Abstract
We have developed a cosmological model by allowing the speed of light c, gravitational constant G and cosmological constant Λ in the Einstein filed equation to vary in time, and solved them for Robertson-Walker metric. Assuming the universe is flat and matter dominant at present, we obtain a simple model that can fit the supernovae 1a data with a single parameter almost as well as the standard ΛCDM model with two parameters, and which has the predictive capability superior to the latter. The model, together with the null results for the variation of G from the analysis of lunar laser ranging data determines that at the current time G and c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH0. This variation of G and c is all what is needed to account for the Pioneer anomaly, the anomalous secular increase of the moon eccentricity, and the anomalous secular increase of the astronomical unit. We also show that the Planck’s constant ħ increases as dħ/dt = 1.8ħH0 and the ratio D of any Hubble unit to the corresponding Planck unit increases as dD/dt = 1.5DH0. We have shown that it is essential to consider the variation of all the physical constants that may be involved directly or indirectly in a measurement rather than only the one whose variation is of interest.
Highlights
Variation of physical constants is a subject that is marred with semantics: What exactly is varying and how is it being measured? There is an ongoing debate about dimensionful and dimensionless constants (e.g., Uzan [1,2], Duff [3], Chiba [4])
The physical constants considered in this work are primarily the speed of light c, the Newton’s gravitational constant
The anomalous secular increase of astronomical unit Astronomical Unit (AU) was first reported by Krasinsky and Brumberg [34] in 2004 as dAU/dt = (15 ± 4) m cy−1 from the analysis of all radiometric measurements of distances between Earth and the major planets they had available over the period 1971–2003, which included the observations of Martian landers and orbiters
Summary
Variation of physical constants is a subject that is marred with semantics: What exactly is varying and how is it being measured? There is an ongoing debate about dimensionful and dimensionless constants (e.g., Uzan [1,2], Duff [3], Chiba [4]). More recently Gohar [15], using his entropic model of the universe and data on supernovae 1a, baryon acoustic oscillations, and cosmic microwave background, has established even more stringent constraint on the variation of α He states that in his model G and c should be increasing with the evolution of the universe, which corroborates our findings in this work. The anomalous secular increase of astronomical unit AU was first reported by Krasinsky and Brumberg [34] in 2004 as dAU/dt = (15 ± 4) m cy−1 from the analysis of all radiometric measurements of distances between Earth and the major planets they had available over the period 1971–2003, which included the observations of Martian landers and orbiters They noted that unexplained secular increase in AU might point to some fundamental features of space time that are beyond the current cosmological understanding according to which the Hubble expansion yields dAU/dt = 1 km cy−1.
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