The Holographic Universe: From Beginning to End

1. The Holographic Universe: From Beginning to End NCHU Workshop, U of M, Oct 18-21, 2010

2. Why did the universe begin its life with low entropy? • Question goes back to Boltzmann. Emphasized in 1960s by Penrose. • Subsumes questions about fine tuning: homogeneity, isotropy, flatness. • Covariant Entropy Bound (Fischler-Susskind-Bousso) 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

3. Holographic Screen of a Causal Diamond Maximal area d-2 surface on the null boundary

5. 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

6. Degrees of Freedom of Quantum Gravity • 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) = dabdmnMIJ • m,npixelation of holoscreen. I,J refer to compact dimensions • DOF of SupersymmetricMassless Particles Penetrating Pixels of Holoscreen • 16 Real Components per pixel implies graviton and gravitino in spectrum

7. 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 • 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)

8. 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

9. 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.

10. The real universe • 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.

11. 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 e-foldings to make CMB causal, enough tilt to get to 10-5

12. Stable dS Space • 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

13. Asymptotically Flat Space Super-Poincare Invariant? • 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 masslesssuperparticles as holoscreen approaches Lorentz invariant two sphere (TB, Fiol, Morisse)

14. 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

15. Quantum Theory of de Sitter Space • 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))

16. Implications for Particle Physics • 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.

17. 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.

18. 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.