[gnuastro-devel] [task #14689] faster ageofuniverse in cosmology library + other cosmo extensions

[Boud Roukema]

URL:
  <http://savannah.gnu.org/task/?14689>

                 Summary: faster ageofuniverse in cosmology library + other
cosmo extensions
                 Project: GNU Astronomy Utilities
            Submitted by: boud
            Submitted on: Tue 03 Oct 2017 02:53:24 PM UTC
         Should Start On: Tue 03 Oct 2017 12:00:00 AM UTC
   Should be Finished on: Tue 03 Oct 2017 12:00:00 AM UTC
                Category: Libraries
                Priority: 5 - Normal
              Item Group: Enhancement
                  Status: In Progress
                 Privacy: Public
        Percent Complete: 20%
             Assigned to: boud
             Open/Closed: Open
         Discussion Lock: Any
                  Effort: 0.00

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Details:

See https://bitbucket.org/broukema/gnuastro/branch/cosmo-dev
for a proof-of-concept of a 100x speed up for Universe ages.
It's a bit hacked but enough to get started on
improving the cosmo functions, I think.

I get the output from commit dd4443a :

ageofuniverse benchmark: old 1.81705  new 0.013959, old/new 130.17
0.815234


I don't think we'll get much of a speed-up in proper distances
compared to https://arxiv.org/abs/1702.0886 (ignore the comments
there about luminosity distance being the main distance; it's
main in terms of observational analysis, but proper distance
is simpler in terms of the FLRW models.)

We would need an analytical integral of (sinh x)^(-2/3), because
d_{radial_comoving} = \int c dt/a(t) - see
http://ned.ipac.caltech.edu/level5/March02/Sahni/Sahni3_2.html

The best that
https://en.wikipedia.org/wiki/List_of_integrals_of_hyperbolic_functions
suggests
would be to rewrite it in terms of \int (sinh x)^(4/3) , which
wouldn't help much. :P

We can implement what looks best for proper distances after re-reading
1702.0886.

The non-flat cases should be added too. 




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