It has been proved by the Red Shift that universe is expanding. But if the universe is actually expanding, it needs energy to do so. I also do not know that with expansion in universe if mass increases.
My question is from where do the universe get the energy to expand? How does it not violate the law of conservation of energy?
How does it not violate the law of conservation of energy?
It does violate the law of conservation of energy.
More precisely, the spacetime that describes our universe at cosmological scales is the FLRW spacetime (see also LCDM). It does not have time translation symmetry, there are no timelike Killing vectors. As a result there is no conserved energy at cosmological scales.
It is also difficult to even define a non-conserved energy for the whole universe. The issues are that due to curvature there is no unique way to add spatially separated vectors and that simultaneity is a matter of convention and will differ in different frames.
