Time Dilation Observed in Type Ia Supernova Light Curves and Its Cosmological Consequences
Abstract
1. Introduction
2. Cosmological Metric with Time Dilation
2.1. Comoving and Proper Time
2.2. Comoving and Proper Speed of Light
3. Physical Differences Between the FLRW and CC Metrics
- Physical meaning of metrics. All vector and tensor quantities in curvilinear coordinate systems are coordinate-dependent. They cannot be directly interpreted in physical terms because their basis vectors are not orthonormal. In cosmology, the primary purpose of evaluating the metric tensor is to express spacetime in coordinates that can be simply translated into physically meaningful quantities. These quantities must always be coordinate-invariant and should be expressed using the orthonormal tetrad of basis vectors (see Appendix A).
- Misleading equivalence between rescaled metrics. A common belief is that the FLRW and CC metrics are physically equivalent because one can be transformed into the other through rescaling or time synchronization (Misner et al. [36], their Equation (27.14)). This is misleading. Although Einstein’s field equations are coordinate-invariant, arbitrarily rescaling components of the metric tensor may have physical consequences. If such a transformation alters physical units (i.e., changes coordinate-invariant quantities), the resulting metrics describe physically different cosmological models.
- Expanding vs. static Universe. The metric of an expanding Universe can be formally transformed into the metric of a static Universe by introducing conformal distance. Although this rescaling is mathematically valid, this transformation does not eliminate the physical distinction between an expanding Universe and a static Universe. Similarly, the transformation of a model with a varying time rate into one with a fixed time rate can be performed by introducing conformal time. However, this transformation does not remove the underlying physical differences between the two models.
- Appropriate cosmological model. Since astronomical observations support both the expansion of space and cosmic time dilation, an appropriate cosmological model should be described by a metric tensor in which both the lapse function and the spatial components vary with time. This model is referred to as the ‘Cosmological Coordinate System (CCS)’, in which all major astronomical bodies remain at rest [45,56,57]. The metric must also reflect that the clock rates associated with these fundamental bodies vary over cosmic time.
4. Physical Origin of Cosmic Time Dilation
5. Discussion
6. Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Riemannian Manifold and Curvilinear Coordinate Systems
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Vavryčuk, V. Time Dilation Observed in Type Ia Supernova Light Curves and Its Cosmological Consequences. Galaxies 2025, 13, 55. https://doi.org/10.3390/galaxies13030055
Vavryčuk V. Time Dilation Observed in Type Ia Supernova Light Curves and Its Cosmological Consequences. Galaxies. 2025; 13(3):55. https://doi.org/10.3390/galaxies13030055
Chicago/Turabian StyleVavryčuk, Václav. 2025. "Time Dilation Observed in Type Ia Supernova Light Curves and Its Cosmological Consequences" Galaxies 13, no. 3: 55. https://doi.org/10.3390/galaxies13030055
APA StyleVavryčuk, V. (2025). Time Dilation Observed in Type Ia Supernova Light Curves and Its Cosmological Consequences. Galaxies, 13(3), 55. https://doi.org/10.3390/galaxies13030055