The theory of gravitational waves in the frame of non-local quantum hydrodynamics (NLQH) is considered. From calculations follow that NLQH equations for “empty” space have the traveling wave solutions belonging in particular to the soliton class. The possible influence and reaction of the background microwave radiation is taken into account. These results lead to the principal correction of the inflation theory and serve as the explanation for the recent discovery of the universe’s cosmic microwave background anomalies. The simple analytical particular cases and numerical calculations are delivered. Proposal for astronomers—to find in the center domain of the hefty cold spot the smallest hot spot as the origin of the initial burst—Big Bang.