from big crunch to big bang with ads/cft. did the universe begin 14 billion years ago? yes ->...
TRANSCRIPT
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