Expansion of Universe?

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I thought I understood this but now question my understanding...........

I don't know how to be explicit with this question in fewer words. Any hel=
p in showing where I'm thinking wrong appreciated.

Suppose humans had been monitoring the universe for 3 billion years now. =
=20

So, we had records from an age of say, 10.7, 11.7, 12.7, and now, 13.7 bill=
ion years, where each of those were the observed age of the universe to the=
CBR veil, beyond which we cannot observe optically. So we have 3 billion =
years worth of observational data forming 4 data points for the distance to=
the CBR, and, galaxies that formed from the ancient CBR gas.

Hopefully the following helps illuminate my error:

At universe age 10.7E9 years, first data point, the light reaching us from =
the CBR would have traveled, well, 10.7E9 years in time and would have trav=
eled 10.7E9 Lyr distance to reach us.

At age 11.7E9 years, the light from the CBR would have traveled for 11.7E9 =
years. And, light from the CBR a billion years earlier would have now form=
ed into infant galaxies, 1 billion years old. Light from those galaxies wo=
uld have traveled 10.7E9 light years to reach us.

At 12.79E9 years age of the universe, the light from the CBR would have tra=
veled for 12.79E9 years to reach us, and we would see galaxies from the pre=
vious two epochs, now at universe age 1 billion and 2 billion years old. T=
he light from those galaxies would have traveled 11.7E9 and 10.7E9 years to=
reach us.

Finally, today, we observe the CBR as having come from the last scatterings=
of the big bang when the universe became transparent about 13.7E9 years ag=
o and we today call that the age of the universe. =20

We would still observe the evolution of galaxies that formed out of the CBR=
gas from epoch 1, 2, 3....with today being epoch 4.

The young galaxies observed would have emitted their light 10.7E9, 11.7E9, =
and 12.7E9 years ago.

The problem is, the galaxies at 10.7E9 light years away haven't moved in ra=
dial distance over the 3 billion years of observations.

What's wrong?

In article ,
writes:

So, we had records from an age of say, 10.7, 11.7, 12.7, and now, 13.7 bill
ion years, where each of those were the observed age of the universe to the
CBR veil, beyond which we cannot observe optically. So we have 3 billion
years worth of observational data forming 4 data points for the distance to
the CBR, and, galaxies that formed from the ancient CBR gas.

Finally, today, we observe the CBR as having come from the last scatterings
of the big bang when the universe became transparent about 13.7E9 years ag
o and we today call that the age of the universe.

We would still observe the evolution of galaxies that formed out of the CBR
gas from epoch 1, 2, 3....with today being epoch 4.

The young galaxies observed would have emitted their light 10.7E9, 11.7E9,
and 12.7E9 years ago.

The problem is, the galaxies at 10.7E9 light years away haven't moved in ra
dial distance over the 3 billion years of observations.

What's wrong?

At least two things. First, you need to understand the difference
between light-travel--time distance (which rarely makes sense as a
distance in cosmology) and proper distance. (There are other types of
distance as well: luminosity distance, angular-size distance,
proper-motion distance.) For proper distance, do you mean the value now
or when the light was emitted? Add to that the fact that the observable
quantity is the redshift, which is related to the scale factor
(independent of the cosmological model). Distance (whichever you
choose) as a function of redshift depends on the cosmological model.
Throw in some non-Euclidean geometry. It's complicated. Read the
literature. There is no point in trying to calculate something, much
less propose something new, if you don't understand the foundations.
You also seem to be confusing three things: the Hubble radius, the CMB,
and the particle horizon. Unless you understand what the Hubble radius
and the particle horizon are and how they evolve with time, it's pretty
much impossible to answer your question.

Again: Take off a few months, read Harrison, UNDERSTAND Harrison, and
come back if you are still confused.