According to Einstein, the universe is a space time continuum that can take one of three forms, determined by the amount of matter and energy it contains.  A universe that is a continuum is an infinite universe.  It is a universe that lacks a beginning and it will never end.  This is the very definition of a continuum.  Only substances that are finite can endings be predicted, thus when the universe is described as having a beginning we should hear second about its predictable ending.   Things that are finite are predictable, such as the elements and radioactive decay. 

Can the universe change shape?  Yes, according to Einstein's equation E=MC^2.  The shape of the universe is determined by the amount of matter and energy it contains.

The possible shapes are as follows:

1. Positive curvature: The cosmos is like a sphere.  Travel far enough and you'll come back to the starting point.  Draw a triangle, and it will have more than 180 degrees.  Without dark energy, this universe will slow, stop and recollapse, with dark energy, the expansion will continue.
2. Flat: You'll never return to your starting point: triangles have precisely 180 degrees, as they do in geometry.  Even without  dark energy, this universe will expand forever, out more and more slowly all the time.  With it, the expansion gets even faster.  This is the shape of our universe according to the latest observations
3. Negative Curvature: Travelers never return: triangles always have less than 180 degrees.  And expansion will barely slow, even without dark energy. 

When the ratio of Matter to energy changes in the Universe, then the Universe can change Shape.

1. Positive curvature:  Ratio of Matter is much greater than energy
2. Flat:  Ratio of Matter to energy is about equal
3. Negative Curvature:  Ratio of Mater is much less than energy (More energy and less mass)