The Causet Mechanism for the Creation of Energy

Sorkin's causet mechanism is generalized to include energy exchange between causet elements and conventional vacuum fluctuations to the inflationary epoch. In this, the dark energy of the adiabatic era is the fluctuating remnant of inflation. The mechanism is also applicable to black hole evaporation.Comment: Dedicated to Rafael Sorkin, to appear in his 60th birthday Festschrif

A Brief Course in Spontaneous Symmetry Breaking I. The Paleolitic Age

The physical world is marked by the phenomenon of spontaneous broken symmetry (SBS) i.e. where the state of a system is assymmetric with respect to the symmetry principles that govern its dynamics. For material systems this is not surprising since more often than not energetic considerations dictate that the ground state or low lying excited states of many body system become ordered i.e. a collective variable, such as magnetization or the Fourier transform of the density of a solid, picks up expectation values which otherwise would vanish by virtue of the dynamical symmetry(isotropy or translational symmetry in the aforementioned examples). More surprising was the discovery of the role of SBS in describing the vacuum or low lyng excitations of a quantum field theory. First came spontaneously broken chiral symmetry which was then applied to soft pion physics. When combined with current algebra, this field dominated particle physics in the 60's. Then came the application of the notion of SBS to situations where the symmetry is locally implemented by gauge fields. In that case the concept of order becomes more subtle. This development lead the way to electroweak unification and it remains one of the principal tools of the theorist in the quest for physics beyond the standard model. This brief review is intended to span the history of SBS with emphasis on conceptual rather than quantitative content. It is a written version of lectures of R.Brout on the ``Paleolithic Age'' and on ``Modern Times'' by F.Englert, i.e. respectively without and with gauge fields.Comment: LaTeX file 28 pages, 9 figures. Presented at the 2001 Corfu Summer Institute on Elementary Particle Physic

The Inflaton and its Mass

In the context of the two fluid model of space-time fluctuations proposed to tame the transplanckian problem encountered in black hole physics, it is postulated that the inflaton is the fluctuation of mode density, ``the vapor component'' of the model. The mass of the inflaton is occasioned by the exchange of degrees of freedom between the ``vapor'' and the ``liquid'', the planckian ``soup'' in which usual ``cisplanckian'' fields propagate. This exchange between vacuum fluctuations is modeled after its counterpart in the real world i.e. black hole evaporation. In order of magnitude, a very rough semiquantitative estimate, would situate the mass somewhere between $10^{-10}$ and $10^{-5}$ planck masses, the largest uncertainty being the mass of the planckian black hole fluctuation i.e. the entropy that one ascribes to it.Comment: LaTex file, 11 page

Of Inflation and the Inflaton

Due to intra-field gravitational interactions, field configurations have a strong negative component to their energy density at the planckian and transplanckian scales, conceivably resulting in a sequestration of the transplanckian field degrees of freedom. Quantum fluctuations then allow these to tunnel into cisplanckian configurations to seed inflation and conventional observed physics: propagating modes of QFT in a geometry which responds to the existence of these new modes through the energy constraint of general relativity, H^2 = \rho/3. That this tunnelling results in geometries and field configurations that are homogeneous allows for an estimate of the mass of the inflaton, m=O(10^{-6}), and the amplitude of the inflaton condensate, \phiav=O(10), both consistent with phenomenology.Comment: 14 page

Who is the Inflaton?

In the context of the two-fluid model introduced to tame the transplanckian problem of black hole physics, the inflaton field of the chaotic inflation scenario is identified with the fluctuation of the density of modes. Its mass comes about from the exchange of degrees of freedom between the two fluids.Comment: extensively revised version presented at the Corfu School and Workshop of Theoretical Physics 200

From Inflation to Dark Energy

It is proposed that after the macroscopic fluctuation of energy density that is responsible for inflation dies away, a class of microscopic fluctuations, always present, survives to give the present day dark energy. This latter is simply a reinterpretation of the causet mechanism of Ahmed, Dodelson, Green and Sorkin, wherein the emergence of space is dropped but only energy considerations are maintained. At postinflation times, energy is exchanged between the "cisplanckian" cosmos and an unknown foam-like transplanckian reservoir. Whereas during inflation, the energy flows only from the latter to the former after inflation it fluctuates in sign thereby accounting for the tiny effective cosmological constant that seems to account for dark energy.Comment: 4 pages, RevTe

Condensation of Planckian Modes and the Inflaton

To confront the transplanckian problem encountered in the backward extrapolation of the cosmological expansion of the momenta of the modes of quantum field theory, it is proposed that there is a reservoir, depository of transplanckian degrees of freedom. These are solicited by the cisplanckian modes so as to keep their density fixed and the total energy density of vacuum at a minimum. The mechanism is due to mode - reservoir interaction, whereupon virtual quantum processes give rise to an effective mode-mode attraction. A BCS condensate results. It has a massless and massy collective excitation, the latter identified with the inflaton. For an effective non dimensional mode-reservoir coupling constant, g approx 0.3, the order of magnitude of its mass is what is required to account for cosmological fluctuations i.e. O(10^-6 -> 10^-5)m_Planck.Comment: Recipient of Honorable Mention in the Gravity Research Foundation Essay competition 2003. 6 page

The Inflaton and Time in the Matter-Gravity System

The emergence of time in the matter-gravity system is addressed within the context of the inflationary paradigm. A quantum minisuperspace-homogeneous minimally coupled inflaton system is studied with suitable initial conditions leading to inflation and the system is approximately solved in the limit for large scale factor. Subsequently normal matter (either non homogeneous inflaton modes or lighter matter) is introduced as a perturbation and it is seen that its presence requires the coarse averaging of a gravitational wave function (which oscillates at trans-Planckian frequencies) having suitable initial conditions. Such a wave function, which is common for all types of normal matter, is associated with a ``time density'' in the sense that its modulus is related to the amount of time spent in a given interval (or the rate of flow of time). One is then finally led to an effective evolution equation (Schroedinger Schwinger-Tomonaga) for ``normal'' matter. An analogy with the emergence of a temperature in statistical mechanics is also pointed out.Comment: 14 pages, late

Time dependent Green functions from Wheeler De Witt solutions

The aim of this article is twofold. First we examine from a new angle the question of recovery of time in quantum cosmology. We construct Green functions for matter fields from the solutions of the Wheeler De Witt equation. For simplicity we work in a mini-superspace context. By evaluating these Green functions in a first order development of the energy ``increment'' induced by matrix elements of field operators, we show that the background geometry is the solution of Einstein equations driven by the mean matter energy and that it is this background which determines the time lapses separating the field operators. Then, by studying higher order corrections, we clarify the nature of the small dimensionless parameters which guarantee the validity of the approximations used. In this respect, we show that the formal expansion in the inverse Planck mass which is sometime presented as the ``standard procedure'' is illegitimate. Secondly, by the present analysis of Green functions, we prepare the study of quantum matter transitions in quantum cosmology. In a next article, we show that the time parametrization of transition amplitudes appears for the same reasons that it appeared in this article. This proves that the background is dynamically determined by the transition under examination.Comment: 25 pages, latex, no figure