GR predicts accelerated expansion of spacetime should create gravitational wave, how? I thought universe does not have a center and the big bang happens everywhere so then where do these early gravitational wave originates? I know you need to accelerate massive object to produce significant gravitational wave so in this case of inflation what is being accelerated excluding space? During this period there shouldn't be any primordial blackhole forming right so they are ruled out?
GR predicts accelerated expansion of spacetime should create gravitational wave, how?
How are gravitational waves generated?
Gravitational waves are disturbances in the curvature of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light.
Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation
gravitational waves are generated by a changing quadrupole moment, which can happen only when there is asymmetrical movement of masses. Since the exact mechanism by which supernovae take place is not fully understood, it is not easy to model the gravitational radiation emitted by them.
The last paragraph quoted is important, the asymmetry.
Gravitational waves are inherent in the general relativity model which describes the effect of the energy momentum on the space time fabric, when there is some asymmetry in the space time curvature.
I thought universe does not have a center and the big bang happens everywhere
so then where do these early gravitational wave originates?
In the early Big Bang standard model, the universe was expanding steadily after the "bang,"no acceleration . The inflation epoch was "invented" so as to explain why there is an inhomogeneity in the cosmic microwave background, which is connected with the concentration of masses we observe ( galaxies, clusters of galaxies). It is supposed that the energy momentum tensor of the early universe has quantum fluctuations, which quantum fluctuations will statistically have asymmetries that lead to the observed inhomogeneities. The quadrupole distributions of those asymmetries will give the gravitational waves. The gravitational waves are effective after some time after the "quantum uncertainty bubble" assumed for the very early universe, at inflation epoch in this plot.
I know you need to accelerate massive object to produce significant gravitational wave so in this case of inflation what is being accelerated excluding space?
By the equation of Einstein, the energy momentum tensor is directly connected to the space time tensor, when space is distorted there is a mass that is distorting it. Without the masses and energies the universe would be flat with nothing in it.
To see a description of how space time and gravitational waves are tied see this.
This is a recent paper discussing the subject.