Approaches to Quantum Gravity

String theory, holography and Quantum Gravity 199
the idea of a low entropy beginning of the universe, and the uniform p = ρ solution
of holographic cosmology provides a counterexample. In that system, there is
an 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 local
observer would not perceive a thermodynamic arrow of time.
However, we have seen at an intuitive level that the requirement that a normal
region of the universe exists at all, and does not immediately subside into the
dense black hole fluid, puts strong constraints on fluctuations in the matter density.
Perhaps when we understand these constraints in a quantitative manner, they
will explain the low entropy of the early universe.
11.3 Quantum theory of de Sitter space
The cosmology of the previous section leads one to study the idealized problem
of de Sitter space-time as the ultimate endpoint, toward which the universe (or at
least the only part of it we will ever observe) is tending. The initial approach taken
by string theorists interested in particle phenomenology was to look for models
of string theory in asymptotically flat space. Arguments based on the locality of
quantum field theory (and the presumption that a similarly local formulation of
string theory should exist) suggested that such a theory should be adequate for
understanding the masses and interactions of particles below the Planck energy.
This program has run into difficulty because no one has found an asymptotically
flat form of string theory, which is not exactly supersymmetric. All attempts to
break supersymmetry lead to, at the very least, a breakdown of string perturbation
theory, and clear indications that the geometry of the resulting space-time is not
asymptotically flat.
I believe that the breaking of supersymmetry in the real world is intimately
connected with the fact that the real world is not asymptotically flat, but instead
asymptotically de Sitter [17]. The phenomenology of particle physics should thus
be derivable from a theory of eternal de Sitter space. The holographic entropy
bound, in the strong form conjectured by Fischler and the present author, indicates
that this is a quantum theory with a finite number of states, and cannot fit
directly into the existing formalism of string theory. 14 It also implies that if such a
theory exists then dS space is stable.
The general formalism described above indicates that the variables for describing
de Sitter space should be fermions which are a section of the spinor bundle over
a pixelated cosmological horizon. The natural SU(2) invariant pixelation of the S 2
14 Except by finding a subset of states in an asymptotically flat or anti-de Sitter string theory, which is
approximately described by de Sitter space, and decouples from the rest of the system.