Old Ideas for New Physicists:1

We review and clarify ideas proposed many years ago for understanding cosmology in a holographic framework. The basic strategy is to use Jacobson's\cite{ted95} identification of Einstein's equations with the hydrodynamic equations of the "Area = 4 Entropy" law for causal diamonds, to identify a quantum system whose hydrodynamics match those of a given space-time. This can be done exactly for a system with any positive cosmological constant, which saturates the entropy bound for all times. The quantum system is a sequence of (cut-off) $1+1$ dimensional CFTs, with central charge proportional to the entropy in causal diamonds along an FRW geodesic. This matches with a recent\cite{BZ} proposal that the modular Hamiltonian of any causal diamond for non-negative c.c. is the $L_0$ generator of such a CFT. When an early de Sitter era is followed by slow roll expansion of the horizon, disjoint horizon volumes (which are gauge copies in an eternal dS space, but become physical due to slow roll expansion of the horizon area) manifest as a dilute gas of black holes in a post-inflationary era. Entropy fluctuations of individual black holes manifest as CMB fluctuations, and the tensor/scalar ratio is suppressed by an extra factor of the slow roll parameter $\epsilon$. Black hole evaporation provides the Hot Big Bang and baryogenesis. Black hole mergers can easily provide a source of primordial BH dark matter that dominates radiation at a temperature of $1$ eV, but numerical simulations are required to determine whether the model can explain the actual dark matter in our universe.
Comment: LaTeX. 27 pages, 2 figures