This has led to more general Dark Energy or Quintessence models:

1. This has led to more general Dark Energy or Quintessence models: Evolving scalar field which ‘tracks’ the matter density Convenient parametrisation: ‘Equation of State’ Can we measure w(z) ?

2. Inflation for astronomers We have been considering but suppose that in the past . From the Friedmann equations it would then be very difficult to explain why it is so close to zero today.

3. Present day ‘closeness’ of matter density to the critical density appears to require an incredible degree of ‘fine tuning’ in the very early Universe. FLATNESS PROBLEM

4. How do we explain the isotropy of the CMBR, when opposite sides of the sky were ‘causally disconnected’ when the CMBR photons were emitted? HORIZON PROBLEM

5. From Guth (1997)

6. time Our world line Now Our past light cone A B CMBR space Big Bang

7. Solution (first proposed by Alan Guth in 1981) is… INFLATION …a period of accelerated expansion in the very early universe.

8. Inflationary solution to the Horizon Problem Limit of observable Universe today INFLATION Small, causally connected region From Guth (1997)

9. Inflationary solution to the Flatness Problem From Guth (1997)

10. Inflationary solution to the Flatness Problem Suppose that in the very early Universe: Suppose there existed Easy to show that:- i.e. vacuum energy will dominate as the Universe expands, and drives to zero De Sitter solution; exponential growth

11. CoBE map of temperature across the sky

12. CMBR fluctuations are the seeds of today’s galaxies LSS formation is sensitive to the pattern, or power spectrum, of CMBR temperature fluctuations

13. Basics of large scale structure formation - 1 • LSS assembled under by gravitational instability • Express in terms of density contrast • Can decompose into Fourier modes • These evolve independently provided the fluctations are • small (linear regime) – evolution depends on parameters • of the background model (at a given epoch)

14. Basics of large scale structure formation - 2 • Density perturbations handled statistically, • e.g. via 2-point correlation function • Assuming statistical homogeneity • Inflationpredicts a primordial • spectrum of the form • with n = 1 Power spectrum; measures strength of clustering on scale, k Harrison-Zel’dovich spectrum

15. Basics of large scale structure formation - 3 • Late time (i.e. today) power spectrum is different; • modified by transfer function – describes principally how • different wavelengths were affected by radiation pressure • before CMBR epoch. • Key points:- • Structure can only grow on scales k smaller than horizon • Scales with small kentered horizon in radiation era; radiation pressure suppresses growth on these scales • When a given scale entered the horizon depends on the expansion rate, and hence on cosmological parameters. • Transfer function also depends on nature of dark matter

16. Basics of large scale structure formation - 4 • Putting all this together: • measuring the present day power spectrum of galaxy • clustering is a sensitive probe of the cosmological model • BUT are galaxies faithful tracers of the mass distribution?…

17. CMBR fluctuations • In many ways the CMBR is a ‘cleaner’ probe of the initial • power spectrum – perturbations are much smaller! • Decompose temperature fluctuations in spherical harmonics • define angular 2-point correlation function:- • = angular power spectrum Spherical harmonics Legendre polynomials

18. Adapted from Lineweaver (1997)

19. The CMBR angular power spectrum is sensitive to many cosmological parameters, which can be estimated by comparing observations with theory Theoretical curve But what do all the squiggles mean?… Max Tegmark (2001)

20. Early Universe too hot for neutral atoms Free electrons scattered light (as in a fog) After ~380,000 years, cool enough for atoms (T ~ 3000K; z ~ 1000); fog clears! Last Scattering Surface

21. Wayne Hu (1998)

22. Simplified CMBR Power Spectrum Damping Adapted from Lineweaver (1997)

23. Simplified CMBR Power Spectrum Sachs-Wolfe Effect Caused by large scale primordial fluctations in gravitational potential on super-horizon scales (inflationary origin?) Photons at LSS are blue / redshifted as they fall down / climb out of potential hills (hotspots) and valleys (cold spots) Size of super-horizon SW effect independent of scale Adapted from Lineweaver (1997)

24. Simplified CMBR Power Spectrum For For ‘Quadrupole’ Adapted from Lineweaver (1997)

25. What about sub-horizon scales?… Universe today is matter dominated i.e. Matter-radiation equality at z ~ 3500

26. What about sub-horizon scales?… (2) (1) • (1) Radiation era ends • Baryonic matter begins to collapse into potential wells as they enter the horizon (‘drags along’ photons); • acoustic oscillations on scales smaller than sound horizon • Last Scattering Surface • Baryons and photons decouple; photons carry ‘imprint’ of acoustic oscillations in density, velocity at LSS • Pattern of acoustic peaks, valleys Adapted from Lineweaver (1997)

27. What about sub-horizon scales?… (2) (1) • (1) Radiation era ends • Baryonic matter begins to collapse into potential wells as they enter the horizon (‘drags along’ photons); • acoustic oscillations on scales smaller than sound horizon • Last Scattering Surface • Baryons and photons decouple; photons carry ‘imprint’ of acoustic oscillations in density, velocity at LSS • Pattern of acoustic peaks, valleys A B C D B D A C Adapted from Lineweaver (1997)

28. Simplified CMBR Power Spectrum Damping Adapted from Lineweaver (1997)

29. Beyond Further anisotropies due to secondary post-LSS effects: (reionisation, Vishniac, S-Z) Strongly damped Can compute CMBR power spectrum using: CMBFAST Sensitive to a large number of parameters

30. Each acoustic peak corresponds to a fixed physical scale We observe peak at a particular angular scale – depends on:- angular diameter distance to LSS Position of peaks constrains Omegas, Hubble parameter – Adapted from Lineweaver (1997)

33. Baryon density constrained by height of peaks

34. Baryon density constrained by height of peaks

35. Q. How can we distinguish degenerate models? • A. Combine observations from different sources… • Hubble constant ( ) • Hubble Diagram of Distant Supernovae • Large Scale Structure / Galaxy Clustering • Strong and weak gravitational lensing • Cluster abundance / baryon fraction • Abundance of light elements / nucleosynthesis • Age of the oldest star clusters • etc, etc … Crucial test of systematic errors

36. Tegmark et al (1998)

37. Hubble diagram of distant supernovae Consider an object of intrinsic luminosity from which we observe a flux Define the Luminosity Distance via:- Distance required to give observed flux if Universe has a flat geometry

38. Hubble diagram of distant supernovae Consider an object of intrinsic luminosity from which we observe a flux Define the Luminosity Distance via:- Actual distance depends on true geometry, and expansion history of the Universe Distance required to give observed flux if Universe has a flat geometry

39. Hubble diagram of distant supernovae Consider an object of intrinsic luminosity from which we observe a flux Define the Luminosity Distance via:- Actual distance depends on true geometry, and expansion history of the Universe Distance required to give observed flux if Universe has a flat geometry

40. Adapted from Schmidt (2002)

41. Distance Modulus Fractional distance change  ½(mag change) e.g. 0.1 mag difference is 5% distance difference Adapted from Schmidt (2002)

42. Type Ia Supernova White dwarf star with a massive binary companion. Accretion pushes white dwarf over the Chandrasekhar limit, causingthermonuclear disruption Good standard candle because:- Narrow range of luminosities at maximum light Observable to very large distances

43. Hubble diagram of distant Type Ia supernovae Models with different matter density Model with positive cosmological constant Model with zero cosmological constant Straight line relation nearby log z Perlmutter (1998) results

44. 2 competing teams:- Supernova Cosmology Project (Saul Perlmutter, LBL) Supernova High-z Project (Brian Schmidt, Mt Stromlo) Consistent Results

45. SNIa measure:- CMBR measures:- Together, can constrain:- Tegmark et al (1998)

46. And the answer is?… Microwave Anisotropy Probe First year WMAP results published Feb 2003

47. From Bennett et al (2003) First year WMAP results published Feb 2003

48. From Bennett et al (2003) Accuracy of measurements across first two peaks sufficient to effectively break most degeneracies

49. From Bennett et al (2003)

50. From Bennett et al (2003)