Academic Training Lectures Rocky Kolb Fermilab, University of Chicago, & CERN

1. Cosmology and the origin of structure Academic Training Lectures Rocky Kolb Fermilab, University of Chicago, & CERN 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. Seeds of structure time origin of small initial perturbations

3. Rocky III: Inflation • Motivation for “acausal” perturbations • Inflation in the cosmic symphony • The alarming phenomenon of particle creation • Inflation phenomenology

4. Acoustic peaks • What are coefficients A & B ? • A nonzero perturbations • in limit • At recombination, baryon-photon fluid undergoes • “acoustic oscillations” • Compressions and rarefactions change • Peaks in correspond to extrema of • compressions and rarefactions Hu

5. Angular power spectrum adiabatic “A” (acausal) isocurvature pert’s (no “A”)

6. Input from the early universe 1. Spectrum of perturbations (power spectrum) CMB correlations on scales greater than Hubble radius(RH~ct)INFLATION 2.Matter content baryons, dark matter (cold, warm, hot), vacuum energy, ……

7. non-inflationary cosmology l ; log l log RH RH last scattering log a non-inflationary cosmology

8. inflationary cosmology l log l log RH ; RH end inflation last scattering log a inflationary cosmology

9. Newton Einstein normal scale factor a time accelerated scale factor a vacuum energy? time

10. Vacuum pressure had to pull piston “negative pressure”

11. log RH ; log l log a

12. Cosmic Symphony (Harmonice Mundi) expansion tempo pizzicato string dominated 10-43 sec.? ??? CBR fluctuations, presto inflation 10-35sec.? gravitational waves, seeds of structure allegro radiation dominated earlier than abundance of the 10,000 yrs. light elements andante matter dominated later than distant quasars 10,000 yrs. and galaxies largo inflation day before acceleration of yesterday the universe movement epoch relic

13. Inflation, as a whole, can be divided into three parts • Beginning • Middle • End eternal inflation, wave function of the universe, did the universe have a beginning ???? density perturbations, gravitational waves, (particle production in the expanding universe) defrosting, heating, preheating, reheating, baryogenesis, phase transitions, dark matter, (particle production in the expanding universe)

14. Potential energy: energy of infinite-wavelength mode Particle content: condensate of infinite-wavelength particles “inflaton” Classical equations of motion

15. An early particle cosmologist .. In mid-1930s, Schrodinger turned to cosmo issues, influenced by Eddington & Lemaitre 1938-1939: Graz Vatican Gent, Belgium Dublin

16. The proper vibrations of the expanding universe Erwin Schrodinger Physica6, 899(1939) .. Introduction: “… proper vibrations [positive and negative frequency modes] cannot be rigorously separated in the expanding universe. … this is a phenomenon of outstanding importance. With particles it would mean production or annihilation of matter, merely by expansion,… Alarmed by these prospects, I have examined the matter in more detail.” Conclusion: “… There will be a mutual adulteration of positive and negative frequency terms in the course of time, giving rise to … the ‘alarming phenomenon’…”

17. An even earlier Graz cosmologist “When the storms rage around us, and the state is threatened by shipwreck, we can do nothing more noble than to lower the anchor of our peaceful studies in the ground of eternity.” - J. Kepler 1600-1630: Graz Prague Linz Sagan Ratisbon

19. Particle creation: finite-wavelength modes not smooth Quantum fluctuations “inflaton”

20. log RH ; log l “quantum fluctuations” “alarming phenomenon” log a

21. patterns of quantum fluctuations

22. Variational Formalism for Quantization: Scalar perturbations in terms of a fieldu Minkowski space (conformal time) mass changes with time

23. Variational formalism for quantization: Einstein gravity Inflaton field Tensor perturbations in terms of Minkowski space (conformal time) changes in time

24. Quantum generation of perturbations: • Wave equation for u • Initially only homogeneous mode. • As evolve, mass is complicated function of time. • Create nonzero momentum mode. • Alarming phenomenon!

25. (When a hammer is your only tool, everything has the appearance of a nail.)

26. Who is the inflaton? ? “inflaton”

27. Top down Bottom up

28. Models of inflation old, new, pre-owned, chaotic, quixotic, ergodic, ekpyrotic, autoerotic, faith-based, free-based, brane, braneless, brainless, supersymmetric, supercilious, natural, supernatural, au natural, hybrid, low-bred, white bread, one-field, two-field, left-field, eternal, internal, infernal, self-reproducing, self-promoting, dilaton, dilettante, …….

29. * *Used for superstrings, supernovae, superconductors, … Model Classification Type I: single-field, slow-roll models (or models that can be expressed as such) Type II: anything else (branes, pre-big-bang, etc.) Type Ia: large-field models Type Ib: small-field models Type Ic: hybrid models

30. large-field (Ia) V(f) V(f) V(f) f f f f hybrid (Ic) small-field (Ib)

31. Quantum generation of perturbations: • Perturbations model-dependent function of H • and how H changes during inflation. • Characterize perturbations in terms of:

32. Quantum generation of perturbations: • Input inflation potential : • Observer-friendly parameters: • Consistency relation: • Inflaton potential :

33. Planck Dodelson, Kinney, Kolb astro-ph/9702156 hybrid r large field 0 0.5 1.0 small field 0.8 0.85 0.9 0.95 1.0 1.05 1.1 n

34. Kinney, Melchiorri, Riotto astro-ph/0007375

35. Harrison-Zel’dovich n = 1.00000 r = 0.00000 Fixed point of ignorance.

36. Polarization pattern Stebbins, Kosowsky, Kamionkowski Seljak & Zaldarriaga E modesB modes (gravitational waves)

37. Kinney astro-ph/9806259

38. Reconstruction parameterized spectra Copeland, Kolb, Liddle, Lindsey Rev. Mod Phys. 97 inflaton potential microwave anisotropies Grivell & Liddle astro-ph/9906327 Bond, Abney, Copeland, Grivell, Kolb, Liddle, Lindsey, Turner, Sourdeep

39. Reconstruction • tensor spectral index in terms of scalar & tensor • (consistency relation) • knowledge of the scale of V requires tensor

40. Power-law spectrum

41. Power-law spectrum

42. Type I models* predict • a (nearly) exact power-law • spectrum of gaussian • super-Hubble-radius • scalar (density) and • tensor (gravitational-wave) perturbations • related by a consistency relation • in their growing mode • in a spatially flat universe. *at least the simplest ones

43. Inflation conclusions The alarming phenomenon of particle creation in the early universe can be studied by looking at the sky!

44. If you can look into the seeds of time And say which grain will grow and which will not, Speak then to me, who neither beg nor fear Your favours nor your hate. -MACBETH (Banquo)

45. Rocky III: Inflation • Motivation for “acausal” perturbations • Inflation in the cosmic symphony • The alarming phenomenon of particle creation • Inflation phenomenology

46. Cosmology and the origin of structure Academic Training Lectures Rocky Kolb Fermilab, University of Chicago, & CERN 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