LightCone Tutorial

1. Getting Started

1.1 Introduction

This tutorial is about the LightCone Tabular Cosmological Calculator for the present 'best-buy' Lambda Cold Dark Matter (LCDM) cosmological model. The LCDM model deals with the large scale dynamics of the cosmos, starting just after (and not including) the earlier possible inflationary phase, which is taken to end at T=0.

The calculator itself deals from a time when the observable universe was 20 thousand times smaller than today (around T=2000 years) and then up to when the observable universe will be 100 times larger than today, around T=89 billion years, 76 billion years into the future. The actual portion we can observe optically today is from when it was 1090 times smaller than today, some 13.75 billion years ago.

In the calculator we denote this size ratio by the parameter S (for Stretch); it means that distances (and wavelengths of photons) have been stretched by S=1090 times since it left the farthest area that we can see; the photons are called the cosmic microwave background (CMB) radiation. Before that time, the cosmic 'soup' was too hot to be transparent. For more description, see the page: LightCone-UserGuide.

1.2 First Hands-on

When you open LightCone, you will be shown a screen that includes this portion (the basic inputs required).

If you have not yet done so, open the real calculator and read the question bullets by simply hovering the mouse over them. If you need more information, read the LightCone-UserGuide. In this tutorial we will concentrate on hands-on exercises.

The calculator is reasonably intuitive and somewhat self-explanatory. Click on a few buttons near the top (i.e. Intro, WMAP, Planck, Calculate) and see what happens. Click and type in a new value for Hubble radius now, watch how the conversion change when you click outside the input box. Then click Calculate and you should get an output table with slightly different values. Play around with the top three input boxes first. Then click Reset Input to restore the original values.

The next three input values controls the "Stretch" range that you want in your table. Read their bullets and play around with Supper, Slowerand Sstep. Then Calculate and repeat until you are comfortable with their effects. As S is the first column, its range and number of steps controls the values and vertical size of the table that you will get.

Next, read the bullet of the Display As: block. Click some of them and then click Calculate. What comes out may look a bit weird, but fortunately you do not have to read what's in there. It is just for copying tables to other places, like to this Wiki. We will later return to the Chart button; it is a fairly advanced feature and needs more explanation than the others.

Now to some more immediately useful stuff. Read the bullet of the 'Column definition and selection' button and then click the button. You will see the following three color-coded groups of setup blocks. They are loosely grouped per parameter type.

Some are brightly colored and some are greyed out. The bright ones represent the 'Basic' set of output columns that is shown on start up. The ticked boxes are green, while the greyed out ones have red crosses for 'not ticked'. Clicking on the tick marks toggle them from 'ticked' to 'not ticked'. Click Calculate to see the effects on the displayed columns.

Before going further, you should read the bullets (bottom right corner) of at least the Basic set of column blocks. Lastly, the decimals box allow you to control the number of decimal points displayed in each column, ranging from 0 to 9. The little radio buttons in the top row have to do with the Chart option. More about that later.

Tick the 'Keep Open' box in the white space and then play around: un-tick some ticked boxes, tick some un-ticked boxes and then Calculate to see the effect on the columns displayed. The names of the buttons in the bottom-right corner are self explanatory.

2. Practical

2.1 First Practical

Click the Reset Input button and select None in Column definition and selection. Then select only the columns that you see in this table.

Find the row that represents a source (say a galaxy) for which the wavelength of the light has been stretched by a factor of S=3.208. Now read off the time when the observed light has left that galaxy. It is T=2.9777 Gy (billion years). Since the time today (at S=1) is near 13.8 Gy, it means that light has traveled for near 11 Gy to reach us. Does this mean that the galaxy is about 11 billion light years from us? Not quite. During the time that the light was on its way, distances have been stretched by a factor 3.208. If we could stop the expansion today and somehow measure the distance to that galaxy, we would have found the distance to be Dnow = 18.248 Gly (billion light years). If we divide this by the stretch factor S=3.2, we get the distance Dthen = 5.688 Gly.

We obviously have 10 rows here, giving a very, very broad overview of distance versus time covering more than 13 billion years of the past and almost 80 billion years of the (possible) future of our universe. A real "Gods-eye" view.

We will leave the other distance categories and the recession speed categories for later and next zoom in at specific epochs in the past.

2.2 Zooming In

Let us say we want to know the time when all observable galaxies was half their present distances from us. The calculator has a nice feature that it can produce just one row - click and enter 2 into the Supper input box and enter 0 for the number of steps. Clock Calculate. S=2 means that all distances have doubles since the light has left the source.

What time do you find? Yes, 5.86 billion years, rounded. This means that the light from that galaxy took 13.78-5.86=7.93 billion years to reach us. As we stated above, it did not cover 7.93 billion light years, though - the distance started out smaller (then) and eventually grew larger (now). You can see that clearly in the Dnow and Dthen columns.

Now let's do a bit of fancy zooming and try to obtain a row that corresponds to the formation of the Solar system, some 4.6 billion years ago. the first thing to do is find out the cosmic time T at that stage. Near the middle of the Conversions table above, you see the Present time, 13.787 Gy. Round it to 13.8 and then subtract the 4.6 from it, giving us the rounded cosmic time when the Solar system formed, T= 9.2 Gy. In the table in section 2.1, you will see that there is no row with that T attached to it, but it must be between the row with S=3.208 and S=1.000. Put these into Supper and Slower in the input section and click Calculate. This table will result:

The fourth row from the bottom gives T=9.2287 Gy, which rounds to what we want: 9.2 Gy. We can obviously zoom in further is we want to be more accurate, but for now, this is fine.

More to follow.

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