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From Big Crunch to Big Bang with AdS/CFT

From Big Crunch to Big Bang with AdS/CFT. Did the universe begin 14 billion years ago? Yes -> horizon, flatness puzzles. L , configuration of extra dimensions. These puzzles rest on the assumption (usually inexplicit) that someone was throwing dice at the beginning.

austin-chaney
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From Big Crunch to Big Bang with AdS/CFT

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  1. FromBig Crunch to Big Bangwith AdS/CFT

  2. Did the universe begin 14 billion years ago? Yes -> horizon, flatness puzzles. L, 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. Steinhardt+NT Cyclic Universe

  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 If you want to see the details, ask me later Symm (classical):xm ->el xm, f->f+2l/c, h->e2l h e.g. V=-V0e-cf . Scaling bg soln: f ~ t-1 . |kt| <<1 Scale symm. -> <df2> ~ h t-2 d3k/k3

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

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

  9. Dual theory is a renormalizable QFT N =4 SYM SU(N) gauge theory, with double trace deformation: -f Tr(F2)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 2 ln is our friend

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

  11. Unstable dual FT V -2 V(f) ~ + RAdSf2 – lff4 Requires unitary boundary condition at o o Y(f) Finite V3:homogeneous component offisquantum mechanical Semiclassical approximation becomes exact there

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

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

  14. After bounce, Y dominated by “mirror” solution e c Imaginary part –i e determined by final argument of wavefunction. Y eoff-fCl c fCl ff

  15. 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,

  16. 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

  17. Scale-Invariant Perturbations improved Tmn -> determine bulk perturbations

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

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

  20. Summary • Attractor bounce with little backreaction for all but narrow range of ff • GLASSy perturbations without contrivance • For the future: • Translation of perturbations into bulk • Model with 4d bulk, 3d dual FT • Thermodynamics • Glue onto positive dark energy phase

  21. 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

  22. Connection with collidingbranes

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