In the limit
Note that no actual infinite limits are required. Just large but finite distances.
I have no prior that says this is a problem
I think you should have. One of three problems, depending on what you expect to happen. (1) If you expect something more complicated to happen for large distances, your theory is more complicated than it initially looks. Doesn't your prior favour simpler theories? (2) If you expect the frequency to pass through zero and continue, your theory will have to (2a) explain what negative frequencies actually mean, why frequency -f isn't just the same as frequency +f with different phase, why we never see anything with negative frequency, etc., or else (2b) if instead it says that negative frequencies are the same as positive, then explain what happens to the frequency after it crosses zero (gets more negative? then -f isn't the same as +f after all. gets less negative? then what we actually end up is a really weird discontinuity at the zero crossing). Again, all this stuff is extra complexity. (3) If you expect the issue not to arise because nature somehow ensures that light never travels far enough for the frequency to reach zero, then your theory needs to explain how that happens. Extra complexity again.
other terms
This sounds like case 1 above.
Something already does happen for large distances.
That's an observable fact. It's redshift.
What causes it?
The standard answer is expansion, which needs inflation and dark energy and an arbitrary multiverse to do that. Al lthings that make the theory more complicated with distance.
Alternatively, what if light doesn't travel forever?
How would such a reality look if things existed farther away than light could travel?
Is it not exactly what is observed?
What is more complex,
0 frequency photons ceasing to be photons,
or
infinite wavelength photons everywhere n...
I am submitting this on behalf of MazeHatter, who originally posted it here in the most recent open tread. Go there to upvote if you like this submission.
Begin MazeHatter:
I grew up thinking that the Big Bang was the beginning of it all. In 2013 and 2014 a good number of observations have thrown some of our basic assumptions about the theory into question. There were anomalies observed in the CMB, previously ignored, now confirmed by Planck:
http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe
We are also getting a better look at galaxies at greater distances, thinking they would all be young galaxies, and finding they are not:
http://carnegiescience.edu/news/some_galaxies_early_universe_grew_quickly
http://mq.edu.au/newsroom/2014/03/11/granny-galaxies-discovered-in-the-early-universe/
B. D. Simmons et al. Galaxy Zoo: CANDELS Barred Disks and Bar Fractions. Monthly Notices of the Royal Astronomical Society, 2014 DOI: 10.1093/mnras/stu1817
http://www.sciencedaily.com/releases/2014/10/141030101241.htm
http://www.nasa.gov/jpl/spitzer/splash-project-dives-deep-for-galaxies/#.VBxS4o938jg
Although it seems we don't have to look so far away to find evidence that galaxy formation is inconsistent with the Big Bang timeline.
http://www.natureworldnews.com/articles/7528/20140611/galaxy-formation-theories-undermined-dwarf-galaxies.htm
http://arxiv.org/abs/1406.1799
Another observation is that lithium abundances are way too low for the theory in other places, not just here:
http://news.nationalgeographic.com/news/2014/09/140910-space-lithium-m54-star-cluster-science/
It also seems there is larger scale structure continually being discovered larger than the Big Bang is thought to account for:
http://www.sciencedaily.com/releases/2014/11/141119084506.htm
D. Hutsemékers, L. Braibant, V. Pelgrims, D. Sluse. Alignment of quasar polarizations with large-scale structures. Astronomy & Astrophysics, 2014
http://www.sciencedaily.com/releases/2013/01/130111092539.htm
These observations have been made just recently. It seems that in the 1980's, when I was first introduced to the Big Bang as a child, the experts in the field knew then there were problems with it, and devised inflation as a solution. And today, the validity of that solution is being called into question by those same experts:
http://www.physics.princeton.edu/~steinh/0411036.pdf
What are the odds 2015 will be more like 2014 where we (again) found larger and older galaxies at greater distances, or will it be more like 1983?