Pasquale Nardone

Thermodynamics and cosmology

A new type of cosmological history which includes large-scale entropy production is proposed. These cosmologies are based on a reinterpretation of the matter-energy stress tensor in Einsteins equations. This modifies the usual adiabatic energy conservation laws, thereby leading to a possible irreversible matter creation. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. This new point of view results from the consideration of thermodynamics of open systems in the framework of cosmology. It appears that the usual initial singularity is structurally unstable with respect to irreversible matter creation. The corresponding cosmological history therefore starts from an instability of the vacuum rather than from a singularity. The universe evolves through an inflationary phase. This appears to be an attractor independent of the initial vacuum fluctuation.

Cosmogenesis and the origin of the fundamental length scale

The creation of the universe is regarded as a self-consistent process in which matter is engendered by the space-time varying cosmological gravitational field and vice versa. Abundant production can occur only if the mass of the particles so created is of the order of the Planck mass (= κ−12. We conjecture that this is the origin of the fundamental length scale in field theory, as it is encountered, for example, in present efforts towards grandunification. The region of particle production is steady state in character. It ceases when the produced particles decay. The geometry of this steady state is characteristic of a de Sitter space. It permits one to estimate the number of ordinary particles presently observed, N. We find log N = O (mτdecay) = O(g−2) = O(102), with the usual estimate of g = O(10− at the Planck length scale. This is not inconsistent with the experimental estimate N ⋍ O(1090). After production, cosmological history gives way to the more conventional scheme of free expansion. The present paper is a self-contained account of our view of cosmological history and the production of matter in a varying gravitational field. Special care has been taken to describe the vacuum correctly in the present context and to perform the necessary subtractions of zero-point effects.

Gravitational instability of empty Minkowski space-time

Abstract It is shown that empty Minkowski space-time is unstable in the presence of a massive scalar quantum field coupled to gravitation, provided the dimensionless parameter Km 2 exceeds the threshold value Km 2 th = 288 π 2 . This instability condition is identical with the existence condition for a recently proposed self-consistent cosmology. This is in strong analogy to a phase transition, with critical point at Km 2 th , the two phases being Minkowski and De Sitter spaces.

From unstable Minkowski space to the inflationary universe

It is shown that Minkowski space is unstable in the context of semiclassical gravity. There exists a threshold mass, of the quantized matter field, which marks the dividing line between stable and unstable vacuum fluctuations of matter in flat space-time. The Minkowski vacuum gravitational-matter system undergoes a phase transition above this “critical point,” the new phase being a self-consistently generated de Sitter Euclidean cosmology. Its total energy is degenerate with respect to that of empty Minkowski space-time. It represents an appropriate candidate for the primeval configuration of an inflationarylike universe.

Periodic loss modulation in a ring laser: influence of inhomogeneous broadening and detuning

The influence of periodic loss modulation was studied analytically for a tuned homogeneously broadened ring cavity with unidirectional beam propagation in a recent paper [ T. Erneux S. M. Baer P. Mandel , Phys. Rev. A35, 1165 ( 1987)]. In this paper we extend these results to assess the influence of inhomogeneous broadening and detuning. We conclude that these two factors do not affect qualitatively the bifurcation diagrams. In addition we determine the bifurcation diagrams when both the pump parameter and the modulation amplitude are taken as control parameters.

From empty Minkowski space towards big-bang singularity

Abstract A new self-consistent cosmological history is exhibited in which the matter-gravitational field system evolves smoothly from a quantum unstable Minkowski vacuum towards a big-bang configuration.

From unstable Minkowski space to inflation

We present a perturbative approach to the equations describing the behavior of a quantum scalar field in a self-consistently generated Robertson-Walker universe. This approach throws new light on the significance of the Minkowskian instability and on the subtraction procedure which shows that a inflation cosmology is a possible future of the Minkowski space.

Scalar trace anomaly and anti-gravitational interaction in a perturbative approach to self-consistent cosmologies

Abstract We present a perturbative approach to the equations controlling the behavior of the recently proposed self-consistent, causal, singularity-free cosmologies. This approach sheds a new light on the threshold mass which governs both the (in)stability of empty Minkowski space and the existence of these cosmologies. An unexpected fact arises at the lower order of this perturbative scheme: the mass of the massive (scalar) field coupled non-minimally to gravitation is completely absorbed in a rescaling of the gravitational constant. The latter becomes negative, thereby causing an effective anti-gravitational interaction when the corresponding mass exceeds the minkowskian instability threshold. Moreover, the source of this effective antigravitational interaction is the usual scalar trace anomaly associated with the residual massless part of the matter field.

Derivation of reference distribution functions for Tokamak-plasmas by statistical thermodynamics

A general approach for deriving the expression of reference distribution functions by statistical thermodynamics is illustrated, and applied to the case of a magnetically confined plasma. The local equilibrium is defined by imposing the minimum entropy production, which applies only to the linear regime near a stationary thermodynamically non-equilibrium state and the maximum entropy principle under the scale invariance restrictions. This procedure may be adopted for a system subject to an arbitrary number of thermodynamic forces, however, for concreteness, we analyze, afterwords, a magnetically confined plasma subject to three thermodynamic forces, and three energy sources: (i) the total Ohmic heat, supplied by the transformer coil; (ii) the energy supplied by neutral beam injection (NBI); and (iii) the RF energy supplied by ion cyclotron resonant heating (ICRH) system which heats the minority population. In this limit case, we show that the derived expression of the distribution function is more general than that one, which is currently used for fitting the numerical steady-state solutions obtained by simulating the plasma by gyro-kinetic codes. An application to a simple model of fully ionized plasmas submitted to an external source is discussed. Through kinetic theory, we fixed the values of the free parameters linking them with the external power supplies. The singularity at low energy in the proposed distribution function is related to the intermittency in the turbulent plasma.

Reference distribution functions for magnetically confined plasmas from the minimum entropy production theorem and the MaxEnt principle, subject to the scale-invariant restrictions

We derive the expression of the reference distribution function for magnetically confined plasmas far from the thermodynamic equilibrium. The local equilibrium state is fixed by imposing the minimum entropy production theorem and the maximum entropy (MaxEnt) principle, subject to scale invariance restrictions. After a short time, the plasma reaches a state close to the local equilibrium. This state is referred to as the reference state. The aim of this Letter is to determine the reference distribution function (RDF) when the local equilibrium state is defined by the above mentioned principles. We prove that the RDF is the stationary solution of a generic family of stochastic processes corresponding to an universal Landau-type equation with white parametric noise. As an example of application, we consider a simple, fully ionized, magnetically confined plasmas, with auxiliary Ohmic heating. The free parameters are linked to the transport coefficients of the magnetically confined plasmas, by the kinetic theory.