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Finite universe and cosmic coincidences

Finite universe and cosmic coincidences. Kari Enqvist, University of Helsinki. COSMO 05 Bonn, Germany, August 28 - September 01, 2005. cosmic coincidences. dark energy why now:   ~ (H 0 M P ) 2 ? CMB why supression at largest scales: k ~1/H 0 ?. UV problem. IR problem.

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Finite universe and cosmic coincidences

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  1. Finite universe and cosmic coincidences Kari Enqvist, University of Helsinki COSMO 05Bonn, Germany, August 28 - September 01, 2005

  2. cosmic coincidences • dark energy • why now:  ~ (H0MP)2 ? • CMB • why supression at largest scales: k ~1/H0 ? UV problem IR problem

  3. Do we live in a finite Universe? • large box: closed universe   1 → L >> 1/H • small box • periodic boundary conditions non-trivial topology: R > few  1/H • non-periodic boundary conditions does this make sense at all? maybe – if QFT is not the full story (not interesting)

  4. CMB & multiply connected manifolds • discrete spectrum with an IR cutoff along a given direction (”topological scale”)  suppression at low l • geometric patterns encrypted in spatial correlators (”topological lensing” – rings etc.) • correlators depend on the location of the observer and the orientation of the manifold (increased uncertainty for Cl ) See e.g. Levin, Phys.Rept.365,2002

  5. a pair of matched circles, Weeks topology (Cornish) • many possible multiple connected spaces • - typically size of the topological domain restricted to be > 1/H0 explains the suppression of low multipoles with another coincidence

  6. KE, Sloth, Hannestad spherical box  IR cutoff L ground state wave function j0 ~ sin(kr)/kr for r < rB radius of the box which boundary conditions? • Dirichlet • wave function vanishes at r = rB → max. wavelength c = 2rB = 2L • → allowed wave numbers knl = (l/2 + n )/rB • 2) Neumann • derivative of wave function vanishes • allowed modes given throughjl(krB ) l/krB – jl+1(krB ) = 0 for each l, a discrete set of k no current out of U.

  7. Power spectrum: continuous → discrete IR cutoff shows up in the Sachs-Wolfe effect Cl = N kkc jl(knl r) PR(knl ) / knl • CMB spectrum depends on: • IR cutoff L ( ~ rB ) • boundary conditions • note: no geometric patterns IR cutoff → oscillations of power in CMB at low l

  8. Sachs-Wolfe with IR cutoff at l = 10

  9. WHY A FINITE UNIVERSE? • observations: suppression, features in CMB at low l • cosmological horizon: effectively finite universe •  holography?

  10. HOLOGRAPHY • Black hole thermodynamics  Bekenstein bound on entropy classical black hole: dA  0, suggests that SBH ~ A  generalized 2nd law dStotal = d(Smatter + ABH/4)  0 R spherical collapse S ~ area violation of 2nd law unless Smatter  2 ER matter with energy E, S ~ volume Bekenstein bound either give up: 1) unitarity (information loss) 2) locality

  11. argue: QFT: dofs ~ Volume; gravitating system: dofs ~ Area  QFT with gravity overcounts the true dofs QFT breaks down in a large enough V • QFT as an effective theory: must incorporate (non-local) constraints to remove overcounting Cohen et al; M. Li; Hsu; ’t Hooft; Susskind argue: locally, in the UV, QFT should be OK  constraint should manifest itself in the IR

  12. (4/3)L34 < LMP 2 WHAT IS THE SIZE OF THE INFRARED CUT-OFF L? - assume: L defines the volume that a given observer can ever observe RH = a t dt/a ’causal patch’ future event horizon Susskind, Banks Li RH ~ 1/H in a Universe dominated by dark energy - maximum energy density in the effective theory: 4 • Require that the energy of the system confined to box L3 should be less than the energy of a black hole of the same size: Cohen, Kaplan, Nelson more restrictive than Bekenstein: Smax ~ (SBH)3/4

  13. the effectively finite size of the observable Universe constrains dark energy: 4 < 1/L2 ~ dark energy = zero point quantum fluctuation

  14. for phenomenological purposes, assume: 1) IR cutoff is related to future event horizon: RH = cL, c is constant 2) the energy bound is saturated:  = 3c2(MP /RH )2 • a relation between IR and UV cut-offs = a relation between dark energy equation of state and CMB power spectrum at low l Friedmann eq. +  = 1: RH = c / (H)now ½

  15. w = -1/3 - 2/(3c)  dark energy equation of state ½ predicts a time dependent w with -(1+2/c) < 3w < -1 Note: if c < 1, then w < -1  phantom; OK? • e.g. for Dirichlet the smallest allowed wave number kc = 1.2/(H0 ) • - the distance to last scattering depends on w, hence the relative position • of cut-off in CMB spectrum depends on w

  16. translating k into multipoles: l = kl (0 -  ) comoving distance to last scattering z* 0 -  =  dz/H(z) 0 H(z)2 = H02 [(1+z)(3+3w)+(1- )(1+z)3] 0 0 w = w(c, ) lc = lc(c)

  17. fits to data: we do not fix kc but take it instead as a free parameter kcut strategy: 1) choose a boundary condition: 2) calculate 2 for each set of c and kcut, marginalising over all other cosmological parameters Parameter Prior Distribution Ω = Ωm + ΩX 1 Fixed h 0.72 ± 0.08 Gaussian Ωbh2 0.014-0.040 Top hat ns 0.6-1.4 Top hat  0-1 Top hat Q - Free b - Free

  18. Neumann

  19. fits to WMAP + SDSS data 95% CL 68% CL Neumann Dirichlet 2 = 1441.4 2 = 1444.8 Best fit CDM: 2 = 1447.5

  20. 95% CL 68% CL Likelihood contours for SNI data WMAP, SDSS + SNI bad fit, SNI favours w ~ -1

  21. other fits: Zhang and Wu, SN+CMB+LSS: c = 0.81  w0 = - 1.03 but: fit to some features of CMB, not the full spectrum; no discretization

  22. conclusions • ’cosmic coincidences’ might exist both in the UV (dark energy) and IR (low l CMB features) • finite universe  suppression of low l • holographic ideas  connection between UV and IR • toy model: CMB+LSS favours, SN data disfavours – but is c constant? • very speculative, but worth watching! E.g. time dependence of w

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