[bug #65195] CosmicCalculator prevents non-flat FLRW calculations; angular diam dist is generically wrong

[Boud Roukema]

URL:
  <https://savannah.gnu.org/bugs/?65195>

                 Summary: CosmicCalculator prevents non-flat FLRW
calculations; angular diam dist is generically wrong
                   Group: GNU Astronomy Utilities
               Submitter: boud
               Submitted: Tue 23 Jan 2024 06:26:13 PM UTC
                Category: CosmicCalculator
                Severity: 3 - Normal
              Item Group: Output not reasonable
                  Status: None
                 Privacy: Public
             Assigned to: None
             Open/Closed: Open
         Discussion Lock: Any


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Follow-up Comments:


-------------------------------------------------------
Date: Tue 23 Jan 2024 06:26:13 PM UTC By: Boud Roukema <boud>
Commit 4aca51a7 prevents non-flat FLRW calculations (for curvature density
parameter values greater than 1e-8 in absolute value). Although LCDM is flat
by definition, there's not much point excluding non-flat models for general
cosmological analysis (e.g. [1]).

I prepared commit
https://codeberg.org/boud/gnuastro/commit/0b01bb6c3f8373f394badd10beac1dd64dcea0b5
for merging into gnuastro, but the problem is that the current code does not
calculate the angular diameter distance at all: it just divides the radial
comoving distance by (1+z), which is valid in the flat case, but not the
general case.

Here are some examples of commit 0b01bb6c, with cross-checks against _cosmdist
0.3.12_ [2]:

*radial comoving distance:* (agreement)

$ for OmLam0 in 0.1 0.8 0.9; do echo 9 | ./cosmdist -r 0 -m 0.9 -l ${OmLam0} ;
done
6105.05  
6851.35  
6986.83  

$  for OmLam0 in 0.0 0.1 0.8 0.9; do ./bin/cosmiccal/astcosmiccal
--properdistance --oradiation=0.0 --omatter=0.9 --olambda=${OmLam0} --H0=70
--redshift=9; done |& grep "^[0-9]" 
6105.053148
6851.349603
6986.825942


*angular diameter distance:* (disagreement in the hyperbolic and spherical
cases)

$ for OmLam0 in 0.0 0.1 0.8 0.9; do echo 9 | ./cosmdist --angular-diameter -r
0 -m 0.9 -l ${OmLam0} ; done
621.97  
610.51  
498.13  
475.85  
$ for OmLam0 in 0.0 0.1 0.8 0.9; do ./bin/cosmiccal/astcosmiccal
--angulardimdist --oradiation=0.0 --omatter=0.9 --olambda=${OmLam0} --H0=70
--redshift=9; done |& grep "^[0-9]" 
601.956856
610.505315
685.134960
698.682594


In the non-flat cases, cosmdist is correct and astcosmiccal is clearly wrong:
for fixed H0 and Omega_{m0}, the hyperbolic (spherical) case gives a greater
(smaller) one-radian-comoving-arclength (= the areal radius, from "area" +
"al"), and correspondingly (dividing by (1+z)), the angular diameter distance
must be greater or smaller; _astcosmiccal_ only gets this right in the flat
case.

What to do about this depends on how people wish to use _astcosmiccal_ in
practice. For the moment, _cosmdist_ is available for general FLRW
cosmological calculations (not completely general, there are checks that could
still be added), without restricting to the flat case or wrongly calculating
angular diameter distances [2].

[1] Yang, Weiqiang; Giarè, William; Pan, Supriya; Di Valentino, Eleonora;
Melchiorri, Alessandro; Silk, Joseph, PRD, 107, 063509,
https://arxiv.org/abs/2210.09865

[2] https://codeberg.org/boud/cosmdist







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