  We investigate cosmological consequences of a generalized early dark energy
(EDE) model where a scalar field behaves as dark energy at various cosmological
epochs for a broad range of parameters such as the energy scale and the initial
field value. We consider power-law and axion-type potentials for such an EDE
field and study how it affects the cosmological evolution. We show that
gravitational wave background can be significantly enhanced to be detected in
future observations such as LISA and DECIGO in some parameter space.
Implications of the EDE model are also discussed for a scenario where a
blue-tilted inflationary tensor power spectrum can explain the recent NANOGrav
15-year signal. We argue that the bounds on the reheating temperature can be
relaxed compared to the case of the standard thermal history.
