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

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.