Time Delay in Robertson-McVittie Spacetime and its Application to Increase of Astronomical Unit

Abstract

We investigated the light propagation by means of the Robertson-McVittie solution which is considered to be the spacetime around the gravitating body embedded in the FLRW (Friedmann-Lema{î}tre-Robertson-Walker) background metric. We concentrated on the time delay and derived the correction terms with respect to the Shapiro's formula. To relate with the actual observation and its reduction process, we also took account of the time transformations; coordinate time to proper one, and conversely, proper time to coordinate one. We applied these results to the problem of increase of astronomical unit reported by Krasinsky and Brumberg (2004). However, we found the influence of the cosmological expansion on the light propagation does not give an explanation of observed value, $d\mathrm{AU}/dt=15\pm 4$ [m/century] in the framework of Robertson-McVittie metric.

15 pages, 1 figure, accepted for publication in New Astronomy

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• Kinematics in Randers-Finsler geometry and secular increase of the astronomical unit
• Application of Time Transfer Function to McVittie Spacetime: Gravitational Time Delay and Secular Increase in Astronomical Unit
• Influence of cosmological expansion in local experiments
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• Planetary motion on an expanding locally anisotropic background
• Effect of inhomogeneity of the Universe on a gravitationally bound local system: A no-go result for explaining the secular increase in the astronomical unit
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