Holographic Dark Energy

1
Holographic Dark Energy

• Preety Sidhu
• 5 May 2006

2
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

3
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

4
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
  systems 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

5
Holographic Cosmology

• Related to the (poorly understood) principles of
  quantum gravity
• Bekenstein max entropy for weakly
  self-gravitating physical system 4D flat
  spacetime S 2pER
• Taken to be max holographic entropy for universe

6
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

7
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 ? p/4
• ?(z) -1(1- p/4)z
• No adjustable parameters, consistent with recent
  cosmological observations

8
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