From Big Crunch to Big Bang with Ad

From Big Crunch to Big Bang with Ad. S/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

Ad. S/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(F 2)2 2 3 parameters N, gt= g. YMN, 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 5 d bulk Cosmological singularity in bulk coincides with f ->oo on boundary

Unstable dual FT V Y(f) Finite V 3: homogeneous component of f is quantum mechanical -2 V(f) ~ + RAd. S f 2 – lff 4 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 2 nd 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-f. Cl Y f. Cl 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 f. Cl

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 f. NL~1) Scalar Adiabatic (But bear in mind this is a 5 d cosmology!)

Summary Attractor bounce with little backreaction for all but narrow range of ff • GLASSy perturbations without contrivance • Ø • • For the future: Translation of perturbations into bulk Model with 4 d bulk, 3 d 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 M 2 branes=Strings: time M theory dimension

Connection with colliding branes