Abstract:
The Einstein equation for the Friedmann-Robertson-Walker metric plays a fundamental
role in cosmology. The direct search of the exact solutions of the Einstein equation
even in this simple metric case is sometime a hard job. Therefore, it is useful to construct solutions
of the Einstein equation using a known solutions of some other equations which are
equivalent or related to the Einstein equation. In this work, we establish the relationship the
Einstein equation with two other famous equations namely the Ramanujan equation and the
Chazy equation. Both these two equations play an important role in the number theory. Using
the known solutions of the Ramanujan and Chazy equations, we find the corresponding
solutions of the Einstein equation.
