Parallel Universes in Non-Equilibrium Dynamics: Negative Initial Velocity, Past Contraction, and the Coexistence of Expanding and Contracting Solutions

We show that the exact solution of Non-Equilibrium Dynamics (NED),

2R

3 − 3ℓpR

2 = 3Kt2 + 12ℓ

2

p

v0 t + 4ℓ

3

p

,

admits two branches for any radius R:

t±(R) =

−2ℓ

2

p

v0 ±

√

4ℓ

4

p

v

2

0 −

Kc

3

K

,

where c = 4ℓ

3

p − 2R3 + 3ℓpR2

. For v0 < 0, one branch describes an expanding universe (t+)

and the other a contracting universe (t−). Both branches originate from the same initial

condition R = 2ℓp, R˙ = v0 < 0. We propose the following hypothesis:

Parallel Universe Hypothesis. The expanding and contracting branches are

two parallel universes that coexist, sharing the same initial condition v0 < 0.

The negative initial velocity v0 < 0 implies that the universe was contracting in the

past. We identify v0 as the contraction velocity near R = 2ℓp. The two branches are dual

to each other: t+ increases with R (expansion), while t− decreases with R (contraction).

The return to R = 2ℓp occurs at t = 0 and t = −4ℓ

2

p

v0/K. We present the hypothesis, its

physical interpretation, and its observational consequences.