# Velocity Cone in expanding universe

1. Nov 15, 2013

### say_cheese

The figures in
http://www.astro.virginia.edu/class/whittle/astr553/Topic16/t16_light_cones.html
are very useful in understanding the various world lines in concordant diagrams. Is there any easy way to see how a velocity cone (at the observer's worldline) from a later time than the Big Bang look like?

Is there any easy way to understand why the light cone has a steep (>2c) slope? Is it the 66.18c that we see in http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html at early time.

In Cosmology, The Science of the Universe, two velocity cones are given, but the later cone seems to be steeper at the beginning.

I guess I am also asking if there is an excel sheet or a program to make the concordance diagram from the conformal time diagram.

2. Nov 15, 2013

### marcus

Those are nice figures by Prof. Whittle. I especially like the top one. If you want to connect Whittle's figure to Jorrie's calculator you first remember that the stretch factor S = 1+z.
Whittle says that a galaxy whose light comes in stretched by factor S = 1.7 (aka z = 0.7) was receding at v = c/2, when it emitted the light we are now getting.
A galaxy with S = 5 (aka z=4) or slightly more was receding at v = 2c, when it emitted the light.

Do you see that information in the figure?

Let us know if you do not see that information displayed in the figure. I or someone else can help you look for it.

Whittle's figure was dated sometime in 2011 so it cannot be using the very latest 2013 model parameters,but it should give approximately the same figures as Jorrie's calculator, so lets compare.

YES! REMARKABLY CLOSE! I ran Jorrie's calculator between S=5 and S=1.7 selecting WMAP data (the older data set) rather than Planck.
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14&16.5&3300&69.8&0.72&0.28\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.200&5.000&1.5689&2.3408&23.932&4.786&7.948&1.71&2.04\\ \hline 0.214&4.670&1.7370&2.5874&23.120&4.951&8.336&1.65&1.91\\ \hline 0.230&4.340&1.9372&2.8795&22.220&5.120&8.762&1.59&1.78\\ \hline 0.249&4.010&2.1785&3.2292&21.213&5.290&9.232&1.52&1.64\\ \hline 0.272&3.680&2.4737&3.6529&20.080&5.457&9.752&1.43&1.49\\ \hline 0.299&3.350&2.8408&4.1727&18.792&5.610&10.328&1.34&1.34\\ \hline 0.331&3.020&3.3063&4.8193&17.312&5.733&10.967&1.24&1.19\\ \hline 0.372&2.690&3.9102&5.6342&15.593&5.797&11.673&1.11&1.03\\ \hline 0.424&2.360&4.7143&6.6721&13.569&5.750&12.448&0.97&0.86\\ \hline 0.493&2.030&5.8176&7.9986&11.157&5.496&13.283&0.80&0.69\\ \hline 0.588&1.700&7.3840&9.6696&8.252&4.854&14.152&0.59&0.50\\ \hline \end{array}}$$

You can see it agrees very closely!

It says Vthen = 0.5 where Whittle says c/2
and it says Vthen = 2.04 where Whittle says 2c.

The differences are probably due to slight differences in the choice of cosmic model parameters. But they are negligible. Essentially everybody is using the same equations.

You can also see in Whittle's figure that the recession speed v = c comes around redshift z = 1.7, which is a wavelength enlargement factor of S = 2.7. Well look at the row labeled S = 2.69 Almost exactly v=c.

Whittle has some very nice course materials! thanks for calling them to our attention.

Last edited: Nov 16, 2013
3. Nov 16, 2013

### say_cheese

Thanks. I do see the figures and see the agreement with Jorrie's calculator. Great!