One of the earliest criticisms of General Relativity when Classical Physics was still prevalent was the dogmatic idea that energy (and mass) must be conserved.Yes, it's a 'fallacy of composition' to expect the universe itself to have the properties of its constituents; also, the conservation of energy has its limits - it is not necessarily conserved under General Relativity (depending on how one defines one's terms).
General Relativity allows some unexpected phenomena that may be relevant to the origins of our universe, such as, as Max Tegmark describes, the potential to produce an infinite volume of spacetime in a finite time and within a finite 'external' volume...
It took Emmy Noether who was hired by David Hilbert who worked with Einstein on General Relativity (or perhaps rivalled him depending on the sources) to show that mathematical symmetry of a dynamical system under position, time or rotation translation determined the conservation law and ultimately there was no conservation law for energy when applied globally to an expanding Universe.
I’m not familiar with Max Tegmark’s work; I’ve seen him turn up on a few Science programs.
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