The cosmological constant problem assumes that the cosmological constant (determined experimentally) can be identified with the vacuum energy density. Theroretical arguments from quantum gravity results in a vacuum energy density which is 122 orders of magnitude too big. In contrast to this, opinions, that say that these are two different things, can be heard sporadically. How can such statements be substantiated? Where are they quoted?
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http://ned.ipac.caltech.edu/level5/Carroll2/Carroll.html Section 1.3 – seVenVo1d Nov 28 '19 at 16:46
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Carroll motivates the mentioned identification with the Lorenz invariance. I‘am interested in arguments which substantiate that the cosmological constant cannot identified with the vacuum energy density. – user185188 Nov 29 '19 at 08:30
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@Reign A more readable version ? – Keith McClary Nov 30 '19 at 05:40
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@user185188 https://arxiv.org/abs/astro-ph/0207347 – seVenVo1d Nov 30 '19 at 06:13
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The short answer, as far as I understand it, is that no matter how you phrase it, there is a problem. If you think the two are different then you still have to explain what happens to the vacuum energy of the quantum fields and the answer ought to be that it's effectively cancelled by a cosmological constant and the cosmological constant we observe is the remaining uncancelled part. So, you still end up with an unnatural/fine-tuned cancellation that needs an explanation. – Sep 04 '21 at 10:19
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4Does this answer your question? About the "worst prediction in all of physics" – Mauricio Sep 04 '21 at 10:21
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Consider the Einstein Field Equations [1]: $$G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu}$$
- $G_{\mu \nu}$ is the Einstein Tensor
- $g_{\mu \nu}$ is the metric tensor
- $T_{\mu \nu}$ is the stress-energy tensor
- $\Lambda$ is the cosmological constant
and $\kappa$ is a constant of nature (that involves the gravitational constant and the speed of light).
Left of the $=$ sign are terms that describe space-time curvature. Right of the $=$ sign are terms that describe energy and momentum density and distribution of matter, radiation and their movement and pressure etc. (As John Archibald Wheeler put it: "Space-time tells matter how to move; matter tells space-time how to curve."
When the field equations are written as above, then $\Lambda$ can be interpreted as constant of nature that describes a pre-bending of space-time or that space-time curvature has a preferred / biased bending.
When $\Lambda$ is moved to the right side of the field equations $$G_{\mu \nu}= \kappa T_{\mu \nu} - \Lambda g_{\mu \nu} $$ then $\Lambda$ can be regarded as part of energy-momentum. This perspective gives rise to the interpretation of $\Lambda$ as energy density of the vacuum. Vacuum means that neither matter nor radiation is present: $T_{\mu\nu}=0$, but with a non-zero $\Lambda$ the vacuum can be interpreted as having energy density.
And there you have it: All of a sudden everyone is wondering about dark enery and where it comes from any why most of the universe is "made" of it, when IMO $\Lambda$ is not more mysterious than why the universe obeys Einstein's equations.
And regarding that "off by a factor of 10122 calculation": According to John Baez, the best what Quantum Field Theory can give is "that value is undetermined", and all other values are based on "naive calculations" that have no predictive power.
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It is a paradox of QED. As the paradox is sofar unresolved, it is a real problem. It is not a cosmological problem at all. QED claims a near infinite zero point energy. Such an energy would have enormous impact and it is safe to say that this cannot be a true prediction.
my2cts
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