Unified Description of Inflation, Radiation Era, and Cosmic Age in Non-Equilibrium Dynamics: F0 = 7Mpc 2/(2ℓp), R ∝ t 2/3 , and the Mnow–Rnow Relation

We present a unified description of the inflation era, radiation era, and cosmic age in

Non-Equilibrium Dynamics (NED) using the exact repulsive force

F0 =

7

2

Mpc

2

ℓp

,

which is derived from the balance functional H with v1 = v2 = 0, y = z = ℓp/2, r = R,

M1 = M2 = Mp, and D = 1. The equation of motion is

(R(R − ℓp)R˙)

′ = F0.

For R ≫ ℓp, this reduces to

R(t) ≈

(

21Mpc

2

4ℓp

)1/3

t

2/3 = 8.60 × 1014 t

2/3 m.

Using this single power law, we obtain:

• At the end of inflation (t ∼ 10−32 s): R ≈ 4.0 × 10−7 m, giving R/(2ℓp) ≈ 1.2 × 1028

,

which is about 123 times the standard inflation factor e

60 ≈ 1026

.

• At the end of the radiation era (t ∼ 5 × 104 years): R ≈ 1.2 × 1023 m, comparable to

the standard value.

• The cosmic age is

tnow =

√

4ℓpMnowRnow

21Mpc

2

,

which gives the relation

MnowRnow ≈ 1.21 × 1080 kg · m

for tnow = 1.38 × 1010 years.

We present a table of Mnow and Rnow values that reproduce the observed cosmic age. The

results show that NED can reproduce the inflation era, radiation era, and cosmic age with

a single power law R ∝ t

2/3

, without invoking R ∝ t

1/2 or exponential expansion.