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Register a new userFake Conformal Symmetry in Conformal Cosmological Models
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We examine the local conformal invariance (Weyl invariance) in tensor-scalar theories used in recently proposed conformal cosmological models. We show that the Noether currents associated with Weyl invariance in these theories vanish. We assert that the corresponding Weyl symmetry does not have any dynamical role.
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We study the extensions of teleparallism in the Kaluza-Klein (KK) scenario by writing the analogous form to the torsion scalar $T_{text{NGR}}$ in terms of the corresponding antisymmetric tensors, given by $T_{text{NGR}} = a,T_{ijk} , T^{ijk} + b,T_{ijk} ,T^{kji} + c,T^{j}{}_{ji} , T^{k}{}_{k}{}^{i}$, in the four-dimensional New General Relativity (NGR) with arbitrary coefficients $a$, $b$ and $c$. After the KK dimensional reduction, the Lagrangian in the Einstein-frame can be realized by taking $2a+b+c=0$ with the ghost-free condition $cleq0$ for the one-parameter family of teleparallelism. We demonstrate that the pure conformal invariant gravity models can be constructed by the requirements of $2a+b=0$ and $c=0$. In particular, the torsion vector can be identified as the conformal gauge field, while the conformal gauge theory can be obtained by $2a+b+4c=0$ or $2a+b=0$, which is described on the Weyl-Cartan geometry $Y_4$ with the ghost-free conditions $2a+b+c>0$ and $c eq0$. We also consider the weak field approximation and discuss the non-minimal coupled term of the scalar current and torsion vector. For the conformal invariant models with $2a+b=0$, we find that only the anti-symmetric tensor field is allowed rather than the symmetric one.
In this paper we continue a study of cosmological perturbations in the conformal gravity theory. In previous work we had obtained a restricted set of solutions to the cosmological fluctuation equations, solutions that were required to be both transverse and synchronous. Here we present the general solution. We show that in a conformal invariant gravitational theory fluctuations around any background that is conformal to flat (backgrounds that include the cosmologically interesting Robertson-Walker and de Sitter geometries) can be constructed from the (known) solutions to fluctuations around a flat background. For this construction to hold it is not necessary that the perturbative geometry associated with the fluctuations itself be conformal to flat. Using this construction we show that in a conformal Robertson-Walker cosmology early universe fluctuations grow as $t^4$. We present the scalar, vector, tensor decomposition of the fluctuations in the conformal theory, and compare and contrast our work with the analogous treatment of fluctuations in the standard Einstein gravity theory.
Keplers rescaling becomes, when Eisenhart-Duval lifted to $5$-dimensional Bargmann gravitational wave spacetime, an ordinary spacetime symmetry for motion along null geodesics, which are the lifts of Keplerian trajectories. The lifted rescaling generates a well-behaved conserved Noether charge upstairs, which takes an unconventional form when expressed in conventional terms. This conserved quantity seems to have escaped attention so far. Applications include the Virial Theorem and also Keplers Third Law. The lifted Kepler rescaling is a Chrono-Projective transformation. The results extend to celestial mechanics and Newtonian Cosmology.
We study spherically symmetric soliton solutions in a model with a conformally coupled scalar field as well as in full conformal gravity. We observe that a new type of limiting behaviour appears for particular choices of the self-coupling of the scalar field, i.e. the solitons interpolate smoothly between the Anti-de Sitter vacuum and an uncharged configuration. Furthermore, within conformal gravity the qualitative approach of a limiting solution does not change when varying the charge of the scalar field - contrary to the Einstein-Hilbert case. However, it changes with the scalar self-coupling.
It is shown that a general radial conformal Killing vector in Minkowski space-time can be associated to a generator of time evolution in conformal quantum mechanics. Among these conformal Killing vectors one finds a class which maps causal diamonds in Minkowski space-time into themselves. The flow of such Killing vectors describes worldlines of accelerated observers with a finite lifetime within the causal diamond. Time evolution of static diamond observers is equivalent to time evolution in conformal quantum mechanics governed by a hyperbolic Hamiltonian and covering only a segment of the time axis. This indicates that the Unruh temperature perceived by static diamond observers in the vacuum state of inertial observers in Minkowski space can be obtained from the behaviour of the two-point functions of conformal quantum mechanics.
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