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. 


Thread Tools  Display Modes 
#1




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 rearranging 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 rearranged 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? 
Ads 
Thread Tools  
Display Modes  


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 