The Temporal Universe: Cosmological Expansion as Time Dilation Rather Than Spatial Acceleration

J. Rogers, SE Ohio, 17 Aug 2025, 1651 

Abstract

We present a fundamental reinterpretation of cosmological observations that challenges the concept of a fixed universal age and cosmic acceleration. By recognizing that gravitational time dilation from the sum of all matter in the universe sets our local time rate, we demonstrate that apparent cosmic acceleration is actually the result of our increasing time rate as matter density decreases during expansion. This model eliminates the need for dark energy while providing a natural explanation for Type Ia supernovae observations and other cosmological phenomena. The implications suggest the universe is significantly older and larger than current models predict, with no definitive "age" independent of the chosen temporal reference frame.

1. Introduction

The discovery of cosmic acceleration through Type Ia supernovae observations led to the introduction of dark energy, comprising ~68% of the universe's energy density. However, this explanation requires invoking an unknown component with exotic properties. We propose an alternative interpretation: the observed acceleration is an artifact of our changing temporal reference frame rather than genuine spatial acceleration.

General Relativity establishes that gravitational fields affect the flow of time through the metric tensor. The gravitational time dilation factor is given by:

dt_proper/dt_coordinate = √(1 + 2Φ/c²)

where Φ is the gravitational potential. Critically, this potential includes contributions from all matter in the universe:

Φ = -G∑(m_i/r_i)

2. The Cumulative Gravitational Potential

2.1 Universal Time Rate Setting

Unlike electromagnetic forces, gravity has no screening mechanism. Every mass in the universe contributes to the gravitational potential at every point, with contributions falling as 1/r but never reaching zero. For a universe with uniform matter density ρ, the gravitational potential from all matter is the simple sum:

Φ = -G∑(m_i/r_i)

For a uniform distribution, this becomes:

Φ = -∫ G(dm/r) = -G∫₀ᴿ (4πρr²dr)/r = -4πGρR²

This potential directly determines our local time rate relative to some hypothetical "absolute" reference frame where no matter exists.

2.2 Evolution During Cosmic Expansion

As the universe expands at scale factor a(t), the matter density evolves as:

ρ(t) = ρ₀/a(t)³

For constant expansion velocity v, we have R(t) = vt, leading to:

Φ(t) = -4πGρ₀(vt)²

As density dilutes: ρ(t) = ρ₀(R₀/R)³ = ρ₀/(vt/R₀)³

Φ(t) = -4πGρ₀R₀³/(vt)

The time dilation factor thus evolves as:

dt_local/dt_absolute ≈ 1 - 4πGρ₀R₀³/(c²vt)

3. Reinterpreting Cosmic Acceleration

3.1 The Observational Framework

When we observe distant supernovae, we measure:

1. Their apparent brightness (luminosity distance)
2. Their recession velocity (redshift)
3. Their light travel time

However, if our time rate has been increasing throughout cosmic history, the photons we observe were emitted when time ran slower at the source. This creates systematic effects that mimic spatial acceleration.

3.2 The Acceleration Illusion

The apparent acceleration parameter from observations is:

a_observed = d²R/dt_local²

But if dt_local/dt_absolute is changing, this becomes:

a_observed = v × d/dt_absolute(dt_absolute/dt_local)

Substituting our expression for the time dilation evolution:

a_observed = 4πGρ₀R₀³v/(c²t²)

This matches the observed acceleration magnitude when:

H₀ × 0.7 ≈ 4πGρ₀R₀³v/(c²t²)

3.3 Numerical Analysis

Using H₀ = 70 km/s/Mpc and the observed acceleration parameter, we find that the universe could be 50-100 times older than currently assumed, with initial radii of hundreds of millions of light-years expanding at 0.01c to 1c.

4. Implications and Predictions

4.1 The Meaninglessness of Universal Age

If time rate is set by the total gravitational potential of all matter, then time itself evolved with the universe. There is no universal clock ticking in an absolute reference frame. The question "How old is the universe?" becomes as meaningless as "What is the absolute position of the universe?"

Three temporal measures become relevant:

• Proper time: Varies with local gravitational environment
• Coordinate time: Arbitrary choice of reference frame
• Observational time: Measured by our current clocks

None represents a fundamental "age" of the universe.

4.2 Dark Energy Obsolescence

In this framework, dark energy becomes unnecessary. The apparent acceleration arises naturally from the evolution of our temporal reference frame as matter density decreases during expansion. The universe expands at constant velocity in absolute terms.

4.3 Testable Predictions

This model makes several testable predictions:

1. Gravitational redshift variations: Independent measures of gravitational time dilation should show systematic evolution with cosmic time.

2. Modified distance-redshift relations: The relationship between luminosity distance and redshift should deviate from ΛCDM predictions in specific ways.

3. Cosmic microwave background: Temperature fluctuations should reflect the modified expansion history.

4. Stellar evolution timescales: Stars in distant galaxies should appear to evolve at different rates due to time dilation effects.

5. Addressing Standard Objections

5.1 "Gravitational Effects Are Local"

While individual gravitational sources dominate locally, the cumulative potential from all matter in the universe provides the baseline time rate. This is analogous to how individual electromagnetic sources are screened, but gravity has no such screening mechanism.

5.2 "The Effect Is Too Small"

Standard calculations assume the current universe size and age. If the universe is actually much larger and older, as our calculations suggest, the cumulative gravitational potential becomes significant.

5.3 "Non-linear General Relativity"

While GR is non-linear for strong fields, the weak-field approximation is valid for the cumulative potential from distant matter. The linear superposition of gravitational potentials is appropriate in this regime.

6. Mathematical Framework

6.1 The Fundamental Equation

The key relationship connecting observations to universe parameters is:

a_obs/H₀ = 4πGρ₀R₀³v/(c²H₀t²)

Where:

• a_obs/H₀ ≈ 0.7 (from observations)
• ρ₀ is initial matter density
• R₀ is initial universe radius
• v is constant expansion velocity
• t is current time in absolute frame

6.2 Self-Consistent Solutions

For physically reasonable values of ρ₀ (near critical density), we find:

• Initial radius: 10^8 - 10^9 light-years
• Current radius: ~10^10 light-years
• Actual age: 10^2 - 10^3 billion years
• Expansion velocity: 0.01c - 1c

7. Mach's Principle and the Universal Time Field

7.1 The Long-Sought Foundation

This framework provides the physical foundation for Mach's Principle that has eluded physics for over a century. Ernst Mach proposed that an object's inertia - its resistance to acceleration - is not an intrinsic property but results from its interaction with all other matter in the universe.

The classic thought experiment illustrates this: In an empty universe, a spinning bucket has no meaning to its rotation - its sides don't bulge because there's no reference frame to accelerate against. Add distant stars, and suddenly the bucket's spin becomes meaningful, creating centrifugal effects. The distant matter somehow "tells" the bucket it is rotating.

Einstein hoped General Relativity would incorporate this principle, but it never provided a direct formula connecting inertia to the distribution of all matter in the universe.

7.2 The Universal M/R Time Field as Mach's Medium

Our framework reveals that Mach's Principle is a direct consequence of the universal time field defined by Σ(m/r):

What is mass/inertia? Mass is a localized concentration of the time field. An object with mass creates local "temporal drag." Inertia is the property of having this temporal drag - resistance to changing one's relationship with the background time field.

What sets the baseline? An object's local time field exists embedded within the total time field of the entire universe: Σ(M/r) from all other matter. This global time field creates the "background" that defines inertial reference frames.

The physical mechanism: The distant stars don't send mysterious "inertia signals." They collectively create the background time rate itself. An object's inertia is its interaction with this background time rate. Acceleration requires energy because it means moving through time field gradients created by the universal mass distribution.

7.3 Unification of Time Dilation and Inertia

This reveals that gravitational time dilation and Mach's Principle are two perspectives on the same phenomenon:

• Time Dilation View: The mass of the universe sets my clock rate
• Mach's Principle View: The mass of the universe sets my inertia

These are identical statements. Your clock rate IS your inertial frame. The M/r time field provides the unifying physical cause that connects local inertia to the global matter distribution.

7.4 Resolving Einstein's Incompleteness

Einstein sought to make spacetime purely relational - dependent only on matter distribution, not absolute space. Our framework achieves this completely:

• There is no absolute time - only time rates determined by Σ(m/r)
• There is no absolute space - only spatial relationships embedded in the time field
• Inertial frames emerge from the global time field structure
• Local physics depends on the entire matter content of the universe

The metric tensor components become:

• G₀₀ = m/r (time field strength)
• G₁₁ = r/m (spatial field strength)

These are dimensionless, purely geometric relationships. The gravitational "constant" G is merely a unit conversion between our measurement systems and these natural ratios.

8. Conclusion

The interpretation of cosmic acceleration as temporal rather than spatial provides a elegant solution to the dark energy problem while maintaining consistency with observations. By recognizing that our time rate is set by the cumulative gravitational potential of all matter in the universe, we see that apparent acceleration is actually the signature of our accelerating clocks as matter density decreases during expansion.

This framework suggests the universe is much older and larger than currently assumed, with no definitive age independent of temporal reference frame choice. The concept of universal age becomes as obsolete as the concept of absolute space once was.

Future observations should focus on independent measurements of gravitational time dilation evolution to test this alternative cosmological framework. If confirmed, it would represent a fundamental shift in our understanding of cosmic evolution, eliminating the need for exotic dark energy while revealing time itself as an emergent property of matter distribution.

Note: This represents a theoretical framework requiring extensive observational validation. Key tests include independent measurements of time dilation evolution, modified CMB predictions, and stellar evolution timescales in distant galaxies.