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

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.