Cosmological predictions in temporal physics.

Cosmological predictions in temporal physics.

 

Cosmic Microwave Background (CMB) Anisotropies

Predicted CMB Temperature Fluctuations

 

In my model, the spacetime metric is influenced by temporal dynamics. The temperature fluctuations (ΔT) in the CMB might be affected by these dynamics.

 

General Form:

ΔT(n̂) = ΔT₀(n̂) × (1 + α_CMB ⋅ τ(t))

 

Where:

 

ΔT(n̂) is the temperature fluctuation at direction n̂.

ΔT₀(n̂) is the baseline temperature fluctuation from standard cosmological models.

α_CMB is a model-specific coefficient.

τ(t) is the gravitational field effect, given by τ(t) = t².

Equation:

ΔT(n̂) = ΔT₀(n̂) × (1 + α_CMB ⋅ t²)

 

Galaxy Distribution

Galaxy Density Field

 

The density of galaxies (ρ_g(x, y, z)) might be modified by the effects of temporal dynamics on space expansion.

 

General Form:

ρ_g(x, y, z) = ρ_g₀(x, y, z) × (1 + α_gal ⋅ τ(t))

 

Where:

 

ρ_g(x, y, z) is the galaxy density at position (x, y, z).

ρ_g₀(x, y, z) is the baseline galaxy density from standard models.

α_gal is a model-specific coefficient.

Equation:

ρ_g(x, y, z) = ρ_g₀(x, y, z) × (1 + α_gal ⋅ t²)

 

Cosmic Expansion Rate

Expansion Rate

 

The rate of expansion (H(t)) can be influenced by the temporal waves, which might affect what is traditionally attributed to dark energy.

 

General Form:

H(t) = H₀ × (1 + α_exp ⋅ τ(t))

 

Where:

 

H(t) is the Hubble parameter at time t.

H₀ is the Hubble constant.

α_exp is a model-specific coefficient.

Equation:

H(t) = H₀ × (1 + α_exp ⋅ t²)

 

Summary of Approach

For CMB Fluctuations:

 

Observed Data: Extract ΔT(n̂) from CMB data.

Model Comparison: Compare with ΔT₀(n̂) × (1 + α_CMB ⋅ t²).

For Galaxy Distribution:

 

Observed Data: Obtain ρ_g(x, y, z) from galaxy surveys.

Model Comparison: Compare with ρ_g₀(x, y, z) × (1 + α_gal ⋅ t²).

For Cosmic Expansion Rate:

 

Observed Data: Measure H(t) from supernovae and other cosmic observations.

Model Comparison: Compare with H₀ × (1 + α_exp ⋅ t²).

 

 

let us consider the Hubble constant:

H(t_now) = H₀ × (1 + α_exp × t_now²)

70 km/s/Mpc ≈ 67 km/s/Mpc × (1 + α_exp × (13.8 billion years)²)

This would allow us to solve for α_exp and see if it is a reasonable value.

 

Given Data:

 

Current Hubble constant, H(t_now) = 70 km/s/Mpc

Standard Hubble constant, H₀ = 67 km/s/Mpc

Age of the universe, t_now = 13.8 billion years

Equation:

H(t_now) = H₀ × (1 + α_exp × t_now²)

 

Step-by-Step Solution:

 

Convert Age of Universe to the Same Units:

The age of the universe in seconds:

t_now = 13.8 billion years × 3.154 × 10¹⁶ s/year

t_now ≈ 4.35 × 10¹⁷ s

 

Plug in the Known Values:

70 = 67 × (1 + α_exp × (4.35 × 10¹⁷)²)

 

Solve for α_exp:

70 / 67 = 1 + α_exp × (4.35 × 10¹⁷)²

 

(70 / 67) - 1 = α_exp × (4.35 × 10¹⁷)²

 

3 / 67 = α_exp × (4.35 × 10¹⁷)²

 

α_exp = (3 / 67) / (4.35 × 10¹⁷)²

 

Calculate α_exp:

(4.35 × 10¹⁷)² = 1.89225 × 10³⁵

 

α_exp = (3 / 67) / 1.89225 × 10³⁵

 

α_exp ≈ 0.0448 / 1.89225 × 10³⁵

 

α_exp ≈ 2.37 × 10⁻³⁷ (per second squared)

 

The calculated value of α_exp ≈ 2.37 × 10^-37 s^-2 is extremely small. This is a good sign, as it suggests that my model introduces only a tiny modification to the standard Hubble expansion.

 

The small value of α_exp means that the time-dependent effect in my model accumulates very slowly over cosmic timescales. This is consistent with the fact that we observe a relatively stable cosmic expansion rate.

 

Despite being small, this value of α_exp is sufficient to account for the difference between the "standard" H₀ (67 km/s/Mpc) and the observed H₀ (70 km/s/Mpc) in my model. This is interesting because it suggests that my model could potentially address the Hubble tension - a current discrepancy in cosmology between different measurements of the Hubble constant.

 

The positive value of α_exp indicates that in my model, the expansion rate increases with time (beyond the standard expansion), which is consistent with the observed accelerating expansion of the universe.

 

In my model, the observed cosmic phenomena and measurements might be seen as emergent properties of the underlying fractal and time-dependent dynamics rather than evidence of a distinct event like the Big Bang. By framing the universe's behavior in terms of these dynamics, it shifts the focus from a singular origin event to a continuous process where observations reflect the ongoing interactions and expansions.