Why is the universe so big?

The size of the universe isn't an accident of its birth, but the result of a process still underway. Since the Big Bang, about 13.8 billion years ago, space itself has been stretching: galaxies aren't fleeing through it, it's the distance between them that grows. Edwin Hubble measured this in 1929 when he observed that distant galaxies recede faster the farther away they are. In 1998, two teams discovered, using supernovae, that this rate is also accelerating, an effect attributed to dark energy.

The age of the cosmos sets a horizon: only light emitted less than 13.8 billion years ago can reach us. But because space has expanded while that light was traveling, the sources that emitted it are now much farther away. That's why the observable universe has a radius of about 46 billion light-years, roughly 93 billion in diameter. That isn't the real size of the universe, but the size of the portion that physics allows us to see.

Nothing suggests the universe ends at that edge. Measurements of the cosmic microwave background, taken by missions like WMAP and Planck, show a flat geometry with great precision, suggesting the cosmos is much larger than the visible portion, perhaps infinite. A phase of inflation in the first fractions of a second would explain why regions so far apart share the same temperature and why space looks so uniform on large scales.

The short answer, then, is that the universe is big because it's old, and because it has never stopped growing.