<<What’s more, there is an energy associated with any given volume of the universe. If that volume increases, the inescapable conclusion is that this energy must increase as well. And yet physicists generally think that energy creation is forbidden.>> This one is easy. The cosmological constant term, Λ g[μν], in Einstein's equation, if interpreted as a stress-energy tensor, implies an energy density u and a pressure P satisfying P = -u. The work done on a body at pressure P when its volume increases by ΔV is -P ΔV. This work increases the energy content of the body by ΔE = -P ΔV, which equals the increase u ΔV in the vacuum energy. <<One final paradox is also worth mentioning. This comes from one of the fundamental assumptions behind Einstein’s theory of general relativity—-that if you look at the universe on a large enough scale, it must be the same in all directions.>> This is not true. The homogeneity of the universe is not a fundamental assumption of general relativity. It is merely a mathematical assumption that leads to simpler solutions of cosmological models. <<The nature of the energy associated with the vacuum is another puzzle. This is variously called the zero point energy or the energy of the Planck vacuum and quantum physicists have spent some time attempting to calculate it. These calculations suggest that the energy density of the vacuum is huge, of the order of 10^94 g/cm^3. This energy, being equivalent to mass, ought to have a gravitational effect on the universe. Cosmologists have looked for this gravitational effect and calculated its value from their observations (they call it the cosmological constant). These calculations suggest that the energy density of the vacuum is about 10^-29 g/cm3. Those numbers are difficult to reconcile. Indeed, they differ by 120 orders of magnitude. How and why this discrepancy arises is not known and is the cause of much bemused embarrassment among cosmologists.>> The universe is what it is. Somebody made an incorrect assumption as to the nature of this dark energy. -- Gene