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Register a new userA Cautionary Note on Cosmological Magnetic Fields
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This note is concerned with potentially misleading concepts in the treatment of cosmological magnetic fields by magnetohydrodynamical (MHD) modelling. It is not a criticism of MHD itself but rather a cautionary comment on the validity of its use in cosmology. Now that cosmological data are greatly improved compared with a few decades ago, and even better data are imminent, it makes sense to revisit original modelling assumptions and examine critically their shortcomings in respect of modern science. Specifically this article argues that ideal MHD is a poor approximation around recombination, since it inherently restricts evolutionary timescales, and is often misapplied in the existing literature.
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A variety of observations impose upper limits at the nano Gauss level on magnetic fields that are coherent on inter-galactic scales while blazar observations indicate a lower bound $sim 10^{-16}$ Gauss. Such magnetic fields can play an important astrophysical role, for example at cosmic recombination and during structure formation, and also provide crucial information for particle physics in the early universe. Magnetic fields with significant energy density could have been produced at the electroweak phase transition. The evolution and survival of magnetic fields produced on sub-horizon scales in the early universe, however, depends on the magnetic helicity which is related to violation of symmetries in fundamental particle interactions. The generation of magnetic helicity requires new CP violating interactions that can be tested by accelerator experiments via decay channels of the Higgs particle.
Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function ansatz invalidates it, as illustrated by the incorrect solutions of [1].
We explore the pitfalls which affect the comparison of the star-formation (SF) relation for nearby molecular clouds with that for distant compact molecular clumps. We show that both relations behave differently in the ($Sigma_{gas}$, $Sigma_{SFR}$) space, where $Sigma_{gas}$ and $Sigma_{SFR}$ are, respectively, the gas and SF rate surface densities, even when the physics of star formation is the same. This is because the SF relation of nearby clouds relates gas and star surface densities measured locally, that is, within a given interval of gas surface density, or at a given protostar location. We refer to such measurements as local measurements, and the corresponding SF relation as the local relation. In contrast, the stellar content of a distant molecular clump remains unresolved. Only the mean SF rate can be obtained from e.g. the clump infrared luminosity. One clump therefore provides one single point to the ($Sigma_{gas}$, $Sigma_{SFR}$) space, that is, its mean gas surface density and SF rate surface density. We refer to this SF relation as a global relation since it builds on the global properties of molecular clumps. Its definition therefore requires an ensemble of cluster-forming clumps. We show that, although the local and global relations have different slopes, this per se cannot be taken as evidence for a change in the physics of SF with gas surface density. It therefore appears that great caution should be taken when physically interpreting a composite SF relation, that is, a relation combining together local and global measurements.
We study a class of non-unitary so(2,d) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so(2,d) modules obeys of natural generalisation of a couple of defining properties of unitary higher-spin singletons. In particular, we find out that upon restriction to the subalgebra so(2,d-1), these representations branch onto a sum of modules describing partially massless fields of various depths. Finally, their tensor product is worked out in the particular case of d=4, where the appearance of a variety of mixed-symmetry partially massless fields in this decomposition is observed.
This paper examines the constricted use of group theory in the studies of pairwise comparisons. The presented approach is based on the application of the famous Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation for multiplicative (ratio) pairwise comparisons has been provided. Counterexamples have been provided to support the theory. In our opinion, the scientific community must be made aware of the limitations of using the group theory in pairwise comparisons. Groups, which are not torsion free, cannot be used for ratios by Levis theorems.
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