A Space & astronomy forum. SpaceBanter.com

If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post: click the register link above to proceed. To start viewing messages, select the forum that you want to visit from the selection below.

Go Back   Home » SpaceBanter.com forum » Astronomy and Astrophysics » Research
Site Map Home Authors List Search Today's Posts Mark Forums Read Web Partners

easy(?) cosmology question: what to integrate to get R(t)

Thread Tools Display Modes
Old January 20th 20, 12:05 AM posted to sci.astro.research
Phillip Helbig (undress to reply)[_2_]
external usenet poster
Posts: 273
Default easy(?) cosmology question: what to integrate to get R(t)

When discussing Friedmann models, the usual approach is to start with
the Friedmann equation then express dr/dt as a function of R, Omega,
lambda, and so on, then re-arranging it to get an expression for dt as a
function of R (scale factor), Omega, and lambda, which can be integrated
to give the lookback time (or time since the big bang) as a function of
the scale factor. This can be re-arranged to express it as a function
of redshift, then one can compute distances as a function of redshift
and so on.

This is standard stuff.

But what about an expression which one can integrate to get R(t), the
scale factor as a function of time?

For special case, one can invert t(R) to get R(t). Of course, if I
numerically calculate t(R), I can invert it to get R(t). But what I
would like is an expression for dR as a function of t which I can
integrate from 0 to t to get R(t), just like I have an expression for dt
as a function of R which I can integrate from 0 to R to get t(R).

Does such a thing exist?

Formally, dR/dt = f(R;Omega,lambda) (with H as a scale factor). The
usual approach is then dt = dr/f, which I can integrate from 0 to R to
get t, which is fine because f = f(R). Algebraically, I can also write
dR = f(R)dt, but I can't integrate it from 0 to t to get R, since f is a
function of R, not of t.

Another way to ask the question: I give you arbitrary Omega
(Omega_matter) and lambda (Omega_Lambda) and ask you to make a plot of
R(t). How would you do it?

I'm pretty sure that one can do it with Jacobian elliptic functions
(essentially the inverse functions of Legendre elliptic integrals).
This is more elegant, and faster, but more difficult to implement.
However, I want something simpler: a function which I can integrate
numerically to get R(t) for arbitrary lambda and Omega. Any ideas?
Old April 30th 20, 06:56 PM posted to sci.astro.research
[email protected]
external usenet poster
Posts: 24
Default easy(?) cosmology question: what to integrate to get R(t)

Analytic solution comes in parametric form which contains elliptic
integral of first kind and other part simple trigonometric function.
Analytic solution can be found in my postings in sci.physics.relativity.
I don't remember date when I posted it, it was couple years ago. (my old
email was ).

Best Regards, Hannu Poropudas


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
One easy question Gerald Kelleher Amateur Astronomy 15 December 22nd 17 04:37 PM
Cosmology question, the metric expansion of space Conrad[_3_] Astronomy Misc 5 May 27th 09 09:33 AM
steady state cosmology question Greg Hennessy Astronomy Misc 0 January 6th 07 11:32 PM
easy question from a newbie Neil Coward Misc 4 March 27th 04 07:58 PM
Cosmology question Denis Taylor UK Astronomy 7 September 26th 03 10:42 AM

All times are GMT +1. The time now is 10:35 AM.

Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.
Copyright 2004-2021 SpaceBanter.com.
The comments are property of their posters.