FromFromBig Crunch to Big BangBig Crunch to Big Bang

with AdS/CFTwith AdS/CFT

Did the universe begin 14 billion years Did the universe begin 14 billion years ago? ago?

YesYes -> horizon, flatness puzzles. -> horizon, flatness puzzles. , , configuration of extra dimensions.configuration of extra dimensions.

These puzzles rest on the assumption These puzzles rest on the assumption (usually inexplicit) that someone was (usually inexplicit) that someone was throwing dice at the beginning. throwing dice at the beginning.

NoNo -> perhaps these puzzles are -> perhaps these puzzles are resolved dynamically. The universe resolved dynamically. The universe selects its own geometry. selects its own geometry.

Cyclic UniverseCyclic UniverseSteinhardt+NSteinhardt+NTT

Clearly, this scenario requires that we resolve the singularity

This talk:

• Quantum Resolution of Cosmological Singularities

• Unexpected bonus: GLASSy perturbations from quantum gravity

work with:

•Ben Craps (Brussels)•Thomas Hertog (Paris)

Scale Invariance from Scale Invariance from Scale InvarianceScale Invariance

If you want to see If you want to see the details, ask me the details, ask me laterlater

AdS/CFT correspondence:AdS/CFT correspondence:

Gravity with Gravity with <0 dual to a<0 dual to a

Conformal Field TheoryConformal Field Theory

Might this be the origin ofMight this be the origin of

scale-invariance?scale-invariance?

A remarkable correspondenceA remarkable correspondence

t i

me

“dual” descriptions

string theory in bulk

QFT on conformal boundary

rr

r is holographic/emergent: time is notr is holographic/emergent: time is not

Maldacena:Maldacena:

Dual theory is a renormalizable QFT Dual theory is a renormalizable QFT NN =4 SYM SU(N) gauge theory, with =4 SYM SU(N) gauge theory, with double trace deformation: -f Tr(double trace deformation: -f Tr(22))22

3 parameters N, g3 parameters N, gt= t= ggYMYMN, fN, f

f is asymptotically free, f is asymptotically free, ff is 1-loop is 1-loop exact at large N, renormalized effective exact at large N, renormalized effective potential is under excellent controlpotential is under excellent control

at small or large gat small or large gt t

22

ln is our friendln is our friend

Holographic CosmologyHolographic Cosmology

Unstable 5d bulkUnstable 5d bulk

rr

??

singularitysingularityCosmological Cosmological singularity in bulk singularity in bulk coincides with coincides with ->o on boundary->o on boundaryoo

Can we go throughCan we go through

Unstable dual FTUnstable dual FT

VV(() ~ + R) ~ + RAdSAdS 22 – – 44-2-2VV

Finite VFinite V33:: homogeneous homogeneous component ofcomponent of isis quantum quantum mechanicalmechanical

Semiclassical Semiclassical approximation approximation becomes exact becomes exact therethere

Requires unitary Requires unitary boundary condition boundary condition at oat ooo

Complex solutions and quantum mechanicsComplex solutions and quantum mechanics

Gaussian wavepackets:Gaussian wavepackets:

Time evolution: semiclassical expansionTime evolution: semiclassical expansion

Implement boundary condition via method Implement boundary condition via method of imagesof images

To To leading leading orderorder

ff

ii(1)(1)

ii(2)(2) Two complex Two complex

trajectoriestrajectories

22ndnd solution has mirror ICs solution has mirror ICs

-> No loss of probability at infinity-> No loss of probability at infinity

Map pt at o to originMap pt at o to originoo

After bounce, After bounce, dominated by dominated by “mirror” solution “mirror” solution

Imaginary part –i Imaginary part –i determined by final determined by final argument of wavefunction. argument of wavefunction.

ff

oo ff--ClClcc

ClCl

acts as UV cutoff on quantum creation of acts as UV cutoff on quantum creation of inhomogeneous modesinhomogeneous modes

To lowest order in 1/ln, is Hankel, no To lowest order in 1/ln, is Hankel, no particle creation (cf. field theory on Milne)particle creation (cf. field theory on Milne)

To next To next order,order,

Positive frequency mode functionPositive frequency mode function

Final result: Final result:

Including quantum creation of Including quantum creation of particles, light Higgs and gauge particles, light Higgs and gauge particles, for particles, for

andand

backreaction is negligible over entire backreaction is negligible over entire bounce, for all but a tiny band of bounce, for all but a tiny band of f f

centred on centred on ClCl

Scale-Invariant PerturbationsScale-Invariant Perturbations

improvedimproved

TT

-> determine bulk perturbations-> determine bulk perturbations

Bulk Properties – background Bulk Properties – background and fluctuationsand fluctuations

Glo

bal ti

me -

>G

lobal ti

me -

>bangbang

Sufficient data to solve Sufficient data to solve boundary problemboundary problem

crunchcrunch

AmplitudeAmplitude ~ N ~ N-1-1 lnln-3/2-3/2 Tilt: red, from running ofTilt: red, from running of

Nearly Gaussian (naïve calc fNearly Gaussian (naïve calc fNLNL~1) ~1) Scalar Scalar

(But bear in mind this is a 5d cosmology!)(But bear in mind this is a 5d cosmology!)

Results:Results:

Adiabatic Adiabatic

• Attractor bounce with little backreaction for Attractor bounce with little backreaction for all but narrow range of all but narrow range of ff

• GLASSGLASSy perturbations without contrivancey perturbations without contrivance

For the future:For the future:• Translation of perturbations into bulk Translation of perturbations into bulk • Model with 4d bulk, 3d dual FT Model with 4d bulk, 3d dual FT • Thermodynamics Thermodynamics • Glue onto positive dark energy phase Glue onto positive dark energy phase

SummarySummary

M-theory model for the bang

M theory dimension

time

Winding M2 branes=Strings:

Perry, Steinhardt & NT, 2004Berman & Perry, 2006Niz+NT 2006,7

Connection with collidingConnection with colliding branesbranes