Essay: Supersymmetry, the Cosmological Constant, and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterizes different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models.     

Letter: Quantum Kaluza-Klein Cosmologies

In the No-boundary Universe with d = 11 supergravity, under the S _n × S _11–n Kaluza-Klein ansatz, the only seed instanton for the universe creation is a S ₇ × S ₄ space. It is proven that for the Freund-Rubin, Englert and Awada-Duff-Pope models the macroscopic universe in which we are living must be 4- instead of 7-dimensional without appealing to the anthropic principle.     

Developments in inflationary cosmology

This talk presents some recent work that has been done in inflationary cosmology. First a brief review is given of the inflation scenario and its basic models. After that, one of the main problems in developing inflationary models has been the requirement of a very flat inflation potential. In solving this problem, supersymmetry has played a major role, and the reasons will be discussed and a specific example of the SUSY hybrid model will be examined. Some problems introduced by SUSY such as the η and gravitino problems will then be discussed. Then in a different direction, the quintessential inflation model will be examined as a proposal where a single scalar field plays the role of both the inflaton at early time and the dark energy field later. The final topic covered is developments in understanding dissipation and particle production processes during the inflationary phase.      

Metastable SUSY Breaking – Predicting the Fate of the Universe

The possibility that supersymmetry (SUSY) could be broken in a metastable vacuum has recently attracted renewed interest. In these proceedings we will argue that metastability is an attractive and testable scenario. The recent developments were triggered by the presentation of a simple and calculable model of metastable SUSY breaking by Intriligator, Seiberg and Shih (ISS), which we will briefly review. One of the main questions raised by metastability is, why did the universe end up in this vacuum. Using the ISS model as an example we will argue that in a large class of models the universe is automatically driven into the metastable state during the early hot phase and gets trapped there. This makes metastability a natural option from the cosmological point of view. However, it may be more than that. The phenomenologically required gaugino masses require the breaking of R-symmetry. However, in scenarios with a low supersymmetry breaking scale, e.g., gauge mediation a powerful theorem due to Nelson and Seiberg places this at odds with supersymmetry breaking in a truely stable state and metstability becomes (nearly) inevitable. Turning around one can now experimentally test whether gauge mediation is realised in nature thereby automatically testing the possibility of a metastability of the vacuum. Indeed, already the LHC may give us crucial information about the stability of the vacuum.     

Supersymmetry of FRW Barotropic Cosmologies

Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K = 0.     

On the Birth of a Closed Hyperbolic Universe

We clarify and develop the results of a previous paper on the birth of a closed universe of negative spatial curvature and multiply connected topology. In particular we discuss the initial instanton and the second topology change in more detail. This is followed by a short discussion of the results.     

Geometrical Lagrangian for a Supersymmetric Yang–Mills Theory on the Group Manifold

Perhaps one of the main features of Einstein's General Theory of Relativity is that spacetime is not flat itself but curved. Nowadays, however, many of the unifying theories like superstrings on even alternative gravity theories such as teleparalell geometric theories assume flat spacetime for their calculations. This article, an extended account of an earlier author's contribution, it is assumed a curved group manifold as a geometrical background from which a Lagrangian for a supersymmetric N=2, d=5 Yang–Mills – SYM, N=2, d=5 – is built up. The spacetime is a hypersurface embedded in this geometrical scenario, and the geometrical action here obtained can be readily coupled to the five-dimensional supergravity action. The essential idea that underlies this work has its roots in the Einstein–Cartan formulation of gravity and in the group manifold approach to gravity and supergravity theories. The group SYM, N=2, d=5, turns out to be the direct product of supergravity and a general gauge group .     

Quantum geometrodynamics: whence,whither?

Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler–DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.

These considerations reveal that the concepts of spacetime and time itself are not primary but secondary ideas in the structure of physical theory. These concepts are valid in the classical approximation. However, they have neither meaning nor application under circumstances when quantum-geometrodynamical effects become important. ...There is no spacetime, there is no time, there is no before, there is no after. The question what happens “next” is without meaning [1].

Dedicated to the memory of John Archibald Wheeler.     

Cosmological dynamics in tomographic probability representation

The probability representation for quantum states of the universe in which the states are described by a fair probability distribution instead of wave function (or density matrix) is developed to consider cosmological dynamics. The evolution of the universe state is described by standard positive transition probability (tomographic transition probability) instead of the complex transition probability amplitude (Feynman path integral) of the standard approach. The latter one is expressed in terms of the tomographic transition probability. Examples of minisuperspaces in the framework of the suggested approach are presented. Possibility of observational applications of the universe tomographs are discussed.     

Tomographic entropy and cosmology

The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free pointlike particle and repulsive oscillator are considered. The notion of tomographic entropy and its properties are used to find some inequalities for the tomographic probability determining the quantum state of the universe. The sense of the inequality as a lower bound for the entropy is clarified.     

Second-Order Linear Differential Equations for Effective Barotropic FRW Cosmologies

In 1999, Faraoni wrote a simple second-order linear differential equation for FRW cosmologies with barotropic fluids. His results have been extended by Rosu, who employed techniques belonging to nonrelativistic supersymmetry to obtain time-dependent effective adiabatic indices. Further extensions are presented here using the known connection between the linear second-order differential equations and Dirac-like equations in the same supersymmetric context. These extensions are equivalent to adding an imaginary part to the effective adiabatic index, which is proportional to the mass parameter of the Dirac spinor. The natural physical interpretation of the imaginary part is related to the particular dissipation and instabilities of the effective barotropic FRW hydrodynamics that are introduced by means of this supersymmetric scheme.     

A supersymmetric Vista for quantum cosmology

A brief overview on the subject of Supersymmetric Quantum Cosmology (SQC) is presented here. Different approaches are described, all of them being inspired by the search of a square root of (quantum) General Relativity. Some new ideas in the form of a list of (still!) open problems and an extensive bibliography are included.