1. From Big Crunch to Big Bang with AdS/CFT

2. Did the universe begin 14 billion years ago? Yes -> horizon, flatness puzzles. , configuration of extra dimensions. 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.

3. Cyclic Universe Steinhardt+NT

4. Clearly, this scenario requires that we resolve the singularity This talk: Quantum Resolution of Cosmological Singularities Unexpected bonus: GLASSy perturbations from quantum gravity

5. work with: Ben Craps (Brussels) Thomas Hertog (Paris)

6. Scale Invariance from Scale Invariance e.g. V=-V 0 e -c  Symm (classical):x  ->e  x ,  ->  +2 /c, h->e 2  h Scaling bg soln:  ~ t -1. Scale symm. -> ~ h t -2 d 3 k/k 3 Scale symm. -> ~ h t -2 d 3 k/k 3. |kt| <<1 If you want to see the details, ask me later

7. AdS/CFT correspondence: Gravity with  <0 dual to a Conformal Field Theory Might this be the origin of scale-invariance?

8. A remarkable correspondence timetime “dual” descriptions string theory in bulk QFT on conformal boundary r r is holographic/emergent: time is not Maldacena:

9. Dual theory is a renormalizable QFT N =4 SYM SU(N) gauge theory, with double trace deformation: -f Tr( 2 ) 2 Dual theory is a renormalizable QFT N =4 SYM SU(N) gauge theory, with double trace deformation: -f Tr( 2 ) 2 3 parameters N, g t= g YM N, f 3 parameters N, g t= g YM N, f f is asymptotically free,  f is 1-loop exact at large N, renormalized effective potential is under excellent control f is asymptotically free,  f is 1-loop exact at large N, renormalized effective potential is under excellent control at small or large g t at small or large g t 2 ln is our friend

10. Holographic Cosmology Unstable 5d bulk r ? singularity Cosmological singularity in bulk coincides with ->o on boundary o Can we go through

11. Unstable dual FT V (  ) ~ + R AdS  2 –   4 -2 V  Finite V 3 : homogeneous component of  is quantum mechanical Semiclassical approximation becomes exact there Requires unitary boundary condition at o o

12. Complex solutions and quantum mechanics Gaussian wavepackets: Time evolution: semiclassical expansion Time evolution: semiclassical expansion Implement boundary condition via method of images To leading order

13. ffff   i (1)  i (2) Two complex trajectories 2 nd solution has mirror ICs -> No loss of probability at infinity Map pt at o to origin o

14. After bounce,  dominated by “mirror” solution  Imaginary part –i  determined by final argument of wavefunction. ffff  o  f - Cl c   Cl 

15.  acts as UV cutoff on quantum creation of inhomogeneous modes To lowest order in 1/ln, is Hankel, no particle creation (cf. field theory on Milne) To next order, Positive frequency mode function

16. Final result: Including quantum creation of  particles, light Higgs and gauge particles, for and backreaction is negligible over entire bounce, for all but a tiny band of  f centred on  Cl

17. Scale-Invariant Perturbations improved T  T  -> determine bulk perturbations

18. Bulk Properties – background and fluctuations Global time -> bang Sufficient data to solve boundary problem crunch

19. Amplitude ~ N -1 ln -3/2 Tilt: red, from running of  Nearly Gaussian (naïve calc f NL ~1) Scalar (But bear in mind this is a 5d cosmology!) Results: Adiabatic

20. Attractor bounce with little backreaction for all but narrow range of  f Attractor bounce with little backreaction for all but narrow range of  f GLASSy perturbations without contrivance GLASSy perturbations without contrivance  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 Summary

21. M-theory model for the bang M theory dimension time Winding M2 branes=Strings: Perry, Steinhardt & NT, 2004 Berman & Perry, 2006 Niz+NT 2006,7

22. Connection with colliding branes