Two-Body Orbit Expansion Due to Time-Dependent Relative Acceleration Rate of the Cosmological Scale FactorReportar como inadecuado

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Italian Ministry of Education, University and Research M.I.U.R., Viale Unità di Italia 68, Bari BA 70125, Italy

Abstract By phenomenologically assuming a slow temporal variation of the percent acceleration rate S̈S -1 of the cosmic scale factor St, it is shown that the orbit of a local binary undergoes a secular expansion. To first order in the power expansion of S̈S -1 around the present epoch t0, a non-vanishing shift per orbit Δr of the two-body relative distance r occurs for eccentric trajectories. A general relativistic expression, which turns out to be cubic in the Hubble parameter H0 at the present epoch, is explicitly calculated for it in the case of matter-dominated epochs with Dark Energy. For a highly eccentric Oort comet orbit with period Pb ≈ 31 Myr, the general relativistic distance shift per orbit turns out to be of the order of Δr ≈ 70 km. For the Large Magellanic Cloud, assumed on a bound elliptic orbit around the Milky Way, the shift per orbit is of the order of Δr ≈ 2–4 pc. Our result has a general validity since it holds in any cosmological model admitting the Hubble law and a slowly varying S̈S-1t. More generally, it is valid for an arbitrary Hooke-like extra-acceleration whose -elastic- parameter κ is slowly time-dependent, irrespectively of the physical mechanism which may lead to it. The coefficient κ1 of the first-order term of the power expansion of κt can be preliminarily constrained in a model-independent way down to a κ1 ≲ 2 x 10-13 year-3 level from latest Solar System’s planetary observations. The radial velocities of the double lined spectroscopic binary ALPHA Cen AB yield κ1 ≲ 10-8 year-3. View Full-Text

Keywords: classical general relativity; cosmology classical general relativity; cosmology

Autor: Lorenzo Iorio



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