Is the Universe finite or infinite?

How large is the Universe? How do we measure its size? How can we even think of measuring something that is believed to be boundless? The enormity of the Universe may be beyond our comprehension, but measuring its size is not. Our measuring sticks are the cosmic microwave background radiation (CMBR) which is relic of the super hot Big Bang radiation cooled down to three Kelvin (-270 degrees Centigrade) with wavelength in the microwave region and cosmological red-shift, increase in the observed wavelength of electromagnetic waves from a receding source.
The size depends on the distinction between “visible” and “observable” Universe. Although there is no general consensus among astronomers about the actual size, one thing they agree on for sure is how far away we can see.
We can argue that if the age of the Universe is 13.7 billion years (see “Universe in age crisis!” TDS July 10, 2012) and since light travels with a finite speed, we can't see anything beyond 13.7 billion light years. (One light year is about six trillion miles.) In reality, we can see lights that were emitted only after the decoupling epoch, a time around 380,000 years after the Big Bang, when radiation broke free from matter and could travel through space unimpeded.
The maximum distance light can travel since the birth of the Universe defines the “cosmic horizon.” Astronomers use the distance to the horizon as the radius of the visible Universe with Earth at the center. It is also known as the Hubble Length and is 13.7 billion light years. But is it really the size of the Universe?
Calculating the size of the Universe is a little tricky. Let us start with the premise that Big Bang is the correct theory of the origin of the Universe. The theory posits that the Universe, born out of a tremendous explosion from an infinitesimally small volume, is undergoing expansion at a rapid rate. It was, however, an explosion of space; not an explosion into space. Consequently, the Universe does not have an "edge" where space just runs out. Hence the cosmic horizon is a boundary in time, not in space. It still lies at the beginning of time - the moment of Big Bang. It exists because we cannot see back to a time before the Universe was born.
As the Universe is expanding at high speed in all directions, the most distant objects we can see were once much closer to us. The recession speed of stellar objects, according to Edwin Hubble, is directly proportional to their distance from us. He also noted from cosmological red shift that farther a galaxy is from us, faster it is moving away from us.
Thus the cosmic horizon is continually expanding outward and the observable Universe is growing larger in radius with each passing second. This implies that since the birth of the Universe, distant stars and galaxies have been pushed away from us far beyond the distance of 13.7 billion light years. The observable Universe, therefore, is much bigger than the visible Universe. The radius of the observable Universe is also referred to as the “comoving distance” because it is increasing with time.
What then is the radius of the Universe today? The answer is given by our measuring sticks cum cosmic storytellers, red shift and CMBR. Without going into the nitty gritty of calculation, they tell us that because of accelerated expansion, it is 94 billion light years across putting the edge of the observable Universe 47 billion light years away from us. Whatever the size is, thanks to the inflationary Universe; it increased our observational power to the extent that we can see or have seen things that are now at least 47 billion light years away from us in all directions.
“Two things are infinite: the Universe and human stupidity; and I'm not sure about the Universe.” Albert Einstein.