Is the total mass of the universe constant in time?
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Since mass and energy are the same according to Einstein's equation I would say that mass is not constant for the universe because the law of conservation of energy has been proven false. It is so because the space itself in which the processes take place is expanding.
You can get a detailed article about it here-http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/
Rajath Radhakrishnan
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Mass is obviously not conserved, as $E=mc^2$ state. But if you want to consider the total mass of the Universe, the problem is that "total" mass (energy) in General Relativity is not well defined, see: Energy conservation in General Relativity