I was listening to one of Leonard Susskind's cosmology lectures. He talks about the factor K having values of +1/0/-1 corresponding to positive/flat/negative curvature. We don't know what the real value of K is. But then as he discussed K at the big bang and K now, it seemed that he was saying that whatever the answer, K was the same then and now. My question: Is there any reason why the curvature of space should be constant in time?