7. Comparison of ECM to General Relativity (GR): Key Cosmological Phenomena and Testable Differences

Soumendra Nath Thakur

February 05, 2025

How ECM accounts for key cosmological observations traditionally explained by General Relativity (GR), particularly gravitational lensing, the cosmic microwave background (CMB), and large-scale structure formation. The break down of ECM’s explanations and highlight testable differences from GR is given below:

1. Gravitational Lensing in ECM vs. GR

How GR Explains Gravitational Lensing

• In GR, gravitational lensing arises from the curvature of spacetime due to massive objects (as described by Einstein’s field equations).

• Light follows geodesics in curved spacetime, bending around galaxies or clusters.

• The amount of lensing depends on the mass-energy distribution described by the Einstein tensor and the stress-energy tensor of matter.

How ECM Explains Gravitational Lensing

• ECM does not rely on spacetime curvature but explains lensing through the gravitational influence of effective mass 

Mɢ = Mᴍ + Mᴅᴇ

• The equation for gravitational attraction remains Newtonian but modified to account for apparent mass effects:

Fɢ = G·Mɢ·m/r²

​

where Mɢ dynamically includes negative apparent mass contributions at intergalactic scales.

• Light bending is thus explained via apparent mass distributions rather than curved spacetime.

• In strong lensing scenarios, ECM predicts that additional dark matter effects might contribute differently than in GR, potentially leading to deviations in lensing maps, especially in large galaxy clusters.

Testable Differences in Gravitational Lensing Predictions

• Galaxy Cluster Lensing Maps: ECM’s lensing should differ subtly from GR due to the way it treats dark matter and dark energy mass contributions.

• Weak Lensing Statistics: The distribution of weak lensing distortions across large-scale structures could reveal differences in how ECM modifies gravitational attraction.

• Time Delays in Multiple Images: ECM may predict slight shifts in time delays between gravitationally lensed images due to its modified mass distribution.

2. Cosmic Microwave Background (CMB) in ECM vs. GR

How GR (ΛCDM) Explains the CMB

• The standard model explains CMB anisotropies as relic fluctuations from the early universe, shaped by photon-baryon interactions and gravitational effects.

• The ΛCDM model fits the observed acoustic peaks in the CMB power spectrum using a balance of:

• Baryonic matter (~5%)

• Dark matter (~27%)

• Dark energy (~68%)

How ECM Explains the CMB

• In ECM, the CMB anisotropies are still interpreted as early-universe fluctuations, but the gravitating mass in ECM differs from ΛCDM.

• Instead of assuming a constant dark energy density (Λ), ECM proposes that Mᴅᴇ emerges dynamically at cosmic scales.

• The effective gravitational influence modifies how density fluctuations grow over time, leading to:

• A slightly different power spectrum of CMB anisotropies.

• Possible shifts in the peak positions and amplitudes of the acoustic oscillations.

Testable Differences in the CMB Predictions

• Shift in the Acoustic Peak Positions: If ECM modifies the growth of structure differently from ΛCDM, the ratio of peak heights in the CMB power spectrum could slightly deviate from GR’s predictions.

• Integrated Sachs-Wolfe (ISW) Effect: ECM predicts different gravitational potential evolutions, affecting how CMB photons gain or lose energy as they traverse cosmic structures.

3. Large-Scale Structure Formation in ECM vs. GR

How GR (ΛCDM) Explains Structure Formation

• In ΛCDM, cosmic structures grow through gravitational instability, where dark matter forms halos that attract baryonic matter.

• Structure formation follows the linear growth equation in GR, which includes contributions from dark matter and dark energy’s repulsive effect.

How ECM Explains Structure Formation

• ECM retains structure formation via gravitational instability but modifies the effective mass governing gravitational attraction:

Mɢ = Mᴍ + Mᴅᴇ

• The growth rate of cosmic structures depends on how Mᴅᴇ evolves over time.

• At galactic and cluster scales, ECM agrees with ΛCDM, but at intergalactic scales, Mᴅᴇ plays a significant role in modifying expansion and structure formation.

Testable Differences in Structure Formation Predictions

• Galaxy Clustering Evolution: If ECM alters how mass clusters over time, this would be reflected in the observed matter power spectrum.

• Baryon Acoustic Oscillation (BAO) Peaks: The shifting of BAO peaks in galaxy distributions could serve as a signature of ECM’s alternative mass interpretation.

• Void Evolution: Large cosmic voids may evolve differently under ECM, providing an observational test of its predictions.

4. Summary: Specific, Testable Differences Between ECM and GR

Click to enlarge

Conclusion: Where ECM Differs from GR and How It Can Be Tested

• ECM does not challenge all of GR, but it offers an alternative way to interpret gravity and mass distribution at large scales.

• It agrees with GR predictions at small scales (e.g., planetary orbits, local gravitational systems) but proposes a different treatment of dark matter and dark energy in cosmic expansion.

• Observational tests such as lensing maps, the CMB power spectrum, galaxy clustering, and BAO peak shifts can distinguish ECM from GR-based ΛCDM.

Thus, ECM provides a mathematically rigorous yet testable alternative to GR’s description of the universe, with clear pathways for empirical validation.