Geometry of the Universe and Its Relation to Entropy and Information

Abstract EN

In an effort to investigate a possible relation between geometry and information, we establish a relation of the Ricci scalar in the Robertson-Walker metric of the cosmological Friedmann model to the number of information N and entropy S.

This is with the help of a previously derived result that relates the Hubble parameter to the number of information N.

We find that the Ricci scalar has a dependence which is inversely proportional to the number of information N and entropy S.

Similarly, a nonzero number of information would imply a finite Ricci scalar, and therefore space time will unfold.

Finally, using the maximum number of information existing in the universe, we obtain a numerical value for the Ricci scalar to be O(10-52) m-2.