Gravitational waves from first order phase transitions as a probe of an early matter domination era and its inverse problem

We investigate the gravitational wave background from a first order phase transition in a matter-dominated universe, and show that it has a unique feature from which important information about the properties of the phase transition and thermal history of the universe can be easily extracted. Also, we discuss the inverse problem of such a gravitational wave background in view of the degeneracy among macroscopic parameters governing the signal.