1 / 22

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.

Download Presentation

Finite universe and cosmic coincidences

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related