Why isn't our universe symmetric? Why were random variations introduced in the spherically symmetric universe after Big Bang which made it non-symmetrical. Since the outcome of a coin toss depend on factors such as torque applied, air resistance etc. By the same logic a spherically symmetric universe should have been symmetrical and the outcomes of quantum processes should have been also same on both the opposite ends.
 A: First off, spherical symmetry isn't really the best description. Cosmological models usually assume that the universe is (approximately) homogeneous and isotropic. That's a higher degree of symmetry than spherical symmetry. Spherical symmetry would normally be used to describe something that has a lower degree of symmetry, so that there is a center. The universe doesn't have a center.
So the question should really be why the universe isn't perfectly homogeneous and isotropic. We don't have any naturalistic principle that prescribes initial conditions for the universe. The perfectly symmetric universe you describe would be a possible set of initial conditions.
Many physicists actually have the opposite feeling compared to yours. They are concerned about the horizon problem, which is that different regions of the universe have the same temperature and other properties, even though they were not in causal contact in the early universe and therefore couldn't come to thermal equilibrium with each other. Inflation gives one possible solution to the horizon problem.
A: Fluctuations of density in the universe naturally become greater with time because matter is attracted to regions that are denser than average, and as a result they get denser still and the other regions less dense. So if there were even tiny density fluctuations in the early universe they would have grown into the density variations we see today - variations like planets, stars, galaxies, clusters, superclusters, etc.
So the question is what caused the original tiny density fluctuations in the early universe? This is one of the (many) issues addressed by the theory of inflation. The density differences were produced by quantum fluctuations in the inflaton field. See the Wikipedia article on primordial fluctuations for more details.
So if the theory of inflation is correct the current inhomogeneities were caused by the uncertainty principle. This is a temptingly plausible explanation, though the theory of cosmic inflation remains only a hypothesis.
