astrometry and the expansion of the universe michael soffel & sergei klioner tu dresden
TRANSCRIPT
![Page 1: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/1.jpg)
Astrometry and the expansion of the universe
Michael Soffel & Sergei Klioner
TU Dresden
![Page 2: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/2.jpg)
Fundamental object for astrometry:metric tensor g
![Page 3: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/3.jpg)
IAU -2000 Resolutions: BCRS (t, x) with metric tensor
![Page 4: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/4.jpg)
BCRS-metric is asymptotically flat;ignores cosmological effects,fine for the solar-system dynamics and local geometrical optics
![Page 5: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/5.jpg)
The cosmological principle (CP):
on very large scales the universe is homogeneousand isotropic
The Robertson-Walker metric follows from the CP
![Page 6: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/6.jpg)
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
![Page 7: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/7.jpg)
Is the CP valid?
A simple fact:
The universe is very clumpy on scales up tosome 100 Mpc
![Page 8: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/8.jpg)
solar-system: 2 x 10 Mpc :
our galaxy: 0.03 Mpc
the local group: 1 - 3 Mpc
-10
![Page 9: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/9.jpg)
The localsupercluster:20 - 30 Mpc
![Page 10: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/10.jpg)
dimensions of great wall:
150 x 70 x 5 Mpc
distance 100 Mpc
![Page 11: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/11.jpg)
Anisotropies in the CMBR
WMAP-data
![Page 12: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/12.jpg)
First peak: 0.9 deg
correspondstoday to about150 Mpc /h
results from horizon scaleat recombination
![Page 13: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/13.jpg)
![Page 14: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/14.jpg)
![Page 15: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/15.jpg)
/ < 10
for
R > 1000 (Mpc/h)
-4
(O.Lahav, 2000)
![Page 16: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/16.jpg)
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
![Page 17: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/17.jpg)
![Page 18: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/18.jpg)
The CP seems to be valid for scales
R > R
with R 400 h Mpc
inhom
inhom
-1
![Page 19: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/19.jpg)
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
![Page 20: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/20.jpg)
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)
![Page 21: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/21.jpg)
Validity of the local expansion hypothesis: unclear
Hint:
The Einstein-Straussolution
matchingsurface S
![Page 22: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/22.jpg)
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
![Page 23: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/23.jpg)
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
![Page 24: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/24.jpg)
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
![Page 25: Astrometry and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden](https://reader036.vdocuments.us/reader036/viewer/2022081516/5697bf9e1a28abf838c94591/html5/thumbnails/25.jpg)
THE END