IF dark energy was not perfectly evenly distributed(as some theories suggest), in other words if some cubic centimeter had a very small difference from another cubic centimeter, would that imply that spatial translation is not invariant, and hence that momentum is not conserved? Or would the laws of physics be the same despite the tiny difference and thus momentum would still be conserved?
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No. One well-explored explanation to dark energy is "quintessence": the idea that dark energy is some sort of scalar field like the Higgs field or the inflaton field. Fields are characterized by their ability to vary from place to place, and in this sense, scalar field dark energy is not much different from ordinary matter. Clearly the distribution of matter is not perfectly homogenous and isotropic, but this inhomogeneity does not screw up momentum conservation. In other words, momentum conservation comes from the idea that the laws of physics don't vary from place to place, though the particular details of the universe might. |
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