Kein Folientitel

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Astrometry and the expansion of the universe
Michael Soffel Sergei Klioner
TU Dresden
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Fundamental object for astrometry metric tensor g
??
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IAU -2000 Resolutions BCRS (t, x) with metric
tensor
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BCRS-metric is asymptotically flat ignores
cosmological effects, fine for the solar-system
dynamics and local geometrical optics
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The cosmological principle (CP) on very large
scales the universe is homogeneous and
isotropic The Robertson-Walker metric follows
from the CP
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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
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Is the CP valid?
A simple fact The universe is very clumpy on
scales up to some 100 Mpc
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solar-system 2 x 10 Mpc
our galaxy 0.03 Mpc
the local group 1 - 3 Mpc
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The local supercluster 20 - 30 Mpc
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dimensions of great wall 150 x 70 x 5
Mpc distance 100 Mpc
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Anisotropies in the CMBR WMAP-data
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First peak ? 0.9 deg corresponds today to
about 150 Mpc /h results from horizon scale at
recombination
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??/? lt 10 for R gt 1000 (Mpc/h)
(O.Lahav, 2000)
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The WMAP-data leads to the present (cosmological)
standard model
Age(universe) 13.7 billion years ?Lum
0.04 ?dark 0.23 ?? 0.73 H0 (71 /-
4) km/s/Mpc
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The CP seems to be valid for scales R gt
R with R ? 400 h Mpc
inhom
-1
inhom
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• 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 -gt renormalization of constants
  (sec- aber)
• expansion of the universe has to be taken into
  account

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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)
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Validity of the local expansion hypothesis
unclear
Hint The Einstein-Straus solution
matching surface S
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• Matching of 1st and 2nd fundamental form on S
• (R R0 )
• plus Einstein eqs.
• r R0 a(T)
• t t(R0,T)
• dt/dT ( 1 - 2 GM/(c2 r))
• M 4?/3 ? r

-1
3
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The swiss cheese model of the universe
Global dynamics given by the RW- metric BUT dis
tance measurements depend upon clumpiness
parameter ? (grav. lensing inside
bubbles) Dyer-Roeder distance (?) observations
? ? 1
Dyer,C., Roeder,R., Ap.J. 174 (1972) L115
181 (1973)
L31 Tomita, K., Prog.Th.Phys. 100 (1998) 79
133 (1999)
155
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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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THE END