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Cosmic influences upon the basic reference system for GAIA

This article discusses the impact of cosmic influences on the basic reference system for GAIA, including the effects of the cosmological principle and the Robertson-Walker metric. It explores the validity of the cosmological principle and presents the consequences of the RW-metric for astrometry. The need for modifications to the present reference system to account for the expansion of the universe is emphasized.

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Cosmic influences upon the basic reference system for GAIA

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  1. Cosmic influences upon the basic reference system for GAIA Michael Soffel & Sergei Klioner TU Dresden

  2. IAU-2000 Resolution B1.3 Definition of BCRS (t, x) with t = x0 = TCB, spatial coordinates x and metric tensor g • post-Newtonian metric in harmonic coordinates determined by potentials w, w i

  3. BCRS-metric is asymptotically flat; ignores cosmological effects, fine for the solar-system dynamics and local geometrical optics

  4. The cosmological principle (CP): on very large scales the universe is homogeneous and isotropic The Robertson-Walker metric follows from the CP

  5. Consequences of the RW-metric for astrometry: - cosmic redshift - various distances that differ from each other: parallax distance luminosity distance angular diameter distance proper motion distance

  6. Is the CP valid? • Clearly for the dark (vacuum) energy • For ordinary matter: likely on very large scales

  7. Anisotropies in the CMBR WMAP-data

  8. -4 / < 10 for R > 1000 (Mpc/h) (O.Lahav, 2000)

  9. The WMAP-data leads to the present (cosmological) standard model: Age(universe) = 13.7 billion years Lum = 0.04 dark = 0.23  = 0.73 (dark vacuum energy) H0 = (71 +/- 4) km/s/Mpc

  10. One might continue with a hierarchy of systems • GCRS (geocentric celestial reference system) • BCRS (barycentric) • GaCRS (galactic) • LoGrCRS (local group) etc. • each systems contains tidal forces due to • system below; dynamical time scales grow if we go • down the list -> renormalization of constants (sec- aber) • BUT: • expansion of the universe has to be taken into account

  11. Tidal forces from the next 100 stars: their quadrupole moment can be represented by two fictitious bodies: BCRS for a non-isolated system

  12. In a first step we considered only the effect of the vacuum energy (the cosmological constant ) !

  13. Various studies: • transformation of the RW-metric to ‚local • coordinates‘ • construction of a local metric for a barycenter in motion • w.r.t. the cosmic energy distribution • transformation of the Schwarzschild de Sitter metric to • LOCAL isotropic coordinates • - cosmic effects: orders of magnitude

  14. Transformation of the RW-metric to ‚local coordinates‘

  15. ‘ Construction of a local metric for a barycenter in motion w.r.t. the cosmic energy distribution

  16. (local Schwarzschild-de Sitter)

  17. Cosmic effects: orders of magnitude • Quasi-Newtonian cosmic tidal acceleration at Pluto‘s orbit • 2 x 10**(-23) m/s**2away from Sun • (Pioneer anomaly: 8.7 x 10**(-10) m/s**2 towards Sun) • perturbations of planetary osculating elements: e.g., • perihelion prec of Pluto‘s orbit: 10**(-5) microas/cen • 4-acceleration of barycenter due to motion of • solar-system in the g-field of -Cen • solar-system in the g-field of the Milky-Way • Milky-Way in the g-field of the Virgo cluster • < 10**(-19) m/s**2

  18. Conclusions If one is interested in cosmology, position vectors or radial coordinates of remote objects (e.g., quasars) the present BCRS is not sufficient  the expansion of the universe has to be considered  modification of the BCRS and matching to the cosmic R-W metric becomes necessary

  19. THE END

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