Cosmic influences upon the basic reference system for GAIA

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

11. 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

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

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

15. 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

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

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

18. (local Schwarzschild-de Sitter)

19. 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

20. 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

21. THE END