Cosmic Tomography via the Redshift Horizon: A Method for Mapping the Trans-CMB Universe

J. Rogers, SE Ohio

Abstract

We propose a novel method, Cosmic Tomography via the Redshift Horizon (CTRH), for mapping the large-scale matter distribution of the universe far beyond the current observational limit of the Cosmic Microwave Background (CMB). This technique is predicated on a reinterpretation of the CMB, treating it not as the "surface of last scattering" from a singular primordial event, but as a "redshift horizon"—a perceptual boundary where the cumulative time dilation from an ancient, vast universe redshifts the light of all background galaxies into a uniform microwave fog. Under this model, the observed temperature anisotropies in the CMB are not primordial fluctuations, but are instead imprints of the large-scale mass distribution (superclusters and voids) lying beyond the horizon. We outline a methodology to de-project these 2D temperature anisotropies into a 3D statistical map of the trans-CMB cosmos. Crucially, we propose a validation technique using "false horizons" within known galaxy survey data (e.g., SDSS, 2dF) to test and calibrate the tomographic reconstruction algorithms, thereby demonstrating the method's viability before its application to the true CMB.

1. Introduction: The CMB as a Shroud, Not a Baby Picture

The standard ΛCDM model of cosmology interprets the Cosmic Microwave Background (CMB) as the afterglow of the Big Bang, a snapshot of the universe approximately 380,000 years after its supposed beginning. In this view, the CMB represents a fundamental physical barrier—the "surface of last scattering"—beyond which the universe was opaque. The temperature anisotropies observed by COBE, WMAP, and Planck are interpreted as the primordial quantum fluctuations that seeded all subsequent cosmic structure.

This paper challenges that foundational assumption. We proceed from the alternative hypothesis that the universe is vastly older and larger than the 13.8 billion-light-year observable sphere. In this framework, the CMB is not a physical wall, but a perceptual horizon. It is the distance at which the cumulative cosmological redshift, arising from the evolving universal time rate (Σ(m/r)), becomes so extreme that the light from all more distant sources is shifted down into the microwave spectrum.

Under this hypothesis, the CMB is the superimposed, time-dilated light of a trillion trillion galaxies. The observed temperature anisotropies (ΔT/T) are therefore not primordial, but are instead gravitational redshift and lensing effects caused by the immense mass concentrations (superclusters and voids) that lie behind this redshift horizon. A line of sight passing through a trans-CMB supercluster will be slightly hotter (gravitationally blueshifted/lensed) than a line of sight passing through a trans-CMB void (gravitationally redshifted/lensed). Nearer galaxies beyond the cmb will appear as hotter spots too. 

This reinterpretation transforms the CMB map from a historical artifact into a present-day backlight, creating the possibility of performing cosmic tomography.

2. The CTRH Methodology

The Cosmic Tomography via the Redshift Horizon method consists of three primary stages:

Stage 1: The Forward Model (Hypothesis Formulation)
The core physical hypothesis is that a simple, linear relationship exists between the observed CMB temperature fluctuation and the integrated mass density fluctuation along that line of sight beyond the horizon:

ΔT(θ, φ) / T₀ ∝ ∫[z=z_cmb to ∞] δρ(r, θ, φ) W(r) dr

Where:

• ΔT(θ, φ) is the temperature anisotropy in a given direction.

• δρ(r, θ, φ) is the mass density fluctuation (the cosmic web) as a function of distance r beyond the CMB.

• W(r) is a weighting kernel that models the decreasing influence of structures at greater distances.

Stage 2: The Inverse Problem (Map Reconstruction)
The goal is to solve the inverse problem: given the known 2D map ΔT(θ, φ) from Planck, reconstruct the most probable 3D map δρ(r, θ, φ) that could have produced it. This is a classic tomographic reconstruction problem, mathematically similar to a medical CT scan. It requires sophisticated statistical algorithms (e.g., Wiener filtering, Bayesian inference) to de-project the 2D shadow into a 3D object.

Stage 3: Calibration and Validation via "False Horizons"
This is the crucial step that makes the CTRH method scientifically rigorous and testable without new observational technology. Instead of immediately applying the reconstruction algorithm to the real CMB, we first validate it on known data.

3. The "False Horizon" Calibration Technique

The logic is simple: if our tomographic method is valid, it should work for any sufficiently distant backlight, not just the CMB. We can simulate this condition by creating artificial "horizons" within our existing 3D maps of the local universe.

Methodology:

1. Select a Data Set: Use a large-scale structure survey with known 3D galaxy positions, such as the Sloan Digital Sky Survey (SDSS). This provides a "ground truth" map of the cosmic web out to several billion light-years.

2. Define a "False Horizon": Choose an arbitrary distance, for example, z=0.5 (approx. 5 billion light-years), and declare it our "false CMB."

3. Generate a "False Backlight Map": For every point on the celestial sphere, calculate the integrated effect of all known matter beyond the false horizon (z > 0.5). Using the principles of gravitational lensing and the Integrated Sachs-Wolfe effect, compute the predicted temperature fluctuation that this "trans-false-horizon" structure would imprint on a hypothetical backlight originating at z=0.5. This creates a synthetic 2D "false CMB" map.

4. Run the Reconstruction Algorithm: Feed this 2D "false CMB" map into the CTRH reconstruction algorithm (from Stage 2) without giving it the ground truth data. The algorithm's task is to reconstruct the 3D mass distribution for z > 0.5 based only on the 2D map.

5. Compare and Calibrate: Compare the algorithm's reconstructed 3D map with the actual, known 3D map of galaxies from the SDSS data. The degree of correlation between the reconstructed map and the ground truth provides a direct, quantitative measure of the algorithm's accuracy. This process allows us to refine the weighting kernel W(r) and other model parameters until the reconstruction is optimized.

By successfully demonstrating that we can map the known universe by treating a nearby shell as a "false horizon," we can build significant confidence that the same method will work when applied to the true CMB horizon.

4. Expected Results and Predictions

1. Validation on Known Data: We predict that the "false horizon" technique will successfully reconstruct the major known structures of the local universe (e.g., the Sloan Great Wall, the Bootes Void) with statistically significant accuracy. The correlation will not be perfect, but it will be far greater than random chance, proving the principle of the method.

2. The First Map of the Trans-CMB Universe: Applying the calibrated algorithm to the real Planck CMB data will produce the first-ever statistical map of the cosmic web for z > 1100. We predict this map will show structures (filaments, clusters, voids) with statistical properties and scales similar to those observed in the local universe.

3. The Falsifiable Prediction for Future Observatories: The resulting 3D map is a concrete, falsifiable prediction. It states that future "Microwave Explorer" orbital observatories should find, for example, a massive supercluster at specific celestial coordinates, corresponding to a major hot spot in the current CMB map.

5. Conclusion: A New Window into the Cosmos

The reinterpretation of the CMB as a redshift horizon opens a revolutionary new window into the universe. The Cosmic Tomography via the Redshift Horizon (CTRH) method provides a concrete, testable procedure for mapping the vast, unseen cosmos that may lie beyond our current perceptual limits.

The proposed "false horizon" calibration technique is the critical first step. It transforms this from a speculative idea into a rigorous scientific program. By using existing galaxy survey data to test and refine our tomographic methods, we can build a robust case for the validity of the underlying hypothesis.

The data is waiting. The tools exist. The only barrier is conceptual. By abandoning the dogmatic assumption of the CMB as a singular, primordial event and treating it instead as an observational horizon, we may find that the map to a universe vastly older and larger than we ever imagined has been in our possession all along.