The Holographic Universe:
From Beginning to End
NCHU Workshop, U of M, Oct 1821, 2010
Why did the universe begin its life
with low entropy?
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Question goes back to Boltzmann. Emphasized
in 1960s by Penrose.
Subsumes questions about fine tuning:
homogeneity, isotropy, flatness.
Covariant Entropy Bound (Fischler-SusskindBousso) provides new insight
INFLATION DOES NOT SOLVE THIS
PROBLEM (and therefore doesn’t explain FRW)
I’ll propose a solution based on holographic
cosmology
Based on work with Fischler and Mannelli
Holographic Screen of a Causal
Diamond
Maximal area d-2 surface on the null boundary
Holographic Space-time
Area = 4 ln dim H plus overlaps define
conformal factor and causal structure
 Jacobson: Thermodynamics of such a
system  Einstein eqns for large
diamonds
 Space-time is NOT a fluctuating quantum
variable, it’s defined by the structure of the
QM Hilbert space
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Degrees of Freedom of Quantum
Gravity
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YT gm Y gm Y = 0  Y = (0, Sa )
Sa (y) Real Components of d – 2 Spinor
Determines Orientation of Holoscreen at y via ST
gm1 … mk S 1<k<d -2 (Cartan – Penrose)
SaI (m) SbJ (n ) + SbJ (n) SaI (m) = dab dmn MIJ
m,n pixelation of holoscreen. I,J refer to
compact dimensions
DOF of Supersymmetric Massless Particles
Penetrating Pixels of Holoscreen
16 Real Components per pixel implies graviton
and gravitino in spectrum
Holographic Cosmology
Introduce a lattice with the topology of flat
3 space on the Big Bang hypersurface
 At each lattice point x define a nested
sequence of Hilbert spaces H (n, x) = Pn
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Define a sequence of unitary operators in
H(nmax , x) : Uk = Vk X Wk where Vk acts
in H (k, x) & Wk in its tensor complement
 Define an overlap H (n, x) = O (n, x,y) X
N(n,x), H (n, y) = O (n, x,y) X N(n,y)
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For lattice nearest neighbors O = P
Consistency conditions for dynamics:
density matrices on all overlaps given by
each observer’s dynamics must be
unitarily equivalent.
The D(ense) B(lack) H(ole) F(luid) is a
solution: Vk (x) = eH(k) all x, O(n,x,y) =
Pn-d(x,y) d = minimal # of lattice steps.
Homogeneous (consistency), isotropic
(large k: locus of equal d ~ a sphere).
H(k) = S S(m) A(m,n,k) S(n) + P : A =
randomly chosen anti-symmetric
For large k, approaches free massless 1 + 1
fermion. P(k) randomly chosen irrelevant
perturbation of this. Define energy density
to be 1+1 energy density. Random
Hamiltonian sweeps out entire Hilbert
space  entropy = that of CFT  p = r
and covariant entropy bound saturated.
Absence of scale implies FRW is flat.
Space-time geometry emergent from QM.
Rotation invariance emergent from overlap
rules in large k limit.
The real universe
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TB & Fischler: heuristic picture as small normal
“percolating fractal” in DBHF.
Today’s lecture, a new attempt: Large k DBHF : Time
avg State at large k is maximally uncertain r in Vk
New overlap rules allow transition to N copies of thy. of
stable dS space (see later) with entropy k ln dim P, which
gives same time avg density matrix. Entropy of this
system the same as that of dS space with “final” c.c.
(determines N, which is a cosmological initial condition)*.
This quantum theory gives a universe that resembles N
horizon volumes of dS space with entropy k: eternal
inflation, but with only a fixed number of horizons
Hard to understand in low energy effective field theory.
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Heuristically, in an as yet unconstructed model
in which inflation ends, will have to put together
these different spherical horizon volumes in a
single 3 space  that 3 space cannot be flat.
Interstices between spheres (>~ ¾ volume) must
carry conformal factor that reduces their volume
to Planck size. Induces random scalar curvature
fluctation. If we attribute this to a random energy
density then Einstein eqns. Imply dr/r ~ 1 (up to
factors of 2p etc.).
Match to a slow roll model, where red tilt allows
smaller fluctuations in CMB
Constraints: no self reproduction, enough efoldings to make CMB causal, enough tilt to get
to 10-5
Stable dS Space
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Two Hamiltonians, H random finite dim (eS)
bounded by ~ 1/R . P commutes with H for low
eigenvalues
[P, H] = MP2 f(P / R MP2 )
Empty dS is infinite temp ensemble for H
P describes localized excitations. Subspace
with eigenvalue E has degeneracy eS – 2pRE (fits
black hole formula). This model explains
qualitative “exptl” features of dS space.
In cosmology. High entropy state is “empty” :
may explain Penrose’s conundrum. We see
physics of P
Asymptotically Flat Space SuperPoincare Invariant?
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Superstring/M-theory Provides Ample Evidence
This is True
Multi-parameter Web of Supersymmetric
Theories in SpaceTime d = 4 … 11
No Consistent AF Space-time w/o SUSY
Holographic formalism provides basis for this:
pixel variables approach degrees of freedom of
massless superparticles as holoscreen
approaches Lorentz invariant two sphere (TB,
Fiol, Morisse)
The Real World Has(?) Positive L
Evidence From Distant Supernovae, Ages
of Globular Clusters/Universe, Large Scale
Structure, Cosmic Microwave Background
 If True: Holographic Principle Implies
Finite Number (ln N = 10120) of Quantum
States (TB – Fischler)
 (1 – 2cd M/rd-3 -(r/R)2 ) = 0
 No Exact Scattering Theory as in
Conventional String Theory
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Quantum Theory of de Sitter Space
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TB, Fischler, Fiol, Morisse
C.c. input parameter, determines number of SaI
(n) Variables (Max holoscreen = cosmological
horizon w/ finite area)
C.c.  0 limiting theory must be isolated
Superpoincare invariant theory – no known
examples – non-generic in low energy SUGRA
TB’s scaling law: gravitino mass: m3/2 ~ L1/4
(only handwaving derivations but implies
superpartners in TeV regime (LHC))
Implications for Particle Physics
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Low scale of SUSY breaking implies Very Low
Energy Gauge Mediation – no SUSY wimp dark
matter.
Axions also problematic because saxion ruins
nucleosynthesis (Carpenter, Dine, Festuccia)
Only plausible dark matter candidate: Hidden
sector neutral baryon with primordial asymmetry
This particle has a magnetic moment (electric?)
because hidden sector constituents charged.
Dark matter dipoles have interesting signals (TB,
Fortin, Thomas) and might have effects on
galactic field.
Conclusions
Holographic cosmology derives
homogeneity isotropy and flatness from
high entropy initial conditions
 Real World might be highest entropy state
that escapes DBHF phase.
 H.C. implies asymptotic dS universe with
c.c. determined by initial conditions (#
DOF in low entropy state). Small c.c.
anthropically determined.
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Theory of small c.c. dS becomes
SUSic, with m3/2 ~ 10 L1/4 . Maybe
fairly unique for fixed c.c.
Low scale of SUSY breaking puts
strong constraints on Terascale
physics (Pyramid Scheme) and dark
matter is almost certainly a neutral
hidden sector baryon, with a
magnetic moment, in this model.