Holographic Dark Energy Preety Sidhu 5 May 2006

Black Holes and Entropy Black holes are “maximal entropy objects” Entropy of a black hole proportional to surface area of event horizon Max entropy for volume of space goes as bounding surface area, not mass

The Holographic Principle All information about a physical system in some region of space is encoded in its boundary surface, not its volume Like all the information in a room encoded in its walls

Information Entropy Information entropy (or Shannon entropy) measure of “randomness” or “uncertainty” in a signal Thermodynamic entropy like amount of Shannon entropy “missing” between classical macroscopic variables and full microscopic description of system’s state Entropy ultimately measured in bits or nats 1 bit = (ln 2) nats  0.69 nats 1 nat ~ 4 Planck areas Total bits related to matter/energy degrees of freedom Maximum info density, for given volume, about enclosed particle states Matter cannot be infinitely subdivided

Holographic Cosmology Related to the (poorly understood) principles of quantum gravity Bekenstein max entropy for weakly self-gravitating physical system [4D flat spacetime]: S ≤ 2πER Taken to be max holographic entropy for universe

Sizes and Scales In quantum field theory –UV cutoff: short wavelength, high energy bound –IR cutoff: long wavelength, low energy bound –Related by limits set by black hole formation UV limit ~ Planck length IR limit ~ “size of universe” –Particle horizon: largest comoving distance from which light could have reached observer today –Event horizon: largest comoving distance from which light will ever reach observer

Vacuum Fluctuations Uncertainty principle for quantum vacuum energy fluctuations, with N degrees of freedom Holographic principle sets N within UV and IR cutoffs One degree of freedom is a maximum entropy of one Boltzmann unit k Corresponds to Ω = π/4  (z) = -1+(1- π/4)z No adjustable parameters, consistent with recent cosmological observations

Holographic Bounds Holographic entropy bound violated for closed universe of particle horizon size Can solve for closed universe: –Replace particle horizon with event horizon –Add negative pressure component –Or Hubble scale IR cutoff with non-minimal coupling to scalar field