Astronomical observations indicate that the cosmological constant is many orders of magnitude smaller than estimated in modern theories of elementary particles. After a brief review of the history of this problem, five different approaches to its solution are described.

/pdf/the-cosmological-constant-problem-130fjuhulq.pdf

The Cosmological Constant Problem

The correspondence between supergravity (and string theory) on AdS space and boundary conformal eld theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic connement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale \holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

https://www.intlpress.com/site/pub/files/_fulltext/journals/atmp/1998/0002/0003/ATMP-1998-0002-0003-a003.pdf

Anti-de Sitter Space, Thermal Phase Transition, And Confinement in Gauge Theories

The cosmological consequences of a pervasive, rolling, self-interacting, homogeneous scalar field are investigated. A number of models in which the energy density of the scalar field red-shifts in a specific manner are studied. In these models the current epoch is chosen to be scalar-field dominated to agree with dynamical estimates of the density parameter, ${\ensuremath{\Omega}}_{\mathrm{dyn}\mathrm{\ensuremath{\sim}}0.2}$, and zero spatial curvature. The required scalar-field potential is ``nonlinear'' and decreases in magnitude as the value of the scalar field increases. A special solution of the field equations which is an attractive, time-dependent, fixed point is presented. These models are consistent with the classical tests of gravitation theory. The E\"otv\"os-Dicke measurements strongly constrain the coupling of the scalar field to light (nongravitational) fields. Nucleosynthesis proceeds as in the standard hot big-bang model. In linear perturbation theory the behavior of baryonic perturbations, in the baryon-dominated epoch, do not differ significantly from the canonical scenario, while the presence of a substantial amount of homogeneous scalar-field energy density at low red-shifts inhibits the growth of perturbations in the baryonic fluid. The energy density in the scalar field is not appreciably perturbed by nonrelativistic gravitational fields, either in the radiation-dominated, matter-dominated, or scalar-field-dominated epochs. On the basis of this effect, we argue that these models could reconcile the low dynamical estimates of the mean mass density with the negligibly small spatial curvature preferred by inflation.

https://link.aps.org/pdf/10.1103/PhysRevD.37.3406

Cosmological Consequences of a Rolling Homogeneous Scalar Field

Supersymmetry, Supergravity and Particle Physics

Dynamical Breaking of Supersymmetry

We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of Zp gauge theories shows that they are associated with an emergent Zp one-form (KalbRamond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear σ-models. It also allows us to expand on Polchinski’s classification of cosmic strings. We argue that in models of quantum gravity, there are no global symmetries, all continuous gauge symmetries are compact, and all charges allowed by Dirac quantization are present in the spectrum. These conjectures are not new, but we present them from a streamlined and unified perspective. Finally, our discussion about string charges and symmetries leads to a more physical and more complete understanding of recently found consistency conditions of supergravity.

Symmetries and Strings in Field Theory and Gravity

We discuss the construction of the analog of an S-matrix for space-times that begin with a Big-Bang and asymptote to an FRW universe with nonnegative cosmological constant. When the cosmological constant is positive there are many such S-matrices, related mathematically by gauge transformations and physically by an analog of the principle of black hole complementarity. In the limit of vanishing $\Lambda$ these become (approximate) Poincare transforms of each other. Considerations of the initial state require a quantum treatment of space-time, and some preliminary steps towards constructing such a theory are proposed. In this context we propose a model for the earliest semiclassical state of the universe, which suggests a solution for the horizon problem different from that provided by inflation.

M theory observables for cosmological space-times

We present calculations of the low-energy mass spectrum and matrix elements of quantum chromodynamics. We employ an isospin doublet of massless quarks and analyze the theory from the strong-coupling limit using a particularly simple lattice Hamiltonian. In the strong-coupling limit the vacuum state has exact local color symmetry, but spontaneously breaks those elements of chiral symmetry which are present in the lattice Hamiltonian. Expansions for masses ($\ensuremath{\pi},\ensuremath{\rho},\ensuremath{\omega},\ensuremath{\sigma},{A}_{1},B,f,$ and nucleon) and matrix elements ${g}_{A}$ in the reciprocal coupling constant are analytically continued to the continuum limit using Pad\'e approximants. The results are in surprisingly good agreement with experiment except for the pion mass. This single failure is traced to the lack of full chiral symmetry in the theory for large lattice spacing and the lack of significant spin-spin forces in low orders of strong-coupling perturbation theory. Higher-order calculations should resolve this problem, but a more realistic Hamiltonian suggested by renormalization-group analyses also looks promising.

Strong-coupling calculations of the hadron spectrum of quantum chromodynamics

http://horn.cs.tau.ac.il/publications/bosonization.pdf

Bosonization of the SU(N) Thirring models

We present a crude Matrix Theory model for Schwarzschild black holes in uncompactified dimension greater than 5. The model accounts for the size, entropy, and long range static interactions of black holes. The key feature of the model is a Boltzmann gas of D0 branes, a concept which depends on certain qualitative features of Matrix Theory which have not previously been utilized in studies of black holes.

http://iopscience.iop.org/article/10.1088/1126-6708/1998/01/008/pdf

Schwarzschild black holes in matrix theory II

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