1. Academic Training Lectures Rocky Kolb Fermilab, University of Chicago, & CERN Cosmology and the origin of structure Rocky I : The universe observed Rocky II :The growth of cosmological structure Rocky III :Inflation and the origin of perturbations Rocky IV :Dark matter and dark energy

2. Linear regime: quantative analysis Jeans analysis Sub-Hubble-radius perturbations (Newtonian) Super-Hubble-radius perturbations (GR) Harrison-Zel’dovich spectrum Dissipative processes The transfer function Linear evolution Non-linear regime: word calculus Comparison to observations A few clouds on the horizon Rocky II : Growth of structure

3. Growth of small perturbations Today (12 Gyr AB) radiation and matter decoupled Before recombination (300 kyr AB) radiation and matter decoupled

4. Seeds of structure time

5. Oxford English Dictionary

6. Assume there is an average density Expand density contrast in Fourier modes Autocorrelation function defines power spectrum Power spectrum

7. Jeans analysis matter density pressure velocity field gravitational potential Perturb about solution* Jeans analysis in a non-expanding fluid:

8. Jeans analysis solutions of the form real: perturbations oscillate as sound waves imaginary: exponentially growing (or decaying) modes gravitational pressure vs. thermal pressure Jeans wavenumber Jeans mass

9. Sub-Hubble-radius (R H =H -1 ) Jeans analysis in an expanding fluid: scale factor a(t) describes expansion, unperturbed solution:* Solution is some sort of Bessel function: growth or oscillation depends on Jeans criterion In matter-dominated era For wavenumbers less than Jeans

10. Super-Hubble-radius (R H =H -1 ) complete analysis not for the faint of heart interested in “scalar” perturbations fourth-order differential equation only two solutions “physical” other two solutions are “gauge modes” which can be removed by a coordinate transformation on the unperturbed metric

11. Reference spacetime: flat FRW Bardeen 1980

13. Reference spacetime: flat FRW Perturbed spacetime (10 degrees of freedom): Bardeen 1980

14. reference flat spatial hypersurfaces actual curved spatial hypersurfaces

15. scalar, vector, tensor decomposition evolution of scalar, vector, and tensor perturbations decoupled    

16. are not sourced by stress tensor decay rapidly in expansion Vector Perturbations: perturbations of transverse, traceless component of the metric: gravitational waves do not couple to stress tensor Tensor Perturbations: couple to stress tensor density perturbations! Scalar Perturbations

17. Super-Hubble-radiusSuper-Hubble-radius in synchronous gauge and uniform Hubble flow gauge in matter-dominated era in radiation-dominated era

18. Harrison-Zel’dovichHarrison-Zel’dovich log k log  kHkH P(k)  k n log k log  kHkH P(k)  k n in matter-dominated era sub Hubble-radius super Hubble-radius

19. Harrison-Zel’dovichHarrison-Zel’dovich log k log  kHkH P(k)  k 1 in radiation-dominated era log k log  kHkH log k log  kHkH “flat” spectrum  2 (k)=k 3 P(k)  const

20. Harrison-Zel’dovichHarrison-Zel’dovich log k log  kHkH P(k)  k 1 in radiation-dominated era no growth sub-Hubble radius growth as t super-Hubble radius “flat” spectrum  2 (k)=k 3 P(k)  const kHkH log k log  P(k) P(k)  k 1 P(k)  k -3 in matter-dominated era power spectrum grows as t 2/3 on all scales

21. Power spectrum for CDM log k log  P(k) P(k)  k 1 P(k)  k -3 k  kk matter-radiation equality

22. Dissipative processes 1. Collisionless phase mixing – free streaming If dark matter is relativistic or semi-relativistic particles can stream out of overdense regions and smooth out inhomogeneities. The faster the particle the longer its free- streaming length. Quintessential example: eV-range neutrinos

23. The evolved spectrum

24. Dissipative processes 1. Collisionless phase mixing – free streaming If dark matter is relativistic or semi-relativistic particles can stream out of overdense regions and smooth out inhomogeneities. The faster the particle the longer its free- streaming length. Quintessential example: eV-range neutrinos 2. Collisional damping – Silk damping As baryons decouple from photons, the photonmean-free path becomes large. As photons escape from dense regions, they can drag baryons along, erasing baryon perturbations on small scales. Baryon-photon fluid suffers damped oscillations.

25. The evolved spectrum

26. Linear evolution z=1000 z=100 z=10 today

27. Linear evolution z=1000 z=100 z=10 today

28. Life ain’t linear! Many scales become nonlinear at about the same time Mergers from many smaller objects while larger scales form N-body simulations for dissipation-less dark matter Hydro needed for baryons Power spectrum well fit if  =  h ~ 0.2 There is more to life than the power spectrum Alex Szalay

29. Large-scalestructurefitswellLarge-scalestructurefitswell

30. Small-scale structure-cusps Moore et al.

31. Small-scale structure-satellites Moore et al.

32. Linear regime: quantative analysis Jeans analysis Sub-Hubble-radius perturbations (Newtonian) Super-Hubble-radius perturbations (GR) Harrison-Zel’dovich spectrum Dissipative processes The transfer function Linear evolution Non-linear regime: word calculus Comparison to observations A few clouds on the horizon Rocky II : Growth of structure

33. Academic Training Lectures Rocky Kolb Fermilab, University of Chicago, & CERN Cosmology and the origin of structure Rocky I : The observed universe Rocky II :The growth of cosmological structure Rocky III :Inflation and the origin of perturbations Rocky IV :Dark matter and dark energy