We study the renormalization group flow in a class of scalar-tensor theories involving at most two derivatives of the fields. We show in general that minimal coupling is self consistent, in the sense that when the scalar self couplings are switched off, their beta functions also vanish. Complete, explicit beta functions that could be applied to a variety of cosmological models are given in a five parameter truncation of the theory in d = 4. In any dimension d > 2 we find that the flow has only a "Gaussian Matter" fixed point, where all scalar self interactions vanish but Newton's constant and the cosmological constant are nontrivial. The properties of these fixed points can be studied algebraically to some extent. In d = 3 we also find a gravitationally dressed version of the Wilson-Fisher fixed point, but it seems to have unphysical properties. These findings are in accordance with the hypothesis that these theories are asymptotically safe. † on leave from SISSA,
Compact stars consisting of fermions with arbitrary masses and interaction
strengths are studied by solving the structure equation of general relativity,
the Tolman-Oppenheimer-Volkoff equations. Scaling solutions are derived for a
free and an interacting Fermi gas and tested by numerical calculations. We
demonstrate that there is a unique mass-radius relation for compact stars made
of free fermions which is independent of the fermion mass. For sufficiently
strong interactions, the maximum stable mass of compact stars and its radius
are controlled by the parameter of the interaction, both increasing linearly
with the interaction strength. The mass-radius relation for compact stars made
of strongly interacting fermions shows that the radius remains approximately
constant for a wide range of compact star masses.Comment: 19 pages, 8 figures, refs. added, version to appear in Physical
Review
We introduce several coordinate-invariant statistical procedures in order to test for alignment of polarizations of electromagnetic radiation from astrophysical sources. A large-scale alignment of optical polarizations from distant quasi-stellar objects (QSOs) has recently been observed by Hutsemékers and collaborators. The new statistical procedures are based on comparing polarizations at different angular coordinates by making a parallel transport. The results of these statistical procedures continue to support the existence of the large-scale alignment effect in the QSO optical polarization data. The alignment is found to be much more pronounced in the data sample with low degrees of polarization, p 2 per cent. This suggests that the alignment may be attributed to some propagation effect. The distance scale over which the alignment effect is dominant is found to be of order 1 Gpc. We also find that a very large-scale alignment is present in the large-redshift, z 1, data sample. In fact, the data sample with z 1 appears to be aligned over the entire celestial sphere. This alignment is seen independent of the degree of polarization of the sources. We discuss possible physical effects, such as extinction and pseudoscalar-photon mixing, which may be responsible for the observations.
Fourth order derivative gravity in 3+1-dimensions is perturbatively renormalizable and is shown to describe a unitary theory of gravitons in a limited coupling parameter space. The running gravitational constant which includes graviton contribution is computed. Generically, gravitational Newton's constant vanishes at short distances in this perturbatively renormalizable and unitary theory.
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