Does the pattern of CMB anisotropies change over cosmic time? Currently, the Universe is about 14 billion years old, and we now see a certain pattern of anisotropies in the cosmic microwave background (CMB).
If we wait another 14 billion years, and repeat the observations, will that pattern change measurably?
I realize that the peak frequency / representative temperature change with the cosmic expansion. My question here is specifically about how the anisotropy pattern may or may not change over cosmic time.
 A: The CMB is sometimes referred to as an image of the last-scattering-surface. The photons reaching us now were last scattered at the time the Universe cooled enough for electrons to bind to protons and became largely transparent. However, this is only a "surface" in the sense that the photons reaching us now all have the same travel time and come from the same distance. At different times, the photons arrive from different distances. Since the entire Universe became transparent at roughly the same time, it's perhaps helpful to think about a last scattering "volume", which fills the entire Universe. At the time of last-scattering, the surface would be immediately surrounding the Earth (well, the matter that would eventually form the Earth, since it didn't exist yet), and move outwards with time to reach its present distance. The "last-scattering-volume" has, of course, hotter (underdense) and cooler (overdense) regions, scattered in 3D space, so as the last-scattering-surface intersects different slices through the volume, the pattern changes smoothly. The statistics of the pattern should remain the same, though, at least assuming what we think we know about cosmology.
There are other late time effects as well. For instance, the CMB is gravitationally lensed by large scale structure, notably galaxy clusters. As CMB photons arriving later will have crossed more evolved structure, they will be more strongly lensed, which will introduce a stronger overall distortion in the pattern. Or there's the Sunyaev-Zel'dovich effect, which is the net boost that CMB photons crossing regions of high relativistic electron density (i.e. galaxy clusters) get. Photons arriving later cross more & bigger clusters (at least until dark energy suppresses structure formation), so the SZ effect is enhanced.
A: The CMB is a snapshot from the time of photon decoupling , at about 380.000 years, and its discovery was crucial in establishing cosmological models. The photons in the CMB have not interacted since then. The ones that interacted by scatters with matter, are out of the CMB photons recorded.
At that time its energy was very high and with the continuous expansion has arrived at the 3K we observe now. In the present Big Bang model, the anisotropies would have been the same at any time recorded after that, only the temperature fitted would be diminishing along the time axis. This should hold true for this type of models in future times, as the CMB would still be recorded from photons that have not interacted since the decoupling, so the snapshot will be the same. 
There exist other models for the end of the universe, and one would have to go to their mathematical predictions to see how the energy would change, but I expect no change in patterns there either.
