23528795
AB - We show that setting the initial velocity to zero, v0 = 0, resolves two problems in Non- Equilibrium Dynamics (NED): the negative initial velocity problem and the parallel universe problem. With v0 = 0, the exact solution reduces to 2R 3 − 3ℓpR 2 = 3Kt2 + 4ℓ 3 p , which has only one branch and one bounce at t = 0. This eliminates the need for v0 < 0 and the associated parallel universe interpretation. We then show that this equation may reproduce the radiation and inflation eras without invoking R ∝ t 1/2 or exponential expansion: • At the end of inflation (t ∼ 10−32 s), R ≈ 1.79 × 10−7 m, giving R/(2ℓp) ≈ 5.5 × 1027 , comparable to or larger than the standard inflation factor e 60 ≈ 1026 . • At the end of the radiation era (t ∼ 5 × 104 years), R ≈ 5.2 × 1022 m, comparable to the standard value. We discuss the cosmic age discrepancy: the NED prediction with v0 = 0 is tnow ≈ 6.74 × 109 years, whereas the standard Friedman cosmology gives tnow ≈ 1.38 × 1010 years. We propose that this discrepancy may arise from the different theoretical frameworks: NED predicts decelerating expansion and a finite asymptotic future, while Friedman cosmology with dark energy predicts accelerating expansion and an infinite future. Finally, we derive the deceleration parameter q0 = 1 2 , which is independent of v0. This is a universal prediction of NED, in direct conflict with the observed value q0 ≈ −0.55. The prediction q0 = +1/2 provides a decisive falsifiable test of NED.
ER -