Holographic Space Time and Cosmology

Tom Banks (work with W.Fischler, T.J. Torres)

Philosophy of Cosmology, September 12-16, 2014

The Takeaway

I HST describes space-time as an infinite set of quantumsystems, each describing a time-like trajectory, withrelationships between shared information.

I Causal diamonds defined by tensor factorization of Hilbertspaces. Dimensions of Hilbert spaces related to area ofholoscreens by theBekenstein-Hawking-Fischler-Susskind-Bousso area formulalnD = A/4 (Planck units) - this is the Holographic Principle.

I Jacobson (1995) showed that the emergent geometry of sucha system will satisfy Einstein’s equations, with stress tensordetermined in terms of the expectation value of theHamiltonian of a local, maximally accelerated Rindler/Unruhtrajectory. Cosmological constant not determined: asymptoticboundary condition relating large proper time and large arealimits.

On Each Overlap, At Each Time, Individual trajectory Hamiltonians and initial states define two density

matrices in the tensor factor. They must be unitarily equivalent, for each pair of trajectories at all times.

Overlap Diamond in Here

The Takeaway

I HST describes space-time as an infinite set of quantumsystems, each describing a time-like trajectory, withrelationships between shared information.

I Causal diamonds defined by tensor factorization of Hilbertspaces. Dimensions of Hilbert spaces related to area ofholoscreens by theBekenstein-Hawking-Fischler-Susskind-Bousso area formulalnD = A/4 (Planck units) - this is the Holographic Principle.

I Jacobson (1995) showed that the emergent geometry of sucha system will satisfy Einstein’s equations, with stress tensordetermined in terms of the expectation value of theHamiltonian of a local, maximally accelerated Rindler/Unruhtrajectory. Cosmological constant not determined: asymptoticboundary condition relating large proper time and large arealimits.

The Takeaway

I HST describes space-time as an infinite set of quantumsystems, each describing a time-like trajectory, withrelationships between shared information.

I Causal diamonds defined by tensor factorization of Hilbertspaces. Dimensions of Hilbert spaces related to area ofholoscreens by theBekenstein-Hawking-Fischler-Susskind-Bousso area formulalnD = A/4 (Planck units) - this is the Holographic Principle.

I Jacobson (1995) showed that the emergent geometry of sucha system will satisfy Einstein’s equations, with stress tensordetermined in terms of the expectation value of theHamiltonian of a local, maximally accelerated Rindler/Unruhtrajectory. Cosmological constant not determined: asymptoticboundary condition relating large proper time and large arealimits.

The Takeaway - Continued

I Einstein’s eqns. are hydrodynamic equations, quantized onlyfor small excitations around ground state (cf. phonons):accounts for string theory in asymptotically flat and AdSspace-times.

I HST cosmo model explains fine tuning of initial conditions asNECESSARY to a universe with local excitations. Genericstate leads to universe which is homogeneous isotropic andflat, but at all times has a single black hole filling the horizonvolume. If number of states is finite this asymptotes to emptydS space. Inflationary era (which is not dS) leads to localexcitations which are smaller black holes. Number of e-folds ofinflation bounded below in order for black holes to evaporatebefore they collide and grow. Crude estimate: eNe > 105.Black hole evaporation reheats the universe to T ∼ 1013 GeV.

The Takeaway - Continued

I Einstein’s eqns. are hydrodynamic equations, quantized onlyfor small excitations around ground state (cf. phonons):accounts for string theory in asymptotically flat and AdSspace-times.

I HST cosmo model explains fine tuning of initial conditions asNECESSARY to a universe with local excitations. Genericstate leads to universe which is homogeneous isotropic andflat, but at all times has a single black hole filling the horizonvolume. If number of states is finite this asymptotes to emptydS space. Inflationary era (which is not dS) leads to localexcitations which are smaller black holes. Number of e-folds ofinflation bounded below in order for black holes to evaporatebefore they collide and grow. Crude estimate: eNe > 105.Black hole evaporation reheats the universe to T ∼ 1013 GeV.

Holographic Cosmology

I Big Bang Non-singular - Place Where Trajectory’s HilbertSpace has minimal dimension.

I Very Early Universe Dominated by sequence of randomHamiltonians converging to cutoff 1 + 1 CFT → flat p = ρFRW → arbitrary positive c.c. . Local Excitations of dSvacuum ensemble arise only as thermal fluctuations. FlatFRW for generic initial states.

I Better model interpolates period of inflation withm4

P � ΛI � Λ, to generate local fluctuations. Predicts CMBfluctuations different from standard slow roll (no tensor tilt,generic tensor 3 pt. functions), but consistent with data.

I QUEFT not a good approximation to cosmology until end ofinflation because CEB saturated. Jacobsonian THEFT doesdescribe hydrodynamics.

Holographic Cosmology

I Big Bang Non-singular - Place Where Trajectory’s HilbertSpace has minimal dimension.

I Very Early Universe Dominated by sequence of randomHamiltonians converging to cutoff 1 + 1 CFT → flat p = ρFRW → arbitrary positive c.c. . Local Excitations of dSvacuum ensemble arise only as thermal fluctuations. FlatFRW for generic initial states.

I Better model interpolates period of inflation withm4

P � ΛI � Λ, to generate local fluctuations. Predicts CMBfluctuations different from standard slow roll (no tensor tilt,generic tensor 3 pt. functions), but consistent with data.

I QUEFT not a good approximation to cosmology until end ofinflation because CEB saturated. Jacobsonian THEFT doesdescribe hydrodynamics.

Holographic Cosmology

I Big Bang Non-singular - Place Where Trajectory’s HilbertSpace has minimal dimension.

I Very Early Universe Dominated by sequence of randomHamiltonians converging to cutoff 1 + 1 CFT → flat p = ρFRW → arbitrary positive c.c. . Local Excitations of dSvacuum ensemble arise only as thermal fluctuations. FlatFRW for generic initial states.

I Better model interpolates period of inflation withm4

P � ΛI � Λ, to generate local fluctuations. Predicts CMBfluctuations different from standard slow roll (no tensor tilt,generic tensor 3 pt. functions), but consistent with data.

I QUEFT not a good approximation to cosmology until end ofinflation because CEB saturated. Jacobsonian THEFT doesdescribe hydrodynamics.

Holographic Cosmology

I Big Bang Non-singular - Place Where Trajectory’s HilbertSpace has minimal dimension.

I Very Early Universe Dominated by sequence of randomHamiltonians converging to cutoff 1 + 1 CFT → flat p = ρFRW → arbitrary positive c.c. . Local Excitations of dSvacuum ensemble arise only as thermal fluctuations. FlatFRW for generic initial states.

I Better model interpolates period of inflation withm4

P � ΛI � Λ, to generate local fluctuations. Predicts CMBfluctuations different from standard slow roll (no tensor tilt,generic tensor 3 pt. functions), but consistent with data.

I QUEFT not a good approximation to cosmology until end ofinflation because CEB saturated. Jacobsonian THEFT doesdescribe hydrodynamics.

Locality, Matrices and Low EntropyI

M1 0 0 . . . 00 M2 0 . . . 0...

......

... 00 0 0 . . . MK

I Matrix elements bilinear in fundamental quantum operators.H = tr P(M), is sum of block operators when initial statesatisfies constraint above. Quasi-local interactions come fromturning on and off non-diagonal matrix elements.

I Individual blocks are massless particles in specific states, blackholes in random (block) state.

I Appropriate choice of Hamiltonian leads to cosmology

p = ρ→ inflation→ Dilute Black Hole Gas.

I Density of black holes ∼ e−6Ne R−3S . If low enough, black

holes evaporate before they coalesce → radiation dominateduniverse.

Locality, Matrices and Low EntropyI

M1 0 0 . . . 00 M2 0 . . . 0...

......

... 00 0 0 . . . MK

I Matrix elements bilinear in fundamental quantum operators.

H = tr P(M), is sum of block operators when initial statesatisfies constraint above. Quasi-local interactions come fromturning on and off non-diagonal matrix elements.

I Individual blocks are massless particles in specific states, blackholes in random (block) state.

I Appropriate choice of Hamiltonian leads to cosmology

p = ρ→ inflation→ Dilute Black Hole Gas.

I Density of black holes ∼ e−6Ne R−3S . If low enough, black

holes evaporate before they coalesce → radiation dominateduniverse.

Locality, Matrices and Low EntropyI

M1 0 0 . . . 00 M2 0 . . . 0...

......

... 00 0 0 . . . MK

I Matrix elements bilinear in fundamental quantum operators.

H = tr P(M), is sum of block operators when initial statesatisfies constraint above. Quasi-local interactions come fromturning on and off non-diagonal matrix elements.

I Individual blocks are massless particles in specific states, blackholes in random (block) state.

I Appropriate choice of Hamiltonian leads to cosmology

p = ρ→ inflation→ Dilute Black Hole Gas.

I Density of black holes ∼ e−6Ne R−3S . If low enough, black

holes evaporate before they coalesce → radiation dominateduniverse.

Locality, Matrices and Low EntropyI

M1 0 0 . . . 00 M2 0 . . . 0...

......

... 00 0 0 . . . MK

I Matrix elements bilinear in fundamental quantum operators.

H = tr P(M), is sum of block operators when initial statesatisfies constraint above. Quasi-local interactions come fromturning on and off non-diagonal matrix elements.

I Individual blocks are massless particles in specific states, blackholes in random (block) state.

I Appropriate choice of Hamiltonian leads to cosmology

p = ρ→ inflation→ Dilute Black Hole Gas.

I Density of black holes ∼ e−6Ne R−3S . If low enough, black

holes evaporate before they coalesce → radiation dominateduniverse.

Locality, Matrices and Low EntropyI

M1 0 0 . . . 00 M2 0 . . . 0...

......

... 00 0 0 . . . MK

I Matrix elements bilinear in fundamental quantum operators.

H = tr P(M), is sum of block operators when initial statesatisfies constraint above. Quasi-local interactions come fromturning on and off non-diagonal matrix elements.

I Individual blocks are massless particles in specific states, blackholes in random (block) state.

I Appropriate choice of Hamiltonian leads to cosmology

p = ρ→ inflation→ Dilute Black Hole Gas.

I Density of black holes ∼ e−6Ne R−3S . If low enough, black

holes evaporate before they coalesce → radiation dominateduniverse.

Meta-Cosmology

I Generalized “multiverse” model in which model universes ofvarying Λ,ΛI ,Ne are embedded in a background p = ρ,Λ = 0cosmology as localized excitations.

I Allows for anthropic selection of these parameters.

I Apart from connection m3/2 ∼ Λ1/4, which determines scaleof SUSY breaking, particle physics is encoded in algebra offundamental variables, and doesn’t change from one universeto another.

I These universes can interact and collide, on time scales whichcannot be determined by local measurements: one of the hugenumber of ways of solving the ”Boltzmann Brain” problem.

Meta-Cosmology

I Generalized “multiverse” model in which model universes ofvarying Λ,ΛI ,Ne are embedded in a background p = ρ,Λ = 0cosmology as localized excitations.

I Allows for anthropic selection of these parameters.

I Apart from connection m3/2 ∼ Λ1/4, which determines scaleof SUSY breaking, particle physics is encoded in algebra offundamental variables, and doesn’t change from one universeto another.

I These universes can interact and collide, on time scales whichcannot be determined by local measurements: one of the hugenumber of ways of solving the ”Boltzmann Brain” problem.

Meta-Cosmology

I Generalized “multiverse” model in which model universes ofvarying Λ,ΛI ,Ne are embedded in a background p = ρ,Λ = 0cosmology as localized excitations.

I Allows for anthropic selection of these parameters.

I Apart from connection m3/2 ∼ Λ1/4, which determines scaleof SUSY breaking, particle physics is encoded in algebra offundamental variables, and doesn’t change from one universeto another.

I These universes can interact and collide, on time scales whichcannot be determined by local measurements: one of the hugenumber of ways of solving the ”Boltzmann Brain” problem.

Meta-Cosmology

I Generalized “multiverse” model in which model universes ofvarying Λ,ΛI ,Ne are embedded in a background p = ρ,Λ = 0cosmology as localized excitations.

I Allows for anthropic selection of these parameters.

I Apart from connection m3/2 ∼ Λ1/4, which determines scaleof SUSY breaking, particle physics is encoded in algebra offundamental variables, and doesn’t change from one universeto another.

I These universes can interact and collide, on time scales whichcannot be determined by local measurements: one of the hugenumber of ways of solving the ”Boltzmann Brain” problem.

There Are More Things in Heaven and Earth...

I HST has new Low Energy DOF which dominate entropy inany causal diamond. Particles and black holes are constrainedstates of these DOF.

I QUEFT is a good approximation only in regimes whereparticles are decoupled from the horizon. Jacobson assures usthat classical field theory is valid as hydrodynamics even inhigh entropy limit.

There Are More Things in Heaven and Earth...

I HST has new Low Energy DOF which dominate entropy inany causal diamond. Particles and black holes are constrainedstates of these DOF.

I QUEFT is a good approximation only in regimes whereparticles are decoupled from the horizon. Jacobson assures usthat classical field theory is valid as hydrodynamics even inhigh entropy limit.