Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden

Fundamental object for astrometry: metric tensor g 

IAU Resolutions: BCRS (t, x) with metric tensor

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

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

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

Is the CP valid? A simple fact: The universe is very clumpy on scales up to some 100 Mpc

solar-system: 2 x 10 Mpc : our galaxy: 0.03 Mpc the local group: Mpc -10

The local supercluster: Mpc

dimensions of great wall: 150 x 70 x 5 Mpc distance 100 Mpc

Anisotropies in the CMBR WMAP-data

First peak:  0.9 deg corresponds today to about 150 Mpc /h results from horizon scale at recombination

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

The WMAP-data leads to the present (cosmological) standard model: Age(universe) = 13.7 billion years  Lum = 0.04  dark = 0.23   = 0.73 H 0 = (71 +/- 4) km/s/Mpc

The CP seems to be valid for scales R > R with R  400 h Mpc inhom

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

The local expansion hypothesis : the cosmic expansion occurs on all length scales, i.e., also locally If true: how does the expansion influence local physics ? question has a very long history (McVittie 1933; Järnefelt 1940, 1942; Dicke et al., 1964; Gautreau 1984; Cooperstock et al., 1998)

Validity of the local expansion hypothesis: unclear Hint: The Einstein-Straus solution matching surface S

Matching of 1st and 2nd fundamental form on S (R = R 0 ) plus Einstein eqs.: r = R 0 a(T) t = t(R 0,T) dt/dT = ( GM/(c^2 r)) M = 4  /3  r 3

The swiss cheese model of the universe Global dynamics given by the RW- metric BUT: distance measurements depend upon clumpiness parameter  (grav. lensing inside bubbles) Dyer-Roeder distance (  ) observations:   1 Dyer,C., Roeder,R., Ap.J. 174 (1972) L (1973) L31 Tomita, K., Prog.Th.Phys. 100 (1998) (1999) 155

Current issues of our work: - optimal matching the RW-metric to the BCRS assuming the local expansion hypothesis - improvements of the transition from the RW to the BCRS-metric - formulation of observables related with distance by means of a new metric tensor

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