Approaches to Quantum Gravity

String theory, holography and Quantum Gravity 199the idea of a low entropy beginning of the universe, and the uniform p = ρ solutionof holographic cosmology provides a counterexample. In that system, there isan arrow of time, but the system maximizes the entropy available to it at all times.As a consequence, it does not contain local observers, but even if it did, a localobserver would not perceive a thermodynamic arrow of time.However, we have seen at an intuitive level that the requirement that a normalregion of the universe exists at all, and does not immediately subside into thedense black hole fluid, puts strong constraints on fluctuations in the matter density.Perhaps when we understand these constraints in a quantitative manner, theywill explain the low entropy of the early universe.11.3 Quantum theory of de Sitter spaceThe cosmology of the previous section leads one to study the idealized problemof de Sitter space-time as the ultimate endpoint, toward which the universe (or atleast the only part of it we will ever observe) is tending. The initial approach takenby string theorists interested in particle phenomenology was to look for modelsof string theory in asymptotically flat space. Arguments based on the locality ofquantum field theory (and the presumption that a similarly local formulation ofstring theory should exist) suggested that such a theory should be adequate forunderstanding the masses and interactions of particles below the Planck energy.This program has run into difficulty because no one has found an asymptoticallyflat form of string theory, which is not exactly supersymmetric. All attempts tobreak supersymmetry lead to, at the very least, a breakdown of string perturbationtheory, and clear indications that the geometry of the resulting space-time is notasymptotically flat.I believe that the breaking of supersymmetry in the real world is intimatelyconnected with the fact that the real world is not asymptotically flat, but insteadasymptotically de Sitter [17]. The phenomenology of particle physics should thusbe derivable from a theory of eternal de Sitter space. The holographic entropybound, in the strong form conjectured by Fischler and the present author, indicatesthat this is a quantum theory with a finite number of states, and cannot fitdirectly into the existing formalism of string theory. 14 It also implies that if such atheory exists then dS space is stable.The general formalism described above indicates that the variables for describingde Sitter space should be fermions which are a section of the spinor bundle overa pixelated cosmological horizon. The natural SU(2) invariant pixelation of the S 214 Except by finding a subset of states in an asymptotically flat or anti-de Sitter string theory, which isapproximately described by de Sitter space, and decouples from the rest of the system.