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Is there somewhere on the internet I can find cosmological redshift data. In particular, I would like to know the redshift around the time when the acceleration of the Universe began to accelerate.

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  • $\begingroup$ Have you looked at the supernova cosmology project papers? $\endgroup$ – Rob Jeffries Aug 6 '17 at 19:52
  • $\begingroup$ @RobJeffries, I did look at the supernova cosmology project and I was able to get data for distance modulus, but I'm looking for redshift data as a function of time. $\endgroup$ – Chris L. Aug 11 '17 at 15:02
  • $\begingroup$ @ChrisL. If you want that, in particular, you're going to have to do some work to convert things that get measured into a quantity you want. Since that conversion is dependent on the cosmological model, you'll have to figure out how to calculate those quantities using the models you want to test. $\endgroup$ – Sean E. Lake Oct 29 '17 at 16:40
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One of the main places where data about galaxies gets aggregated is the NASA Extragalactic Database (NED). For example, here's the information page for M101 with the default cosmology in their search form. In particularly you want to look at the redshift-independent distances, and the redshift data points. Using the 'Metric Distance' you can calculate the cosmological redshift it would have if it weren't moving (for a given cosmology) by numerically inverting equation 15 from Hogg's cosmology calculations summary paper (probably have to numerically integrate, too).

Note that the peculiar velocity (velocity relative to Hubble flow) is usually around hundreds of kilometers per second. So, for any redshift greater than about $0.01$ (equivalent to a radial velocity of about $3,000\operatorname{km}\operatorname{s}^{-1}$) is almost certainly entirely dominated by the cosmological redshift of the object. There are a lot of databases replete with redshifts of galaxies that stretch back to round $z=1$ for ordinary galaxies, and much further carefully selected galaxies and active galactic nuclei/quasars. For example: Sloan Digital Sky Survey (SDSS), DEEP2, the AGN and Galaxy Evolution Survey (AGES), and Galaxy and Mass Assembly (GAMA). This list is nowhere near complete, of course.

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Redshift of the time when the universe started to accelerate: From Friedmann's equations: $$\dot{a}=aH=H_0\sqrt{\Omega_{m0}/a+a^2\Omega_{\Lambda 0}}$$ required is: $\ddot{a}>0$. Calculation gets you $$a=\left(\frac{\Omega_{m0}}{2\Omega_{\Lambda 0}}\right)^{1/3} \approx 0.6$$ $\rightarrow z=1/a-1 = 0.67$

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