- Department of Physics, Institute of Basic Science, Sungkyunkwan University, Suwon, Republic of Korea
The Robertson–Walker (RW) metric, derived from the cosmological principle and Weyl’s postulate, characterizes the
1 Introduction
The contemporary
The traditional RW metric can derive a specific relationship regarding cosmological time dilation (TD) based on the postulate of a constant speed of light. However, it is not directly derived from the metric’s fundamental principles. Various projects using supernova light curves (Leibundgut et al., 1996; Riess et al., 1997; Foley et al., 2005; Blondin and Tonry, 2007; Blondin et al., 2008; White et al.), gamma-ray bursts (Band, 1994; Norris et al., 1994; Wijers and Paczynski, 1994; Meszaros and Meszaros, 1996; Lee and Petrosian, 1997; Chang, 2001; Crawford; Zhang et al., 2013; Singh and Desai, 2022), and quasars (Hawkins, 2001; Dai et al., 2012; Lewis and Brewer, 2023) have attempted to measure cosmological TD, but conflicting results have prevented convincing detection. The speed of light in the RW metric might change with cosmic time without clear rules determining TD, just like other physical parameters like temperature and mass density. This variation supports the hypothesis of a varying speed of light (VSL) (Lee, 2021; Lee, 2023a; Lee, 2023b; Lee, 2024). In the RW universe, a hypersurface of specific time defines uniform physical quantities such as temperature or density, and these quantities are cosmologically redshifted due to the universe’s expansion.
One can rewrite the RW metric with the possibility of the VSL as follows:
Physical quantities like the scale factor
where SMC stands for the standard model cosmology and
2 Methods
In an expanding universe described by the RW metric, galaxies uniformly recede from each other, and TD affects clocks differently depending on the distance. Whether the speed of light is constant or not influences local clock rates, thus playing a crucial role in understanding TD. Therefore, it is important to obtain the precise relationship of TD by comparing observational data such as distant Type Ia supernovae (SNeIa) light curves and spectral evolution.
Supernova light curves (LCs) track brightness changes over time, crucial for understanding their evolution and properties, especially for SNeIa used as cosmological standard candles. Comparing LCs across different distances reveals TD effects due to cosmic expansion, indicating the stretching of distant LCs compared to nearby LCs. The spectral evolution of SNeIa provides a reliable method to measure aging and confirm TD, offering insights into the Universe’s expansion rate and dark energy dynamics.
We present aging rate measurements of 13 high-redshift SNeIa data provided in Blondin et al. (2008), as shown in Table 1. These data are derived from a sample of 35 spectra of 13 SNeIa in the redshift range
Table 1. Aging rate measurements from SNeIa observation (Blondin et al., 2008).
We perform a least-square fit to the data using the SMC and meVSL model predictions. The fitting is given by
where
3 Results
The aging rate analysis based on the SMC, using
Table 2. A simple
Figure 1. Time dilation for two models with data points. The dashed line depicts the SC prediction of TD. The thick solid line represents the best-fit value predicted TD of the meVSL model. The shaded region represents the 1-
4 Discussion
We derived the time dilation formula in the minimally extended varying speed of light model as
Author contributions
SL: conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, project administration, resources, validation, visualization, writing–original draft, and writing–review and editing.
Funding
The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This research was funded by the National Research Foundation of Korea (NRF), funded both by the Ministry of Science, ICT, and Future Planning (grant no. NRF-2019R1A6A1A10073079) and the Ministry of Education (grant no. NRF-RS202300243411).
Acknowledgments
The author is grateful for the invitation to present at the ‘Frontiers in Astronomy and Space Sciences: A Decade of Discovery and Advancement, 10th Anniversary Conference’. Additionally, the author would like to express his gratitude to the editor, who requested a mini-review related to this presentation.
Conflict of interest
The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Keywords: varying speed of light, cosmological time dilation, supernovae, cosmological redshift, standard model cosmology
Citation: Lee S (2024) Constraining the minimally extended varying speed of light model using time dilations. Front. Astron. Space Sci. 11:1453806. doi: 10.3389/fspas.2024.1453806
Received: 24 June 2024; Accepted: 09 July 2024;
Published: 02 August 2024.
Edited by:
Julio Navarro, University of Victoria, CanadaReviewed by:
Elmo Benedetto, University of Salerno, ItalyCopyright © 2024 Lee. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Seokcheon Lee, skylee@skku.edu