Is it possible to estimate the number of galaxies in the universe? According to this article the observable universe may contain 2 trillion galaxies.
Assuming we know the large-scale curvature of the universe thanks to standard model of cosmology, can we estimate the number of galaxies in the entire universe based on the number of galaxies in the observable universe?
To put it another way, if you can only observe a small patch of an FLRW spacetime, but enough to estimate the scale factor, you should be able to estimate the total "volume" of the universe, right?
 A: Well, we know that universe may be infinite, and this is compatible with the standard model.  If that is true, and if the cosmological principle is correct (so, for instance, the universe is not mostly empty with only the bit we can see containing galaxies), then the number of galaxies is not finite. So, no, you can't estimate the number: the best you can hope for is to estimate the number we can see.
A: Just to add a couple of comments:
1) The latest data from supernova type Ia measurements indicates that the total density parameter Ωt is slightly greater than 1, about 1.02, indicating a closed universe. This would be consistent with a finite and unbounded topology.
2) The notion that the universe began from a point singularity, the "Big Bang", 13.8 Gyrs ago, is now widely accepted. Thus it was obviously finite in extent at that time. In order for the universe to have evolved to a state of infinite volume requires expansion at infinite velocity, which I maintain is a logical impossibility. For v = dx/dt to be infinite, either dx must be infinite for any value of dt, or dt must be exactly zero and neither one, IMHO, has a reasonable basis in physical reality. Thus to evolve to an infinite universe would mandate a second "creation event" --- no matter how rapid an expansion may be, the resulting volume will ALWAYS be finite.
A: It is incredibly difficult to answer this. First and foremost, there are many factors that need to be assumed such as the life time of a galaxy, the number of stars in a galaxy (correlated to its mass), and what one considers a galaxy. The first thing one can do is look at the CMB and find the energy of the universe by tracing it back to the moment of the big bang. With that energy, you must assume a certain amount is matter and then with that amount, partition that mass into each galaxy. That would give an incredibly rough answer but scientists have not mapped the entire visible universe yet so we cannot yet count the galaxies. 
