# Chronology of recessional velocity

1. Jul 3, 2014

### yogi

Does anyone have a reference to a site plotting the cosmological recessional velocity over the time span from the decoupling era to the present (i.e, the recessional velocity profile).

Thanks,

Yogi

2. Jul 3, 2014

### marcus

Sure, the Lightcone calculator can give you either a table or a curve plotted. Bear in mind that in order to have a well defined speed you have to specify some particular distance. The speed will depend on the distance chosen.

Click on the Lightcone link (e.g. in my signature) and when it comes up change Slower to one---that means the table will end with the present. then press calculate.

It is already set, as default value, to start at decoupling (recombination) Supper=1090.

Then to add a column that shows the growth speed of a particular distance, one which has size 14.4 Gly as of today, open the column selection menu and check the box for a'R0, then press calculate again.

If you want it to make a plot of that speed over time, just ask, its easy.

3. Jul 3, 2014

### marcus

Yogi, I did what I suggested you do, but also Unchecked a number of columns to make the table cleaner, not so crowded with other information. This shows the growth speed history of one particular distance, one which today is 14.4 Gly and growing at exactly 1.00 c. But back at recombination time it was smaller by factor 1090 and growing at about 21 c.
So at that time its size was 14.4/1090 Gly.

You will only see the beginnings of exponential growth. If you want to see pronounced acceleration and more recognizable near-exponential growth, then you should include some future in the table. But you asked for recombination up to the present so that is what I've tabulated here.
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&a'R_{0} (c) \\ \hline 0.001&1090.000&0.0004&21.023\\ \hline 0.001&863.334&0.0006&18.232\\ \hline 0.001&683.804&0.0008&15.881\\ \hline 0.002&541.606&0.0012&13.885\\ \hline 0.002&428.979&0.0017&12.180\\ \hline 0.003&339.773&0.0025&10.712\\ \hline 0.004&269.117&0.0036&9.443\\ \hline 0.005&213.154&0.0052&8.340\\ \hline 0.006&168.829&0.0075&7.377\\ \hline 0.007&133.721&0.0107&6.533\\ \hline 0.009&105.913&0.0153&5.791\\ \hline 0.012&83.889&0.0219&5.138\\ \hline 0.015&66.444&0.0312&4.561\\ \hline 0.019&52.627&0.0445&4.051\\ \hline 0.024&41.683&0.0634&3.600\\ \hline 0.030&33.015&0.0902&3.200\\ \hline 0.038&26.150&0.1282&2.845\\ \hline 0.048&20.712&0.1823&2.530\\ \hline 0.061&16.405&0.2590&2.250\\ \hline 0.077&12.993&0.3679&2.002\\ \hline 0.097&10.291&0.5223&1.782\\ \hline 0.123&8.151&0.7414&1.587\\ \hline 0.155&6.456&1.0518&1.415\\ \hline 0.196&5.114&1.4908&1.265\\ \hline 0.247&4.050&2.1099&1.135\\ \hline 0.312&3.208&2.9777&1.026\\ \hline 0.394&2.541&4.1804&0.942\\ \hline 0.497&2.013&5.8131&0.888\\ \hline 0.627&1.594&7.9554&0.873\\ \hline 0.792&1.263&10.6323&0.907\\ \hline 1.000&1.000&13.7872&1.000\\ \hline \end{array}}$$

Last edited: Jul 3, 2014
4. Jul 4, 2014

### marcus

I wanted a plot including some future, so I could show real acceleration, so I changed the S range to be from 10 to 0.1, not so far back into the past. This goes from year 545 million out to around 52 billion.

You can see acceleration kicks in sometime between year 7 billion and year 8 billion. Here are the numbers:
$${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&a'R_{0} (c) \\ \hline 0.100&10.000&0.545&1.757\\ \hline 0.117&8.577&0.687&1.628\\ \hline 0.136&7.356&0.865&1.509\\ \hline 0.158&6.310&1.089&1.399\\ \hline 0.185&5.412&1.370&1.299\\ \hline 0.215&4.642&1.723&1.208\\ \hline 0.251&3.981&2.165&1.126\\ \hline 0.293&3.415&2.716&1.053\\ \hline 0.341&2.929&3.403&0.990\\ \hline 0.398&2.512&4.250&0.939\\ \hline 0.464&2.154&5.286&0.901\\ \hline 0.541&1.848&6.536&0.878\\ \hline 0.631&1.585&8.015&0.873\\ \hline 0.736&1.359&9.728&0.890\\ \hline 0.858&1.166&11.661&0.932\\ \hline 1.000&1.000&13.787&1.000\\ \hline 1.166&0.858&16.069&1.098\\ \hline 1.346&0.743&18.307&1.218\\ \hline 1.553&0.644&20.621&1.367\\ \hline 1.792&0.558&22.988&1.548\\ \hline 2.068&0.484&25.392&1.764\\ \hline 2.387&0.419&27.822&2.019\\ \hline 2.754&0.363&30.269&2.317\\ \hline 3.179&0.315&32.726&2.664\\ \hline 3.668&0.273&35.191&3.067\\ \hline 4.233&0.236&37.660&3.534\\ \hline 4.885&0.205&40.133&4.074\\ \hline 5.638&0.177&42.608&4.699\\ \hline 6.506&0.154&45.084&5.420\\ \hline 7.509&0.133&47.561&6.253\\ \hline 8.665&0.115&50.038&7.215\\ \hline 10.000&0.100&52.516&8.326\\ \hline \end{array}}$$

#### Attached Files:

• ###### recession.png
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Last edited: Jul 4, 2014
5. Jul 4, 2014

### yogi

As always Marcos. another well presented tutorial and much appreciated, Thank You.

Yogi.

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