marcus said:
The "lost to view" is more a matter of redshifting to the point of being undetectable.
That's a side effect of what I meant, yes. The key point is that light emitted by the object will never reach us. See below.
PeterDonis said:
I was also right
.
Here's why. The
proper distance to the Hubble radius continues to increase. But the
coordinate distance to the Hubble radius decreases when the expansion is accelerating (while it increases if the expansion is decelerating). And if we're trying to figure out whether light emitted by a "comoving"object will ever reach another "comoving" object, it's the
coordinate distance (in "comoving" coordinates) that counts.
Let's work this out by hand too. The coordinate distance ##r## is the proper distance ##R## divided by the scale factor ##a##. If we plug in our equation for ##R## at the Hubble radius from post #7, we get
$$
r^2 = \frac{3}{a^2 \left(8 \pi \rho + \Lambda \right)}
$$
So the time dependence of ##r## at the Hubble radius depends on the time dependence of ##a##.
For a matter-dominated universe (that is spatially flat), we have ##a \propto t^{2/3}## and ##\rho \propto a^{-3}##. If we neglect ##\Lambda##, that gives ##r \propto t^{2/3}##, which is increasing with time.
For a dark energy-dominated universe (that is spatially flat), we have ##a \propto e^t## and ##\Lambda## constant. If we neglect ##\rho##, that gives ##r \propto e^{-2t}##, which is decreasing with time.
The reason it's the coordinate distance that matters is simple: a given "comoving" object is always at the same ##r## coordinate. So whether or not that object can send us light signals depends on the ##r## coordinate of the Hubble radius relative to the object's ##r## coordinate. If the ##r## coordinate of the Hubble radius is increasing with time, then "comoving" objects will gradually "come into view" as their ##r## coordinate comes inside the Hubble radius. But if the ##r## coordinate of the Hubble radius is decreasing with time, then "comoving" objects will gradually go out of view as their ##r## coordinate goes outside the Hubble radius.
(If we want to think of things in terms of proper distance, what is happening is that, during the matter-dominated phase, the proper distance to the Hubble radius was increasing faster than the proper distance between "comoving" observers. But during accelerated expansion, the proper distance to the Hubble radius increases
slower than the proper distance between "comoving" observers. Using coordinate distance just makes this easier to see because "comoving" observers are always at the same ##r## coordinate.)
