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Published on: August 17, 2016
Theoretical foundations of the chronometric cosmology
1Massachusetts Institute of Technology, Cambridge, Mass, 02139.
Summary
This study refines the redshift-distance relation in chronometric cosmology using advanced mathematical physics. Quantum dispersion and deviations from theoretical predictions are found to be negligibly small.
Area of Science:
- Cosmology
- Theoretical Physics
- Quantum Mechanics
Background:
- The standard cosmological model relies on the redshift-distance relation.
- Chronometric cosmology offers an alternative framework for understanding the universe's expansion.
- Previous derivations of the redshift-distance relation in this theory used less formal methods.
Purpose of the Study:
- To rigorously derive and analyze the redshift-distance relation within chronometric cosmology.
- To quantify deviations from the established theoretical prediction z = tan(2)(r/2R).
- To investigate the impact of quantum effects and wave properties on cosmological measurements.
Main Methods:
- Utilizing self-adjoint operators in global Hilbert spaces to represent physical quantities.
- Performing computations for a cut-off plane wave in 2D and a scalar spherical wave in 4D.
- Incorporating photon spin into the wave calculations for a more complete model.
Main Results:
- Explicit bounds were calculated for the deviation of the theoretical redshift-distance relation.
- Both the deviation and quantum dispersion in redshift were found to be unobservably small.
- A parallel classical treatment yielded similar results, reinforcing the findings.
Conclusions:
- The chronometric theory's redshift-distance relation is robust under rigorous mathematical treatment.
- Quantum effects and wave properties do not significantly impact observable cosmological distances.
- The findings support the validity of the chronometric theory's predictions for the universe's expansion.
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