Triad representation of the Chern-Simons state in quantum gravity

We investigate a triad representation of the Chern-Simons state of quantum gravity with a non-vanishing cosmological constant. It is shown that the Chern-Simons state, which is a well-known exact wavefunctional within the Ashtekar theory, can be transformed to the real triad representation by means of a suitably generalized Fourier transformation, yielding a complex integral representation for the corresponding state in the triad variables. It is found that topologically inequivalent choices for the complex integration contour give rise to linearly independent wavefunctionals in the triad representation, which all arise from the one Chern-Simons state in the Ashtekar variables. For a suitable choice of the normalization factor, these states turn out to be gauge-invariant under arbitrary, even topologically non-trivial gauge-transformations. Explicit analytical expressions for the wavefunctionals in the triad representation can be obtained in several interesting asymptotic parameter regimes, and the associated semiclassical 4-geometries are discussed. In restriction to Bianchi-type homogeneous 3-metrics, we compare our results with earlier discussions of homogeneous cosmological models. Moreover, we define an inner product on the Hilbert space of quantum gravity, and choose a natural gauge-condition fixing the time-gauge. With respect to this particular inner product, the Chern-Simons state of quantum gravity turns out to be a non-normalizable wavefunctional.Comment: Latex, 30 pages, 1 figure, to appear in Phys. Rev.

The exact cosmological solution to the dynamical equations for the Bianchi IX model

Quantum geometrodynamics in extended phase space describes phenomenologically the integrated system ``a physical object + observation means (a gravitational vacuum condensate)''. The central place in this version of QGD belongs to the Schrodinger equation for a wave function of the Universe. An exact solution to the ``conditionally-classical'' set of equations in extended phase space for the Bianchi-IX model and the appropriate solution to the Schrodinger equation are considered. The physical adequacy of the obtained solutions to existing concepts about possible cosmological scenarios is demonstrated. The gravitational vacuum condensate is shown to be a cosmological evolution factor.Comment: LaTeX, 14 pages, to be published in Int. J. Mod. Phys.

The linearization of the Kodama state

We study the question of whether the linearization of the Kodama state around classical deSitter spacetime is normalizable in the inner product of the theory of linearized gravitons on deSitter spacetime. We find the answer is no in the Lorentzian theory. However, in the Euclidean theory the corresponding linearized Kodama state is delta-functional normalizable. We discuss whether this result invalidates the conjecture that the full Kodama state is a good physical state for quantum gravity with positive cosmological constant.Comment: 14 pages, statement on the corresponding Yang-Mills case correcte

Evolution of the Scale Factor with a Variable Cosmological Term

Evolution of the scale factor a(t) in Friedmann models (those with zero pressure and a constant cosmological term Lambda) is well understood, and elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58, 689 (1986)]. Developments in particle physics and inflationary theory, however, increasingly indicate that Lambda ought to be treated as a dynamical quantity. We revisit the evolution of the scale factor with a variable Lambda-term, and also generalize the treatment to include nonzero pressure. New solutions are obtained and evaluated using a variety of observational criteria. Existing arguments for the inevitability of a big bang (ie., an initial state with a=0) are substantially weakened, and can be evaded in some cases with Lambda_0 (the present value of Lambda) well below current experimental limits.Comment: 29 pages, 12 figures (not included), LaTeX, uses Phys Rev D style files (revtex.cls, revtex.sty, aps.sty, aps10.sty, prabib.sty). To appear in Phys Rev

Follow-up regimes for sick-listed employees: A comparison of nine north-western European countries

The Covid-19 pandemic has revealed the importance of social protection systems, including income security, when health problems arise. The aims of this study are to compare the follow-up regimes for sick-listed employees across nine European countries, and to conduct a qualitative assessment of the differences with respect to burden and responsibility sharing between the social protection system, employers and employees. The tendency highlighted is that countries with shorter employer periods of sick-pay typically have stricter follow-up responsibility for employers because, in practice, they become gatekeepers of the public sickness benefit scheme. In Germany and the UK, employers have few requirements for follow-up compared with the Nordic countries because they bear most of the costs of sickness absence themselves. The same applies in Iceland, where employers carry most of the costs and have no obligation to follow up sick-listed employees. The situation in the Netherlands is paradoxical: employers have strict obligations in the follow-up regime even though they cover all the costs of the sick-leave themselves. During the pandemic, the majority of countries have adjusted their sick-pay system and increased coverage to reduce the risk of spreading Covid-19 because employees are going to work sick or when they should self-quarantine, except for the Netherlands and Belgium, which considered that the current schemes were already sufficient to reduce that risk

Follow-up regimes for sick-listed employees : A comparison of nine north-western European countries

The Covid-19 pandemic has revealed the importance of social protection systems, including income security, when health problems arise. The aims of this study are to compare the follow-up regimes for sick-listed employees across nine European countries, and to conduct a qualitative assessment of the differences with respect to burden and responsibility sharing between the social protection system, employers and employees. The tendency highlighted is that countries with shorter employer periods of sick-pay typically have stricter follow-up responsibility for employers because, in practice, they become gatekeepers of the public sickness benefit scheme. In Germany and the UK, employers have few requirements for follow-up compared with the Nordic countries because they bear most of the costs of sickness absence themselves. The same applies in Iceland, where employers carry most of the costs and have no obligation to follow up sick-listed employees. The situation in the Netherlands is paradoxical: employers have strict obligations in the follow-up regime even though they cover all the costs of the sick-leave themselves. During the pandemic, the majority of countries have adjusted their sick-pay system and increased coverage to reduce the risk of spreading Covid-19 because employees are going to work sick or when they should self-quarantine, except for the Netherlands and Belgium, which considered that the current schemes were already sufficient to reduce that risk