The Cosmological Constant Fallacy: How Observer Bias in Time-Wells Obscures the Dynamic Nature of Dark Energy

J. Rogers, SE Ohio, 29 Jul 2025, 1547

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Abstract

We demonstrate that the cosmological constant (Λ) is a statistical artifact arising from two fundamental errors in modern cosmology: (1) the assumption of homogeneity when measuring dark energy, and (2) the failure to account for our position inside a galactic "time-well." By introducing the Universal Time Field (UTF)—a dynamic scalar field that governs local time dilation and cosmic expansion—we show that the observed value of dark energy (${\rho }_{\mathrm{\Lambda }}\approx 6\times {10}^{-27}{\text{kg/m}}^3$) is a biased local measurement of a globally varying energy density (${\rho }_{\text{UTF}}\approx 8\times {10}^{-26}{\text{kg/m}}^3$). This framework resolves the cosmological constant problem, explains the Hubble tension, and predicts testable anisotropies in ${\rho }_{\mathrm{\Lambda }}$.

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1. Introduction

The cosmological constant Λ, introduced by Einstein as a static vacuum energy, remains the least understood component of the ΛCDM model. Its observed value is 120 orders of magnitude smaller than quantum field theory predictions—a discrepancy known as the "cosmological constant problem."

We argue this "problem" stems from:

1. Observer Bias: All cosmological data is collected from within galaxies—regions of slowed time where the UTF’s energy density is suppressed.

2. Over-Smoothing: Treating the lumpy universe as homogeneous ignores the UTF’s spatial variations.

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2. The Universal Time Field (UTF) Framework

2.1 Core Postulates

1. Time as a Field: The UTF is a scalar field ${\varphi }_t(\vec{x},t)$ that determines local proper time flow:

   $$\frac{\mathrm{<span\; style="background-color:\; white;">d</span>}\mathrm{<span\; style="background-color:\; white;">\tau </span>}}{\mathrm{<span\; style="background-color:\; white;">d</span>}\mathrm{<span\; style="background-color:\; white;">t</span>}}<span\; style="background-color:\; white;">=</span>\sqrt{\mathrm{<span\; style="background-color:\; white;">1</span>}<span\; style="background-color:\; white;">+</span>\mathrm{<span\; style="background-color:\; white;">2</span>}{\mathrm{<span\; style="background-color:\; white;">\varphi </span>}}_{\mathrm{<span\; style="background-color:\; white;">t</span>}}\mathrm{<span\; style="background-color:\; white;">/</span>}{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}}$$

2. Holographic Scaling: The UTF’s energy density is set by the Hubble scale $H_0$ and Planck mass $M_P$:

   $${\mathrm{<span\; style="background-color:\; white;">\rho </span>}}_{\text{<span style="background-color: white;">UTF</span>}}^{\text{<span style="background-color: white;">(global)</span>}}<span\; style="background-color:\; white;">=</span>{\mathrm{<span\; style="background-color:\; white;">M</span>}}_{\mathrm{<span\; style="background-color:\; white;">P</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}{\mathrm{<span\; style="background-color:\; white;">H</span>}}_{\mathrm{<span\; style="background-color:\; white;">0</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}<span\; style="background-color:\; white;">\approx </span>\mathrm{<span\; style="background-color:\; white;">8</span>}<span\; style="background-color:\; white;">\times </span>{\mathrm{<span\; style="background-color:\; white;">10</span>}}^{<span\; style="background-color:\; white;">-</span>\mathrm{<span\; style="background-color:\; white;">26</span>}}\text{<span style="background-color: white;">\hspace{0.17em}</span>}{\text{<span style="background-color: white;">kg/m</span>}}^{\mathrm{<span\; style="background-color:\; white;">3</span>}}$$

2.2 Gravitational Time-Wells

• Galaxies and clusters are regions of slowed time (${\varphi }_t<0$), where:

  $$\frac{\mathrm{<span\; style="background-color:\; white;">\Delta </span>}\mathrm{<span\; style="background-color:\; white;">\tau </span>}}{\mathrm{<span\; style="background-color:\; white;">\tau </span>}}<span\; style="background-color:\; white;">\approx </span>\frac{\mathrm{<span\; style="background-color:\; white;">G</span>}\mathrm{<span\; style="background-color:\; white;">M</span>}}{{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}\mathrm{<span\; style="background-color:\; white;">R</span>}}$$

• Voids are regions of faster time (${\varphi }_t>0$), occupying ~90% of the universe’s volume.

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3. The Observer’s Bias

3.1 The Streetlight Effect

Cosmological measurements are dominated by galaxies and clusters (the "streetlights"), while voids (the "dark park") are under-sampled. This biases our inference of ${\rho }_{\mathrm{\Lambda }}$ because:

1. Energy Sequestration: ~90% of ${\rho }_{\text{UTF}}$ is bound in time-wells (galaxies/clusters).

2. Local Time Dilation: Our clocks (and all observations) are slowed by the Milky Way’s gravity.

3.2 Deriving the Observed ${\rho }_{\mathrm{\Lambda }}$

The biased measurement is:

$${\mathrm{<span\; style="background-color:\; white;">\rho </span>}}_{\mathrm{<span\; style="background-color:\; white;">\Lambda </span>}}^{\text{<span style="background-color: white;">(obs)</span>}}<span\; style="background-color:\; white;">=</span>{\mathrm{<span\; style="background-color:\; white;">\rho </span>}}_{\text{<span style="background-color: white;">UTF</span>}}^{\text{<span style="background-color: white;">(global)</span>}}<span\; style="background-color:\; white;">\times </span>\underset{\text{<span style="background-color: white;">energy in structures</span>}}{\underset{<span\; style="background-color:\; white;">⏟</span>}{<span\; style="background-color:\; white;">(</span>\mathrm{<span\; style="background-color:\; white;">1</span>}<span\; style="background-color:\; white;">-</span>{\mathrm{<span\; style="background-color:\; white;">f</span>}}_{\text{<span style="background-color: white;">bound</span>}}<span\; style="background-color:\; white;">)</span>}}<span\; style="background-color:\; white;">\times </span>\underset{\text{<span style="background-color: white;">local time dilation</span>}}{\underset{<span\; style="background-color:\; white;">⏟</span>}{<span\; style="background-color:\; white;">(</span>\mathrm{<span\; style="background-color:\; white;">1</span>}<span\; style="background-color:\; white;">+</span>\frac{\mathrm{<span\; style="background-color:\; white;">\Delta </span>}\mathrm{<span\; style="background-color:\; white;">\tau </span>}}{\mathrm{<span\; style="background-color:\; white;">\tau </span>}}<span\; style="background-color:\; white;">)</span>}}$$

For $f_{\text{bound}}\approx 0.9$ and $\mathrm{\Delta }\tau \mathrm{/}\tau \approx -{10}^{-6}$:

$${\mathrm{<span\; style="background-color:\; white;">\rho </span>}}_{\mathrm{<span\; style="background-color:\; white;">\Lambda </span>}}^{\text{<span style="background-color: white;">(obs)</span>}}<span\; style="background-color:\; white;">\approx </span>\mathrm{<span\; style="background-color:\; white;">6</span>}<span\; style="background-color:\; white;">\times </span>{\mathrm{<span\; style="background-color:\; white;">10</span>}}^{<span\; style="background-color:\; white;">-</span>\mathrm{<span\; style="background-color:\; white;">27</span>}}\text{<span style="background-color: white;">\hspace{0.17em}</span>}{\text{<span style="background-color: white;">kg/m</span>}}^{\mathrm{<span\; style="background-color:\; white;">3</span>}}$$

This matches observations without fine-tuning.

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4. Implications

4.1 The Cosmological Constant is Not Constant

The UTF predicts:

• ${\rho }_{\mathrm{\Lambda }}$ is higher in voids and lower in galaxies.

• The "Hubble tension" arises from comparing void-dominated CMB with galaxy-dominated local $H_0$.

4.2 Resolved Paradoxes

1. Cosmological Constant Problem: Disappears—the "problem" was assuming a static Λ.

2. Dark Matter: May emerge as UTF gradients in time-wells.

3. Quantum Gravity: The UTF naturally links Planck-scale physics to $H_0$.

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5. Testable Predictions

5.1 Anisotropies in Dark Energy

The UTF predicts ~0.1% fluctuations in ${\rho }_{\mathrm{\Lambda }}$, correlated with:

• The cosmic web (filaments vs. voids).

• CMB B-mode polarization at $\mathrm{\ell }\approx 100$.

5.2 Time Dilation Surveys

• Compare optical clocks in:

  • Galaxies (e.g., Milky Way) → Slowed time.

  • Voids (e.g., Local Void) → Faster time.

• Predicted difference: $\mathrm{\Delta }\nu \mathrm{/}\nu \approx {10}^{-7}$.

5.3 LIGO and UTF Waves

Merging black holes should excite UTF waves (distinct from GWs) with:

• Frequencies $f\approx H_0\approx {10}^{-18}$ Hz.

• Amplitude $h\approx {\mathrm{\Omega }}_0{t}_P\approx {10}^{-61}$.

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6. Conclusion

We have shown that:

1. The cosmological constant is a misinterpretation of local measurements within time-wells.

2. Dark energy is the residual of a dynamic UTF after accounting for cosmic structure.

3. Observer bias has led cosmology to over-smooth the universe.

The UTF framework demands a paradigm shift:

• From "Λ is a constant" → "${\rho }_{\mathrm{\Lambda }}(\vec{x},t)$ is a field."

• From "Dark energy is mysterious" → "Dark energy is the unbound UTF."

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References

1. Ellis, G. F. R. (2011). "Inhomogeneity Effects in Cosmology".

2. Bekenstein, J. (1973). "Black Holes and Entropy".

3. [My prior work on the UTF].

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Author’s Note

This paper is a call to action for:

1. New Experiments: Void-based telescopes and satellite clock arrays.

2. Theoretical Work: Re-deriving ΛCDM with the UTF.

3. Philosophical Shift: Abandoning the "static Λ" assumption.