Transcript Slide 1

From
Big Crunch to Big Bang
with AdS/CFT
Did the universe begin 14 billion years
ago?
Yes -> horizon, flatness puzzles.
configuration of extra dimensions.
L,
These puzzles rest on the assumption
(usually inexplicit) that someone was
throwing dice at the beginning.
No -> perhaps these puzzles are
resolved dynamically. The universe
selects its own geometry.
Steinhardt+NT
Cyclic Universe
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
If you want to see
the details, ask me
later
AdS/CFT correspondence:
Gravity with
L<0 dual to a
Conformal Field Theory
Might this be the origin of
scale-invariance?
A remarkable correspondence
“dual” descriptions
Maldacena:
QFT on
conformal
boundary
t
i
m
e
r
string
theory
in bulk
r is holographic/emergent: time is not
Dual theory is a renormalizable QFT
N =4 SYM SU(N) gauge theory, with
double trace deformation: -f Tr(F2)2
2
3 parameters N, gt= gYMN, f
f is asymptotically free, bf is 1-loop
exact at large N, renormalized effective
potential is under excellent control
at small or large gt
ln is our friend
Holographic Cosmology
Can we go through
?
singularity
r
Unstable 5d bulk
Cosmological
singularity in bulk
coincides with
f ->oo on boundary
Unstable dual FT
V
Y(f)
Finite V3:
homogeneous
component of
f is quantum
mechanical
-2
V(f) ~ + RAdS f2 – lff4
Requires unitary
boundary condition
at oo
Semiclassical
approximation
becomes exact
there
Complex solutions and quantum mechanics
Gaussian wavepackets:
Time evolution: semiclassical expansion
To
leading
order
Implement boundary condition via
method of images
Map pt at oo to origin
ci(1)
c
ci(2)
cf
Two complex trajectories
2nd solution has mirror ICs
-> No loss of probability at infinity
After bounce, Y dominated by
“mirror” solution
e
c
Imaginary part –i e determined by final
argument of wavefunction.
e oc ff-fCl
Y
fCl
ff
e acts as UV cutoff on quantum creation of
inhomogeneous modes
Positive frequency mode function
To lowest order in 1/ln,
is Hankel, no
particle creation (cf. field theory on Milne)
To next
order,
Final result:
Including quantum creation of
f particles, light Higgs and gauge
particles, for
and
backreaction is negligible over entire
bounce, for all but a tiny band of ff
centred on fCl
Scale-Invariant Perturbations
improved
Tmn
-> determine bulk perturbations
Sufficient data to solve
boundary problem
Global time ->
Bulk Properties –
background and fluctuations
crunch
bang
Results:
Amplitude ~ N-1 ln-3/2
Tilt: red, from running of lf
Nearly Gaussian (naïve calc fNL~1)
Scalar
Adiabatic
(But bear in mind this is a 5d cosmology!)
Summary
Attractor bounce with little backreaction for
all but narrow range of ff
• GLASSy perturbations without contrivance
•

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For the future:
Translation of perturbations into bulk
Model with 4d bulk, 3d dual FT
Thermodynamics
Glue onto positive dark energy phase
M-theory model for the bang
Perry, Steinhardt & NT, 2004
Berman & Perry, 2006
Niz+NT 2006,7
Winding M2 branes=Strings:
time
M theory dimension
Connection with colliding branes