Invariance under complex transformations, and its relevance to the cosmological constant problem

In this paper we study a new symmetry argument that results in a vacuum state with strictly vanishing vacuum energy. This argument exploits the well-known feature that de Sitter and Anti- de Sitter space are related by analytic continuation. When we drop boundary and hermiticity conditions on quantum fields, we get as many negative as positive energy states, which are related by transformations to complex space. The paper does not directly solve the cosmological constant problem, but explores a new direction that appears worthwhile.Comment: Some clarifications and references adde

The mathematical basis for deterministic quantum mechanics

If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.Comment: 17 pages, 3 figures. Minor corrections, comments and explanations adde

A symmetry for vanishing cosmological constant: Another realization

A more conventional realization of a symmetry which had been proposed towards the solution of cosmological constant problem is considered. In this study the multiplication of the coordinates by the imaginary number $i$ in the literature is replaced by the multiplication of the metric tensor by minus one. This realization of the symmetry as well forbids a bulk cosmological constant and selects out $2(2n+1)$ dimensional spaces. On contrary to its previous realization the symmetry, without any need for its extension, also forbids a possible cosmological constant term which may arise from the extra dimensional curvature scalar provided that the space is taken as the union of two $2(2n+1)$ dimensional spaces where the usual 4-dimensional space lies at the intersection of these spaces. It is shown that this symmetry may be realized through spacetime reflections that change the sign of the volume element. A possible relation of this symmetry to the E-parity symmetry of Linde is also pointed out.Comment: The version to appear in PLB. The terms "non-orientable space" and "extra-dimensional tranlation" are replaced by "space whose volume element changes sign under extra dimensional reflections" and "extra dimensional reflections", respectively; and typos are correcte

Vacuum driven accelerated expansion

It has been shown that an improved estimation of quantum vacuum energy can yield not only acceptable but also experimentally sensible results. The very idea consists in a straightforward extraction of gravitationally interacting part of the full quantum vacuum energy by means of gauge transformations. The implementation of the idea has been performed in the formalism of effective action, in the language of Schwinger's proper time and the Seeley-DeWitt heat kernel expansion, in the background of the Friedmann-Robertson-Walker geometry.Comment: 11 pages, 2 figures, minor improvements, final preprint version, published version: http://www3.interscience.wiley.com/journal/120847180/abstract, devoted to the memory of professor Ryszard Raczka on the occasion of the 11th anniversary of his deat

Human papillomavirus and natural history of cervical intraepithelial neoplasia : clinical consequences

Cervical cancer is the second most common cancer in women world-wide after breast cancer. Each year, there are approximately 437,000 new cases of invasive cancer of the cervix diagnosed and more than 200,000 women die from the disease, 79% of which occur in developing countries. In the Netherlands approximately 715 new cases of cervical cancer are diagnosed each year with an age-standardised incidence rate of 8,6 new cases per 1 00,000 women. The age-standardised mortality rate for the Netherlands has been estimated at 2,4 deaths per 1 00,000 women with a total of 234 deaths reported in 1995. The average age-standardised mortality rate of developing countries is 2,5 f1mes that of industrialised areas

A symmetry for vanishing cosmological constant

Two different realizations of a symmetry principle that impose a zero cosmological constant in an extra-dimensional set-up are studied. The symmetry is identified by multiplication of the metric by minus one. In the first realization of the symmetry this is provided by a symmetry transformation that multiplies the coordinates by the imaginary number i. In the second realization this is accomplished by a symmetry transformation that multiplies the metric tensor by minus one. In both realizations of the symmetry the requirement of the invariance of the gravitational action under the symmetry selects out the dimensions given by D = 2(2n+1), n=0,1,2,... and forbids a bulk cosmological constant. Another attractive aspect of the symmetry is that it seems to be more promising for quantization when compared to the usual scale symmetry. The second realization of the symmetry is more attractive in that it is posible to make a possible brane cosmological constant zero in a simple way by using the same symmetry, and the symmetry may be identified by reflection symmetry in extra dimensions.Comment: Talk in the conference IRGAC 2006, 2nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelon

Complex Lagrangians and phantom cosmology

Motivated by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with PT symmetry, we show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. The model is based on a classical complex Lagrangian of a scalar field. Specific symmetry properties analogous to PT in non-Hermitian quantum mechanics lead to purely real equation of motion.Comment: 11 pages, to be published in J.Phys.A, refs. adde

Renormalization-group running cosmologies and the generalized second law

We explore some thermodynamical consequences of accelerated universes driven by a running cosmological constant (CC) from the renormalization group (RG). Application of the generalized second law (GSL) of gravitational thermodynamics to a framework where the running of the CC goes at the expense of energy transfer between vacuum and matter, strongly restricts the mass spectrum of a (hypothetical) theory controlling the CC running. We find that quantum effects driving the running of the CC should be dominated by a trans-planckian mass field, in marked contrast with the GUT-scale upper mass bound obtained by analyzing density perturbations for the running CC. The model shows compliance with the holographic principle.Comment: 8 pages, final version to appear in Phys. Lett.