Signature change induces compactification

It is shown -- using a FRW model with ${\bf S}^3 \times {\bf S}^6$ as spatial sections and a positive cosmological constant -- that classical signature change implies a new compactification mechanism. The internal scale factor is of the order $\Lambda^{-1/2}$, and the solutions are stable against small perturbatons. In the case of compactified ${\bf S}^6$, it is shown that the effective four-dimensional space-time metric has Lorentzian signature, undergoes exponential inflation in ${\bf S}^3$ and is unique. Speculations concerning relations to quantum cosmology and conceivable modifications are added.Comment: 31 pages, LaTeX, 4 Figures are available on request as hard copies. Some clarifications are included concerning the particular model of signature change considered; misprints corrected and some references adde

Space-time dimension, Euclidean action and signature change

This talk is devoted to the problem how to compute relative nucleation probabilities of configurations with different topology and dimension in quantum cosmology. Assuming the semiclassical approximation, the usual formula for the nucleation probability induced by the no-boundary wave function is $P_{NB}\approx\exp(-I)$, where $I$ is the Euclidean action, evaluated at a solution of the Euclidean Einstein equations with effective cosmological constant $\Lambda$. Relative probabilities of different configurations are usually compared at equal values of $\Lambda$. When configurations with different dimensions are admitted (the $n$-dimensional gravitational constant being subject to a rather mild restriction), as e.g. ${\bf S}^n$ for any $n$, this procedure leads to the prediction that the space-time dimension tends to be as large as possible. In this contribution, I would like to propose an alternative scheme, namely to compare the probabilities $P_{NB}\approx\exp(-I)$ at equal values of the {\it energy} $E$, instead of the {\it energy density} $\Lambda$. As a result, the space-time dimension settles at $n=4$. Attempts to predict the topology of the spacelike slices lead to the candidates ${\bf S}^3$ and ${\bf S}^1\times {\bf S}^2$. Since the ''process'' of nucleation (possibly connected with decoherence) is not well known in detail, we expect that either {\it both} configurations may be realized with roughly equal probability, or the {\it latter} one is favoured. Finally, we comment on the analogous situation based on the tunneling wave function.Comment: 11 pages, LaTeX, 3 Figures are available as hard copies; Talk given at the 3rd Alexander Friedmann international seminar on gravitation and cosmology; St. Petersburg, July 4 - 12, 199

Reduzierte Bodenbearbeitung im Ökologischen Landbau: Einfluss auf Leistung und Struktur der Bodenmikroorganismengemeinschaft

Problemstellung/Ziele: Im Projekt ‚Ökologische Bodenbewirtschaftung’ (PÖB) der Stiftung Ökologie und Landbau, Bad Dürckheim, wird seit 1995 am Standort Rommersheim, Rheinhessen, eine differenzierte Grundbodenbearbeitung mit den Varianten Pflug (P), Zweischichtenpflug (LP) und Schichtengrubber (LC) durchgeführt. Ziel der Untersuchungen war es, vertiefende Einsichten in die Reaktion der mikrobiellen Biomasse auf die differenzierte Bodenbearbeitung unter den besonderen Bedingungen des Ökologischen Landbaus zu erhalten. Hypothesen: Eine reduzierte (LP) und konservierende (LC) Bodenbearbeitung führt im Vergleich zum Pflug (P) zu einer Anreicherung und Sequestrierung sowie einer qualitativen Modifikation von organischer Bodensubstanz und mikrobieller Biomasse. Die funktionelle und strukturelle Diversität der Bodenmikroorganismen-Gemeinschaft wird hierdurch ebenfalls modifiziert. Methoden: Im Frühjahr 2001 wurden Bodenproben aus Grünbrache-Parzellen in vierfacher Wiederholung je Bodenbearbeitungsvariante differenziert nach Ober- (0-15cm) und Unterkrume (15-25cm) entnommen und hinsichtlicher der Gehalte an organischer Substanz (trockene Veraschung), mikrobieller Biomasse (CFE-C) und Aktivität (Infrarotgasanalysator) sowie der funktionellen Diversität (community level substrate utilization profiles – BIOLOG GN2) untersucht. Die strukturelle Diversität wurde mittels Phospholipid-Fettsäure (PLFA) und Phospholipid-Etherlipide (PLEL) –Muster analysiert. Ergänzend wurde die Qualität der organischen Bodensubstanz durch eine Kaltwasser-Extraktion und der spektroskopischen Eigenschaften untersucht. Fazit: Reduzierte und konservierende Bodenbearbeitung modifiziert die Organische Bodensubstanz, die Leistung sowie die funktionelle und strukturelle Diversität von Bodenmikroorganismen-Gemeinschaften

Mode decomposition and unitarity in quantum cosmology, Talk given at the Second Meeting on Constrained Dynamics and Quantum gravity, Santa Margherita Ligure, September 17-21, 1996

Contrary to common belief, there are perspectives for generalizing the notion of positive and negative frequency in minisuperspace quantum cosmology, even when the wave equation does not admit symmetries. We outline a strategy in doing so when the potential is positive. Also, an underlying unitarity structure shows up. Starting in the framework of the Klein-Gordon type quantization, I am led to a result that relies on global features on the model, and that is possibly related to structures encountered in the refined algebraic quantization scheme.Comment: 5 pages, LaTeX (no figures

Complex lapse, complex action and path integrals

Imaginary time is often used in quantum tunnelling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the ``3+1'' action for the Einstein gravitational field minimally coupled to a Klein-Gordon field, allowing the lapse function to be complex yields a complex action which generates both the usual Lorentzian theory and its Riemannian analogue, and in particular allows a change of signature between the two. The action and variational equations are manifestly well defined in the Hamiltonian representation, with the momentum fields consequently being complex. The complex action interpolates between the Lorentzian and Riemannian actions as they appear formally in the respective path integrals. Thus the complex-lapse theory provides a unified basis for a path-integral quantum theory of gravity involving both Lorentzian and Riemannian aspects. A major motivation is the quantum-tunnelling scenario for the origin of the universe. Taken as an explanation for the observed quantum tunnelling of particles, the complex-lapse theory determines that the argument of the lapse for the universe now is extremely small but negative.Comment: 12 pages, Te