Lightcone 1.0 tabular cosmology calculator

[marcus]

New release of Jorrie's tabular calculator.
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone1.0/LightCone.html

this is clearly the best on-line cosmology calculator for the general user on the web.
Hands down.

Lightcone rules. that's all there is to say. Check it out.

to get column definitions and explanations of the various quantities being tabulated (scale factor, Hubble radius R, proper distance now D, and then D_then
just click the button that says "show column setup"

when you know the information therein, click the same button which now says "hide column setup"

Congratulatons Jorrie. Great job!

==================

PS the D_then column sketches the proper distance outline of the past lightcone. Gives its radius at each stage of past history. So the tabulator's name is appropriate. That column is of central importance. All the galaxies we are now seeing live on that lightcone (which because of expansion has its own distinctive non-conical shape.)

 

[Mordred]

The new Planck vs WMAP option setting is particularly handy as it allows one to compare how the difference in the values affect the light cones. As there is new changes please report any browser related errors to Jorrie. The more PF members we can get testing various browser, phones and mobile devices. Yes it works on these as well the better chance Jorrie has on maximizing the flexibility of usage.

 

[Mordred]

The new tool tips and columns really helps in usage. I took one of Marcus previous examples and tried to narrow down just how long the Universe was close to static. This is the period when the matter/dark energy was close to being balanced.

First I kept the inputs as default, turned all my column selections on, increased the number of decimal places to 6 and set steps at 100. Click calculate.

then I looked for the period of time where A R^o was lowest. This showed around 7.4 to 7.8 G yr.

I looked over on the S column and picked two S values surrounding that period in time. In this case 1.68 which I set for S_upper, S_lower I set for 1.64. As I didn't need as many rows I set steps to 30.

Between S 1.653333 and 1.650667 A R⁰ is the smallest values. so the universe was almost balanced for a very short period of time cosmologically speaking. Roughly 200 million years.

to post on the forum I simply click PF format tab. then click calculate and then copy the results and post on the forum.

$${\scriptsize \begin{array}{|c|c|}\hline R_{0} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.92&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize \begin{array}{|r|r|} \hline S=z+1&a=1/S&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&a'R_{0} \\ \hline 1.680000&0.595238&7.425739&9.821697&8.187321&4.873405&14.687083&22.664831&0.872703\\ \hline 1.678667&0.595711&7.433501&9.829625&8.174286&4.869511&14.690984&22.690599&0.872692\\ \hline 1.677333&0.596184&7.441368&9.837561&8.161085&4.865512&14.694792&22.716505&0.872681\\ \hline 1.676000&0.596659&7.449143&9.845502&8.148050&4.861605&14.698704&22.742355&0.872671\\ \hline 1.674667&0.597134&7.457022&9.853451&8.134849&4.857593&14.702524&22.768345&0.872661\\ \hline 1.673333&0.597610&7.464908&9.861406&8.121648&4.853575&14.706351&22.794376&0.872652\\ \hline 1.672000&0.598086&7.472702&9.869366&8.108612&4.849648&14.710282&22.820350&0.872644\\ \hline 1.670667&0.598563&7.480600&9.877334&8.095411&4.845617&14.714120&22.846464&0.872636\\ \hline 1.669333&0.599042&7.488505&9.885309&8.082210&4.841579&14.717964&22.872620&0.872628\\ \hline 1.668000&0.599520&7.496417&9.893290&8.069008&4.837535&14.721815&22.898818&0.872621\\ \hline 1.666667&0.600000&7.504334&9.901278&8.055807&4.833484&14.725671&22.925058&0.872615\\ \hline 1.665333&0.600480&7.512259&9.909272&8.042605&4.829427&14.729534&22.951340&0.872609\\ \hline 1.664000&0.600962&7.520189&9.917273&8.029404&4.825363&14.733403&22.977664&0.872603\\ \hline 1.662667&0.601443&7.528126&9.925280&8.016202&4.821292&14.737278&23.004031&0.872599\\ \hline 1.661333&0.601926&7.536070&9.933293&8.003000&4.817215&14.741159&23.030440&0.872594\\ \hline 1.660000&0.602410&7.544119&9.941314&7.989633&4.813032&14.744947&23.056990&0.872591\\ \hline 1.658667&0.602894&7.552075&9.949341&7.976432&4.808942&14.748841&23.083484&0.872588\\ \hline 1.657333&0.603379&7.560038&9.957374&7.963230&4.804845&14.752740&23.110021&0.872585\\ \hline 1.656000&0.603865&7.568106&9.965414&7.949863&4.800642&14.756547&23.136700&0.872583\\ \hline 1.654667&0.604351&7.576082&9.973461&7.936661&4.796531&14.760459&23.163322&0.872582\\ \hline 1.653333&0.604839&7.584164&9.981514&7.923294&4.792315&14.764278&23.190087&0.872581\\ \hline 1.652000&0.605327&7.592252&9.989573&7.909927&4.788091&14.768102&23.216895&0.872581\\ \hline 1.650667&0.605816&7.600247&9.997639&7.896725&4.783961&14.772033&23.243647&0.872581\\ \hline 1.649333&0.606306&7.608348&10.005712&7.883358&4.779724&14.775871&23.270541&0.872582\\ \hline 1.648000&0.606796&7.616456&10.013791&7.869991&4.775480&14.779714&23.297480&0.872583\\ \hline 1.646667&0.607287&7.624570&10.021876&7.856624&4.771229&14.783564&23.324462&0.872585\\ \hline 1.645333&0.607780&7.632691&10.029968&7.843257&4.766971&14.787420&23.351487&0.872588\\ \hline 1.644000&0.608273&7.640819&10.038066&7.829890&4.762707&14.791282&23.378557&0.872591\\ \hline 1.642667&0.608766&7.648953&10.046171&7.816523&4.758435&14.795151&23.405670&0.872594\\ \hline 1.641333&0.609261&7.657093&10.054283&7.803156&4.754157&14.799026&23.432828&0.872599\\ \hline 1.640000&0.609756&7.665341&10.062400&7.789624&4.749771&14.802807&23.460130&0.872604\\ \hline \end{array}}$$

 

[marcus]

Great use of Lightcone! It looks like you have found the inflection point in this graph
http://ned.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg
that is the place where the slope stops declining and starts to increase.
You have found that it happens around year 7.600 billion

In the row labeled S=1.650...

For people who aren't familiar with the idea of an inflection point, look at the heavy solid curve in "Figure 14" I linked to and judge by eye where you think the curve changes from convex to concave. It is hard to see exactly but it is very easy to see in the table, because the rightmost column is actually proportional to the slope of the curve!

Up to year 7.6 billion the slope is decreasing, then it reaches a minimum and starts to increase (so it begins to look like "acceleration" and have more resemblance to exponential growth. Thanks Mordred. Definitely an effective use of Lightcone calculator.

 

[Mordred]

Here is the cool part you turn off the rows to make it all easier to see. Also easier to show on the forum.

$${\scriptsize \begin{array}{|c|c|}\hline R_{0} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.92&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize \begin{array}{|r|r|} \hline S=z+1&a=1/S&T (Gy)&a'R_{0} \\ \hline 1.658&0.603136&7.556056&0.872586\\ \hline 1.657&0.603379&7.560038&0.872585\\ \hline 1.657&0.603622&7.564121&0.872584\\ \hline 1.656&0.603865&7.568106&0.872583\\ \hline 1.655&0.604108&7.572093&0.872582\\ \hline 1.655&0.604351&7.576082&0.872582\\ \hline 1.654&0.604595&7.580172&0.872581\\ \hline 1.653&0.604839&7.584164&0.872581\\ \hline 1.653&0.605083&7.588157&0.872581\\ \hline 1.652&0.605327&7.592252&0.872581\\ \hline 1.651&0.605571&7.596248&0.872581\\ \hline 1.651&0.605816&7.600247&0.872581\\ \hline 1.650&0.606061&7.604346&0.872581\\ \hline 1.649&0.606306&7.608348&0.872582\\ \hline 1.649&0.606551&7.612451&0.872582\\ \hline 1.648&0.606796&7.616456&0.872583\\ \hline \end{array}}$$