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Formation and Evolution of the Large Scale Structure

Formation and Evolution of the Large Scale Structure. Large Scale Structure of the Universe. Somewhat after recombination -- density perturbations are small on nearly all spatial scales. Dark Ages, prior to z=10 -- density perturbations in dark matter and baryons grow;

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Formation and Evolution of the Large Scale Structure

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  1. Formation and Evolutionof theLarge Scale Structure

  2. Large Scale Structure of the Universe Somewhat after recombination -- density perturbations are small on nearly all spatial scales. Dark Ages, prior to z=10 -- density perturbations in dark matter and baryons grow; on smaller scales perturbations have gone non-linear, d>>1; small (low mass) dark matter halos form; massive stars form in their potential wells and reionize the Universe. z=3 -- Most galaxies have formed; they are bright with stars; this is also the epoch of highest quasar activity; galaxy clusters are forming. Growth of structure on large (linear) scales has nearly stopped, but smaller non-linear scales continue to evolve. z=0 -- Small galaxies continue to get merged to form larger ones; in an open and lambda universes large scale (>10-100Mpc) potential wells/hill are decaying, giving rise to late ISW. Picture credit: A. Kravtsov, http://cosmicweb.uchicago.edu/filaments.html

  3. P(k)~kn Harrison-Zel’dovich n=1 Matter Power Spectrum:from inflation to today A different convention: plot P(k)k3

  4. log(t) lambda domination lambda-matter equality z=1 matter domination recombination; production of CMB z=1200 sub-horizon matter-radiation equality z=4 x 103 super-horizon radiation domination end of inflation z>>1010 infla- tion Planck time log(rcomov) Evolution of density fluctuations: the set-up Growth rate of a density perturbation depends on the epoch (i.e. what component dominates global expansion dynamics at that time), and whether a perturbation k-mode is super- or sub-horizon.

  5. P(k) P(k) k k P(k) k P(k) k How did the matter power spectrum go from Harrison-Zeldovich to this ? lambda domination log(t) lambda-matter equality z=1 matter domination recombination; production of CMB z=1200 sub-horizon matter-radiation equality z=4 x 103 super-horizon radiation domination end of inflation z>>1010 infla- tion Planck time log(rcomov) Growth rate of a density perturbation depends on the epoch (i.e. what component dominates global expansion dynamics at that time), and whether a perturbation k-mode is super- or sub-horizon.

  6. fluid pressure is not important on super-horizon scales, so it makes no difference whether recombination has taken place or not. MD log(t) CMB MRE inflation log(rcomov) RD log(t) CMB MRE inflation log(rcomov) Linear growth of density perturbations:Super-horizon, w comp. dominated, pre & post recomb. Friedmann eq: different patches of the Universe will have slightly different average densities and curvatures:

  7. Linear growth of density perturbations:Sub-horizon, radiation dominated, pre recombination dark matter has no pressure of its own; it is not coupled to photons, so there is no restoring pressure force at all. Jeans linear perturbation analysis applies: log(t) zero CMB radiation dominates, and because radiation does not cluster  all dk=0… MRE inflation log(rcomov) …but the rate of change of dk’s can be non-zero growing “decaying” mode mode

  8. Linear growth of density perturbations:Sub-horizon, matter dominated, pre & post recomb. dark matter has no pressure of its own; it is not coupled to photons, so there virtually no restoring pressure force. Jeans linear perturbation analysis applies: log(t) zero also, can assume that total density is the critical density at that epoch: CMB MRE inflation log(rcomov) Two linearly indep. solutions: growing mode always comes to dominate; ignore decaying mode soln. Structure growth begins and ends with matter domination growing decaying mode mode

  9. Linear growth of density perturbations:Sub-horizon, lambda dominated, pre & post recomb. dark matter has no pressure of its own; it is not coupled to photons, so there is virtually no restoring pressure force. Jeans linear perturbation analysis applies: log(t) zero can assume the amplitude of perturbations is zero, because lambda, which dominates, does not cluster: CMB MRE inflation log(rcomov) Two linearly indep. solutions: growing mode always comes to dominate; ignore decaying mode soln. “growing” decaying mode mode

  10. Linear growth of density perturbations:Sub-horizon, curvature dominated, pre & post recomb. dark matter has no pressure of its own; it is not coupled to photons, so there virtually no restoring pressure force. Jeans linear perturbation analysis applies: log(t) zero can assume the amplitude of perturbations is zero, because curvature, which dominates, does not cluster: CMB MRE inflation log(rcomov) Two linearly indep. solutions: growing mode always comes to dominate; ignore decaying mode soln. “growing” decaying mode mode

  11. Linear growth of density perturbations:dark matter, baryons, and photons log(t) CMB MRE amplitude of perturbation inflation log(rcomov)

  12. log(t) P(k) k high-k small scale perturbations grow fast, non-linearly P(k) Evolution of matter power spectrum Now z=1 k baryonic oscillations appear – the P(k) equivalent of CMB T power spectrum CMB P(k) MRE k sub-horizon perturb. do not grow during radiation dominated epoch P(k) k P(k) k Harrison-Zeldovich spectrum P(k)~k from inflation P(k) EoIn k log(rcomov) log(k)

  13. Transfer Functions Transfer function is defined as follows, where the two relevant epochs are the end of inflation and matter-radiation equality, and later epoch if there shape changes in P(k). Peacock; astro-ph/0309240

  14. Growth of large scale structure Dark Matter density maps from N-body simulations Recent epoch: dark matter or dark energy dominated? During matter dominated epoch, fractional overdensity grows as the scale factor. The corresponding potential fluctuations stay constant, because decrease in average density and increase in linear size combined compensate for d ~ a Standard spatially flat Wmatter=1.0 fractional overdensity ~1/(1+z) 350 Mpc the Virgo Collaboration (1996)

  15. Growth of large scale structure Dark Matter density maps from N-body simulations Lambda (DE) spatially flat Wmatter=0.3 fractional overdensity ~const Standard spatially flat Wmatter=1.0 fractional overdensity ~1/(1+z) 350 Mpc the Virgo Collaboration (1996)

  16. Growth of large scale structure In linear theory gravitational potential decays if DE or negative curvature dominate late time expansion Lambda (DE) spatially flat Wmatter=0.3 gravitational potential ~(1+z) Standard spatially flat Wmatter=1.0 gravitational potential ~const 350 Mpc the Virgo Collaboration (1996)

  17. Energy Energy Energy Energy Late Integrated Sachs-Wolfe (ISW) Effect If a potential well evolves as a photon transverses it, the photon’s energy will change Sachs & Wolfe (1967) ApJ 147, 73 Crittenden & Turok (1996) PRL 76, 575 photon gains energy after crossing a potential well potential well Look for correlation between CMB temperature fluctuations and nearby structure. Detection of late ISW effect in a flat universe is direct evidence of Dark Energy

  18. Detecting late ISW Late ISW is detected as a cross-correlation, CCF on the sky between nearby large scale structure and temperature fluctuations in the CMB. NVSS 1.4 GHz nearly full sky radio galaxies; median z~0.8 HEAO1 hard X-rays full sky median z~0.9 Lines are LCDM predictions, not fits to data Note: points are highly correlated Boughn & Crittenden (2005) NewAR 49, 75, astro-ph/0404470

  19. log(t) P(k) k high-k small scale perturbations grow fast, non-linearly P(k) Evolution of matter power spectrum Now z=1 k baryonic oscillations appear – the P(k) equivalent of CMB T power spectrum CMB P(k) MRE k sub-horizon perturb. do not grow during radiation dominated epoch P(k) k P(k) k Harrison-Zeldovich spectrum P(k)~k from inflation P(k) EoIn k log(rcomov) log(k)

  20. log(t) Growth of perturbationswith and without DM inflation lambda dom. matter domination radiation domination CMB MRE Planck time end of inflation lambda-matter equality log(rcomov) without dark matter with dark matter Growth of baryonic perturbations without DM: given that the observed fluctuations in the potential at the CMB (z=1000) on horizon scales are ~10-5 , and assuming linear growth of perturbations gives snow=sCMB (1+z) = 0.01. However, today on these scales we see rms overdensities ~10-100 times larger. Coles & Lucchin

  21. Many waves superimposed Baryonic Acoustic Oscillations One wave around one center: Wave starts propagating at Big Bang; end at recombination. The final length is the sound crossing horizon at recomb. (Change of color means recombination.)

  22. Narrow feature: standard ruler (sound crossing horizon at recombination) Matter power spectrum - observations Baryonic Acoustic Oscillations (BAO) SDSS and 2dF galaxy surveys from k-space to real space BAO bump gal. corr. fcn. comoving r (Mpc/h) Eisenstein et al. astro-ph/0501171 Percival et al. astro-ph/0705.3323

  23. Clustering of SDSS galaxies: epochs ofequality and recombination Luminous red galaxies, z ~ 0.35 sound horizon size at recombination Wmh2=0.12, 0.13, 0.14 galaxy correlation function Wmh2=0.130+/-0.011 Eisenstein et al. astro-ph/0501171

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