Spontaneous breaking of conformal invariance, solitons and gravitational waves in theories of conformally invariant gravitation

We study conformal gravity as an alternative theory of gravitation. For conformal gravity to be phenomenologically viable requires that the conformal symmetry is not manifest at the energy scales of the other known physical forces. Hence we require a mechanism for the spontaneous breaking of conformal invariance. In this paper we study the possibility that conformal invariance is spontaneously broken due to interactions with conformally coupled matter fields. The vacuum of the theory admits conformally non-invariant solutions corresponding to maximally symmetric space-times and variants thereof. These are either de Sitter space-time or anti-de Sitter space-time in the full four space-time dimensions or in a lower dimensional sub-space. We consider in particular normalizable, linearized gravitational perturbations around the anti-de Sitter background. Exploiting the conformal flatness of this space-time, we show to second order, that these gravitational fluctuations, that are taken to be fourier decomposable, carry zero energy-momentum. This squares well with the theorem that asymptotically flat space-times conformal gravity contain zero energy and momentum \cite{bhs}. We also show the possibility of domain wall solitons interpolating between the ground states of spontaneously broken conformal symmetry that we have found. These solitons necessarily require the vanishing of the scalar field, repudiating the recent suggestion \cite{f} that the conformal symmetry could be quarantined to a sterile sector of the theory by choosing an appropriate field redefinition.Comment: 21 pages, 2 figures, colour viewing helpful, version to be published in PR

Detection of Circulating Filarial Antigen

Affinity binding to specific solid phase antibody, immune complex binding to Raji cells or PEG precipitation of immune complexes was used in conjunction with Western blotting to detect circulating filarial antigen in filarial sera. A high molecular weight antigen was present in free as well as complex form. PEG precipitation method revealed specific filarial antigens in the low molecular weight region also

Static and dynamic calibrations of MSFC's plug-nozzle special test section /redesigned 1967/

Calibration of plug nozzle special test sectio

Transient and asymptotic properties of robust adaptive controllers in the presence of non-coercive Lyapunov functions

— Adaptive control architectures often make use of Lyapunov functions to design adaptive laws. We are specifically interested in adaptive control methods, such as the well-known L1 adaptive architecture, which employ a parameter observer for this purpose. In such architectures, the observation error plays a critical role in determining analytical bounds on the tracking error as well as robustness. In this paper, we show how the non-existence of coercive Lyapunov operators can impact the analytical bounds, and with it the performance and the robustness of such adaptive systems

Monochromatic plane-fronted waves in conformal gravity are pure gauge

We consider plane-fronted, monochromatic gravitational waves on a Minkowski background, in a conformally invariant theory of general relativity. By this we mean waves of the form: g_{\mu\nu}=\eta_{\mu\nu}+\epsilon_{\mu\nu}F(k\cdotx), where $\epsilon_{\mu\nu}$ is a constant polarization tensor, and $k_\mu$ is a lightlike vector. We also assume the coordinate gauge condition $|g|-1/4\partial_\tau(|g|1/4g^{\sigma\tau})=0$ which is the conformal analog of the harmonic gauge condition $g^{\mu\nu}\Gamma_{\mu\nu}^\sigma=-|g|-1/2\partial_\tau(|g|1/2g^{\sigma\tau})=0, where$\det[g_{\mu\nu}]\equivg$. Requiring additionally the conformal gauge condition$g=-1$surprisingly implies that the waves are both transverse and traceless. Although the ansatz for the metric is eminently reasonable when considering perturbative gravitational waves, we show that the metric is reducible to the metric of Minkowski space-time via a sequence of coordinate transformations which respect the gauge conditions, without any perturbative approximation that \in{\mu}{\nu} be small. This implies that we have, in fact, exact plane-wave solutions; however, they are simply coordinate/conformal artifacts. As a consequence, they carry no energy. Our result does not imply that conformal gravity does not have gravitational wave phenomena. A different, more generalized ansatz for the deviation, taking into account the fourth-order nature of the field equation, which has the form$g_{\mu\nu}=\eta_{\mu\nu}+B_{\mu\nu}(n\cdotx)G(k\cdotx)$, indeed yields waves which carry energy and momentum [P.D. Mannheim, Gen. Relativ. Gravit. 43, 703 (2010)]. It is just surprising that transverse, traceless, plane-fronted gravitational waves, those that would be used in any standard, perturbative, quantum analysis of the theory, simply do not exist.Comment: 5 pages, no figures, version published, substantial changes to the presentation, conclusions unaltered, title change