Phys/Astro 689: Lecture 3. The Growth of Structure

Transcription

1 Phys/Astro 689: Lecture 3 The Growth of Structure

2 Last time Examined the milestones (zeq, zrecomb, zdec) in early Universe Learned about the WIMP miracle and searches for WIMPs

3 Goal of Lecture Understand how fluctuations grow Inflation provides the primordial power spectrum, P ~ k n. We want the power spectrum at later times to follow the seeds of galaxies.

4 Some basics Inflation creates density contrasts, These perturbations are modified in the early Universe, e.g., by growth pressure dissipation/damping

5 Some basics Assumptions of homogeneity and isotropy reduce Einstein s equations of GR to 2 equations: the Friedmann Equations, P = pressure (1), (2), and EOS describe evolution of a(t), P(t), --> from (1),

6 The Growth of Structure Let s try to understand this plot: baryons first

7 First: Jeans Mass collapse for oscillations for

8 The Growth of Structure Horizon scale: lh = 2c/H lh ~ a also: lh ~ fluctuations smaller than horizon oscillate, larger can grow

9 The Growth of Structure Sound speed Sound speed varies as mix of radiation/matter domination changes.

10 The Growth of Structure Loss of radiation pressure, sound speed set by thermal motion of baryons; precipitous drop in Jeans length/mass.

11 The Growth of Structure Point: Scales above the yellow line can grow. Perturbation scales below yellow line oscillate (or are damped).

12 The Growth of Structure CDM: stops feeling the presence of photons before baryons (green line is shifted to earlier epochs)

13 The Growth of Structure Region 2: stagnation of CDM perturbations (tff > texp) Region 3: damping

14 The Growth of Structure Dissipation: photons can diffuse out of oscillating structures and reduce the amplitude of the fluctuation.

15 The Growth of Structure Worked out (on board): growth changes from exponential to linear,

16 The Growth of Structure

17 The Growth of Structure This translates directly into at zdec for baryons But Baryons never reach the regime where What about DM? Yet another argument for DM! (We see galaxies today.)

18 HDM A different evolution for HDM Perturbations are damped due to streaming of relativistic particles No growth of DM halos prior to zeq Growth of structure mimics baryon evolution

19 The Power Spectrum Possible modifications to IPS: CDM: stagnation of small scales during radiation dominated era Damping of small scales HDM: free-streaming of neutrinos

20 The Transfer Function The primordial power spectrum is processed as we have seen. The processing is the Transfer Function, P(k) = Pi(k) x T 2 (k) Depends on cosmological parameters and DM type

21 The Power Spectrum Let P(k) ~ k n n > -1 has more power on small scales, n < -1 has more power on large scales For n > -1, fluctuations increase with k (decreasing size): large scales preserve homogeneity and isotropy n = 1 is Zel dovich spectrum : scale-free

22 The Power Spectrum best fit from Planck et al: n = 0.96 For our CDM cosmology, damping in radiation dominated era, T 2 (k) ~ k -4 (for scales smaller than the horizon) For n = 1, P(k) ~ k on large scales, P(k) ~ k -3 on small scales

23 The Power Spectrum Some features: if k increases, so does overdensity: small things form first spread in formation times, overdensity ~ a(t). So at z=1, structures were collapsing with quarter the size of z=0 (for n=1)

24 The Density Field The fluctuation field can be described as a series of sine waves If the phases,, of the waves are uncorrelated, then the density field is gaussian Use perturbation theory to describe evolution ( << 1 is linear regime, > 1 is non-linear regime)

25 The Density Field For a gaussian random field, the distribution of values at N random field points is is two-point correlation function i.e., Gaussian field is completely described by two-point correction function

26 The Density Field A Fourier superposition of waves : V = volume; k = wavenumber = The Fourier transform of the 2-point correlation function is the Power Spectrum:

27 The Power Spectrum In other words, we can use the observed 2pt correlation function of galaxies to measure the Power Spectrum

28 Measuring the 2-pt Correlation Function 1983

29 Measuring the 2-pt Correlation Function

30 Measuring the 2-pt Correlation Function

31 The Power Spectrum linear regime This is not necessarily the initial power spectrum!

32 Growth Function Normalization of the power spectrum today (matter dominated) compared to the initial inflationary conditions, normalized by the CMB fluctuations are characterized by, the RMS fluctuations of the density field on 8 Mpc/h scales

33 From the Power Spectrum to Galaxies Now that we can describe the initial fluctuations in the early Universe, we need to get from these seed perturbations to galaxies How? Next time: analytic/semi-analytic solutions Later: simulations