We don't know for sure. The planet Mercury shrank as its core cooled. We expect the Earth will also shrink a little in the next..say...10 billion years as its core cools. If we use Mercury as a model, it shrank perhaps by 10 kilometers in 5 billion years, so we would expect the Earth to shrink by 1 centimeter in 5000 years or 0.002 millimeters in 1 year. There is no way to measure this to confirm it directly, but you might look for a change in the speed of rotation of the Earth over millions of years in the fossil record. This is just a guess.