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2. Distance Scale, Hubble Constant & the Age of the Universe

One of the most important parameters in determining the fate of the Universe as a whole, is the present day expansion rate of the Universe, which is encapsulated in the value of the Hubble constant H0. Its value sets the age of the Universe and specifies the value of the critical density rhocr, and through this route the geometry of the Universe.

From the Hubble law (2) it is evident that in order to determine its value we need to determine the expansion velocity (redshift) as well as the distance of extragalactic objects, but within a redshift such that space-curvature effects do not affect distances (43). A further concern is that local gravitational effects produce peculiar velocities, that are superimposed on the general expansion. This can easily be seen in the toy model of (2), if we allow chi ident chi(t). Then


with the factor on the right being the peculiar velocity. Since the observer as well as the extragalactic object, of which the distance we want to measure, have peculiar velocities then the above equation becomes:

Equation 35 (35)

where v(0) is the velocity of the observer and r hat is the unit vector along the line-of-sight to the extragalactic object. It is then obvious that in order to measure H0, the local velocity field should be measured and the extragalactic distances corrected accordingly. It is easily seen that if both observer and galaxy take part in a coherent bulk flow, having the same amplitude at the observer and galaxy positions, then the right-hand part of (35) vanishes. In general however, one needs good knowledge of the velocity field in order to correct distances adequately.

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