Diagram of Hubble

As previously, we adjusted the relation in the band U We have, this time, fixed the value of the parameter $\Omega _ { \rm M}$

Figures 10.21 respectively show the diagram of Hubble and the diagram of residuals magnitudes out of U, compared to an empty model of universes, obtained by this adjustment. The line in full feature represents each time the model of universe with cosmological constant.

Figure 10.20: Diagram of Hubble for a batch of 12 supernovæ near and 3 supernovælointaines. In full feature, a model of universe with cosmological constant, in indent, an open universe without cosmological constant and in dotted line, the model Einstein-With Sitter (flat and without cosmological constant).

The value of $\Omega _ { \rm M}$ data by the adjustment is:

$$\Omega_{\rm M}= 0.22^{+0.3}_{-0.25}$$ (10.8)

The value of $\Omega _ \Lambda$ data by this adjustment is thus 0.78. That is to say a good agreement with measurement that we found previously and with measurements of (riess1998, perlmutter1999, tonry2003 and knop2003). Moreover, this analysis rests on a batch of data completely independent of the preceding analyses, by considering a new estimator of distance (magnitude in the filter U to the maximum).

The errors here are dominated by the measuring accuracy the magnitude out of U to the maximum (0.04 and 0.07 magnitude for both supernovæ most remote) and uncertainty over the value of the factor of spreading out (0.08 and 0.04 for 2001gn and 2001gy).

Figure 10.21: The batch of supernovæ close and remote in in the diagram of variation to the model of universe empties for 4 models of universe. (see figure 10.5 for more precision.)