This remark appears, for example, in a book Hiding in the Mirror by Lawrence Krauss, page 231. A number of questions arise in regards to this remark. If the mechanism that leads to dark energy, so called, is unknown, how can it be determined that phenomena at small scales do not also manifest such a mechanism? It could be that the mechanism results in a variety of phenomena at smallish scales that have not yet been connected to the unknown mechanism that causes so-called dark energy. This first objection is therefore that determining that an unknown mechanism primarily has effects at cosmological scales is unconvincing, since the mechanism is unknown. A second objection arises in light of 4/3 scaling, itself a manifestation of the principle of dimensional capacity. 4/3 scaling does appear at scales ranging from molecular, in the 4/3 fractal envelope of Brownian motion and in the 4/3 entropy that appears in an intermediate step in the derivation of Stefan’s Law about black body radiation up to, possibly, expanding cosmological space. If 4/3 scaling accounts for the 1998 astronomical observations leading to the idea of dark energy, then it would be incorrect to say dark energy effects are primarily at large scales. What do you think?
A simple and quite straightforward qualitative argument why Einstein's cosmological term is considered to be relevant only on large distances is that it depends only on g_mn themselves, not on their derivatives. Locally terms with derivatives will be more important than globally, where they average out.
One can easily quantify this, by using the cosmological equations to get an upper bound for \(|\Lambda|\) and then one can look at how unimportant this term becomes in the Solar system.
Dr. Schmelzer,
Thank you for your reply.
I assume you are correct about the relationship between Lambda as used by Einstein and his GR equations. I don't know enough about GR to say otherwise.
Suppose however that the cosmic scale or stretch factor is not (contrary to what is generally assumed) related to Einstein's GR equations. Then where are we?
On the other hand, suppose Lambda is related to Einstein's GR equations. Then physics should have explained DE already (no?) but it has not. Can the failure of the GR equations to account for DE be overcome within existing theory?
Or, in other words, if the GR equations and Friedmann's solutions for cosmology don't explain DE, then maybe Lambda and GR don't go hand in hand in the way supposed?
Further, if DE and FLRW metric don't go together in the way physics mostly supposes, might revision or replacement of the FLRW metric be an option?
Dear Robert Shour
Using the Einstein equations with \(\Lambda\neq 0\) is the standard approach. I cannot tell you anything about other approaches to DE, I simply don't know enough about them to comment. The meaning of "explaining DE" is too vague to comment too.
Within GR as it is, without \(\Lambda\), there is Wiltshire's "timescape universe" which explains acceleration as a fake created by inhomogeneity and our location in a dense region, outside the holes.
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