Here we define a numerical function to compute for the dust+ cosmology. We do not limit it to cases where there is a Big Bang, but rather, if there is loitering, we only require that be greater than the redshift at which we are computing . We do however only consider , relevant to the mean redshift of the Lyman- forest of QSO triplet.
Here is a plot for a dust-only cosmology. Note that varies by less than . over all possible values of .
Again a plot of for a dust-only cosmology, but restricted to the "interesting" range of where varies by less than .
Here a plot of for flat +dust cosmology, which shows much more variation than the dust only models.
Finally plots of for arbitrary +dust cosmology:
or in a different form
In the above plot the yellow lines indicate contours of as indicated, left-to-right. The grayscale gives another inidicator of . Black indicates there is no-Big Bang and the loitering redshift is less than 2.35, so that there really is no redshift 2.35 to measure at. The red line indicates the parameters for a loitering solution; below the red line there is no Big Bang. There is a tiny region (you cannot really see it) between the red line and the black where there is no Big Bang but there is a . The green circle targets the theoretically preferrred flat dust-only model. The blue line indicates the traditional dust-only models, and the aqua line the fashionable flat +dust cosmologies. To the left of the aqua line the universe is negatively spatially curved ("open") and to the right it has positive curvature ("closed"). Below the blue line the cosmological constant is positive, providing positive energy density, while above it is negative.
Here is a closer view of parts of the above plot