How can you determine distances to obejcts further away than 13.72 billion light years?

Question

I was checking out this calculator where you can calculate distance to distant astronomical objects from redshift.

Here are some values:

z=0.1 > distance (light travel time) 1.31 billion lightyears

z=0.5 > distance 5.093 billion light years

z=1.0 > distance 7.817 billion light years

z=2.0 > distance 10.404 billion light years

z=4.0 > distance 12.162 billion light years

z=8.0 > distance 13.075 billion light years

z=20 > distance 13.54 billion light years

z=100 > distance 13.704 billion light years

z=1000 > distance 13.72 billion light years

Basically, even if something is infinitely redshifted, using the formula to get distance from redshift that cosmologists use, it will not reside further away than 13.72 billion light years.

Obviously according to reigning theory we should not be able to find something more distant than 13.8 billion light years away.

However, if there is something wrong with the model and there are galaxies out there who sent out the light we now observe for more than 13.72 billion light years we will not be able to identify them using the standard "distance as a function of redshift" formula.

Question: Are there other methods for estimating the "light travel time" that could help identifying hypothetically existing highly redshifted objects/galaxies who sent out the light we now see for more than 13.72 billion years ago?

Answer 1

It doesn't make sense to treat the light travel time times $c$ as a distance when the light travel time is large, because of spacetime curvature.

In a comment you implied that you want to know the distance from the object at the time it emitted the light, rather than the distance now. In that case, it would make the most sense to use the angular size distance, which is also reported by Wright's calculator.

There is no way to determine the light travel time from a telescope image, but you can measure angular size, and from that and the linear size you can calculate the angular size distance. Comparing it to a theoretical prediction is a possible test of the model. I think it is a weak test because there is a lot of uncertainty in the estimation of linear size, but I don't know much about it.