Astrometry and the expansion of the universe

Michael Soffel & Sergei Klioner

TU Dresden

Fundamental object for astrometry:metric tensor g

IAU -2000 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 homogeneousand isotropic

The Robertson-Walker metric follows from the CP

Consequences of the RW-metricfor 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 tosome 100 Mpc

solar-system: 2 x 10 Mpc :

our galaxy: 0.03 Mpc

the local group: 1 - 3 Mpc

-10

The localsupercluster:20 - 30 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

correspondstoday to about150 Mpc /h

results from horizon scaleat 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 = 0.04dark = 0.23 = 0.73

H0 = (71 +/- 4) km/s/Mpc

The CP seems to be valid for scales

R > R

with R 400 h Mpc

inhom

inhom

-1

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 tosystem below; dynamical time scales grow if we godown 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-Straussolution

matchingsurface S

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/(c^2 r))

• M = 4/3 r

-1

3

The swiss cheese model of the universe

Global dynamicsgiven by the RW-metric

BUT:

distance measurementsdepend uponclumpiness parameter (grav. lensinginside 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

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

THE END