my question is simple. let me lay it out. the furthest galaxies we have imaged are say 13.2 million light years away. this is evidence that galaxies were forming just half a billion years after the big bang. therefore we are seeing them in the past just 500 million years after the big bang.
but, how did they get 13.2 billion light years away in just 500 million years?
I do finally know the answer to this question, but what i would really like is an astrophysicist to show me some numbers to back it up.
No, we were much closer together than 13 Gly (billion light years) when the universe was only a few hundred million years old. The universe has been expanding as the light we are seeing now was travelling, and we are much farther away now.
The following results for galaxy GV-z11 were obtained by numerically solving for time and distance versus redshift using the Einstein and Friedmann equations of the Lambda-CDM model with FLRW metric (see EJN's post above), following David W. Hogg, "Distance Measures in Cosmology," 2000.
Inputs for the calculations are the following.
z = 11.09 (redshift of galaxy GN-z11)
Planck 2015 Parameters (normalized to critical density, 3 Ho^2 / 8 Pi G)
Ho = 67.74 km/s-Mpc (Hubble parameter now)
OmegaM = 0.3089 (total matter density, baryon + dark matter)
OmegaR = 0 (radiation density is now negligible)
OmegaK = 0 (curvature, assuming flat universe)
OmegaL = 0.6911 (dark energy density, or cosmological constant)
Results of the model using above parameters are as follows.
Age of universe now (Gyr): 13.80
Age of universe then (Gyr): 0.410
Horizon of universe now (Gly): 46.26
Horizon of universe then (Gly): 3.83
Distance of source now (Gly): 32.19
Distance of source then (Gly): 2.66
Light travel time (Gyr): 13.39
Note that distances above are the line-of-sight or longitudinal comoving distance. They are equivalent to the proper distance or space-like separation at the given time.
A google search on "cosmological calculator" should lead to several web pages that will produce similar results using these same inputs. Slightly different numbers will result from other Hubble parameter values, densities, etc. that are often used.
Note that I'm a retired phycisist, but only an "armchair astrophysicist," and you did ask for numbers.
Edited by gvk, 22 October 2018 - 07:37 PM.