Holographic Dark EnergyHolographic Dark Energy

Preety Sidhu5 May 2006

Black Holes and EntropyBlack 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 PrincipleThe 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 EntropyInformation 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 CosmologyHolographic 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 ScalesSizes 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 FluctuationsVacuum 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 BoundsHolographic 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