1. Science of the Dark Energy Survey Josh Frieman Fermilab and the University of Chicago Astronomy 41100 Lecture 2, Oct. 15, 2010

2. DES Collaboration Meeting 2 Go to: http://astro.fnal.gov/desfall2010/Home.html Science Working group meetings on Tuesday. Plenary sessions Wed-Fri.

3. 3 Cosmological Constant as Dark Energy Einstein: Zel’dovich and Lemaitre:

4. Cosmological Constant  as Dark Energy Quantum zero-point fluctuations: virtual particles continuously fluctuate into and out of the vacuum (via the Uncertainty principle). Vacuum energy density in Quantum Field Theory: Theory: Data: Pauli Cosmological Constant Problem

5. Dark Energy: Alternatives to Λ The smoothness of the Universe and the large-scale structure of galaxies can be neatly explained if there was a much earlier epoch of cosmic acceleration that occurred a tiny fraction of a second after the Big Bang: Primordial Inflation Inflation ended, so it was not driven by the cosmological constant. This is a caution against theoretical prejudice for Λ as the cause of current acceleration (i.e., as the identity of dark energy).

6. Light Scalar Fields as Dark Energy Perhaps the Universe is not yet in its ground state. The `true’ vacuum energy (Λ) could be zero (for reasons yet unknown). Transient vacuum energy can exist if there is a field that takes a cosmologically long time to reach its ground state. This was the reasoning behind inflation. For this reasoning to apply now, we must postulate the existence of an extremely light scalar field, since the dynamical evolution of such a field is governed by JF, Hill, Stebbins, Waga 1995

7. 7 Scalar Field as Dark Energy (inspired by inflation) Dark Energy could be due to a very light scalar field , slowly evolving in a potential, V(  ): Density & pressure: Slow roll: V  

8. Scalar Field Dark Energy Ultra-light particle: Dark Energy hardly clusters, nearly smooth Equation of state: usually, w >  1 and evolves in time Hierarchy problem: Why m/  ~ 10  61 ? Weak coupling: Quartic self-coupling  < 10  122 General features: m eff < 3H 0 ~ 10 -33 eV (w < 0) (Potential > Kinetic Energy) V ~ m 2  2 ~  crit ~ 10 -10 eV 4  ~ 10 28 eV ~ M Planck aka quintessence V   10 28 eV (10 –3 eV) 4

9. The Coincidence Problem Why do we live at the `special’ epoch when the dark energy density is comparable to the matter energy density?  matter ~ a -3  DE ~ a -3(1+w) a(t) Today

10. Scalar Field Models & Coincidence V V  Runaway potentials DE/matter ratio constant (Tracker Solution) Pseudo-Nambu Goldstone Boson Low mass protected by symmetry (Cf. axion) JF, Hill, Stebbins, Waga V(  ) = M 4 [1+cos(  /f)] f ~ M Planck M ~ 0.001 eV ~ m e.g., e –  or  –n M Pl Ratra & Peebles; Caldwell, etal `Dynamics’ models (Freezing models) `Mass scale’ models (Thawing models) 

11. PNGB Models Tilted Mexican hat: Frieman, Hill, Stebbins, Waga 2005 Spontaneous symmetry breaking at scale f Explicit breaking at scale M Hierarchy protected by symmetry f M4M4

12. 12 Caldwell & Linder Dynamical Evolution of Freezing vs. Thawing Models Measuring w and its evolution can potentially distinguish between physical models for acceleration

13. Runaway (Tracker) Potentials Typically  >> M planck today. Must prevent terms of the form V(  ) ~  n+4 / M planck n up to large n What symmetry prevents them?

14. 14 Perturbations of Scalar Field Dark Energy If it evolves in time, it must also vary in space. h = synchronous gauge metric perturbation Fluctuations distinguish this from a smooth “x-matter ” or  Coble, Dodelson, Frieman 1997 Caldwell et al, 1998

15. 15 Dark Energy Interactions Couplings to visible particles must be small Couplings cause long-range forces Carroll 1998 Attractive force between lumps of  Frieman & Gradwohl 1990, 1992 Example: scalar field coupled to massive neutrino

16. What about w <  1? The Big Rip H(t) and a(t) increase with time and diverge in finite time e.g, for w=-1.1, t sing ~100 Gyr Scalar Field Models: need to violate null Energy condtion  + p > 0: for example: L =  (  ) 2  V Controlling instability requires cutoff at low mass scale Modified Gravity models apparently can achieve effective w < –1 without violating null Energy Condition Caldwell, etal Hoffman, etal

17. Modified Gravity & Extra Dimensions 4-dimensional brane in 5-d Minkowski space Matter lives on the brane At large distances, gravity can leak off brane into the bulk, infinite 5 th dimension Dvali, Gabadadze, Porrati Acceleration without vacuum energy on the brane, driven by brane curvature term Action given by: Consistency problems: ghosts, strong coupling

18. Modified Gravity 18 Weak-field limit: Consider static source on the brane: Solution: In GR, 1/3 would be ½ Characteristic cross-over scale: For modes with p<<1/r c : Gravity leaks off the brane: longer wavelength gravitons free to propagate into the bulk Intermediate scales: scalar-tensor theory

19. Cosmological Solutons Modified Friedmann equation: Early times: H>>1/r c : ordinary behavior, decelerated expansion. Late times: self-accelerating solution for (-) For we require At current epoch, deceleration parameter is corresponds to w eff =-0.8

20. Growth of Perturbations Linear perturbations approximately satisfy: Can change growth factor by ~30% relative to GR Motivates probing growth of structure in addition to expansion rate

21. Modified Gravity: f(R) This particular realization excluded by solar system tests, but variants evade them: Chameleon models hide deviations from GR on solar system scales

22. 22 Bolometric Distance Modulus Logarithmic measures of luminosity and flux: Define distance modulus: For a population of standard candles (fixed M), measurements of  vs. z, the Hubble diagram, constrain cosmological parameters. flux measure redshift from spectra

23. 23 Distance Modulus Recall logarithmic measures of luminosity and flux: Define distance modulus: For a population of standard candles (fixed M) with known spectra (K) and known extinction (A), measurements of  vs. z, the Hubble diagram, constrain cosmological parameters. denotes passband

24. 24 K corrections due to redshift SN spectrum Rest-frame B band filter Equivalent restframe i band filter at different redshifts (i obs =7000-8500 A)

25. 25 Absolute vs. Relative Distances Recall logarithmic measures of luminosity and flux: If M i is known, from measurement of m i can infer absolute distance to an object at redshift z, and thereby determine H 0 (for z<<1, d L =cz/H 0 ) If M i (and H 0 ) unknown but constant, from measurement of m i can infer distance to object at redshift z 1 relative to object at distance z 2 : independent of H 0 Use low-redshift SNe to vertically `anchor’ the Hubble diagram, i.e., to determine

26. 26 SN 1994D Type Ia Supernovae as Standardizable Candles

27. 27

28. 28 SN Spectra ~1 week after maximum light Filippenko 1997 Ia II Ic Ib

29. Type Ia Supernovae Thermonuclear explosions of Carbon-Oxygen White Dwarfs White Dwarf accretes mass from or merges with a companion star, growing to a critical mass~1.4M sun (Chandrasekhar) After ~1000 years of slow cooking, a violent explosion is triggered at or near the center, and the star is completely incinerated within seconds In the core of the star, light elements are burned in fusion reactions to form Nickel. The radioactive decay of Nickel and Cobalt makes it shine for a couple of months

30. 30 Type Ia Supernovae General properties: Homogeneous class* of events, only small (correlated) variations Rise time: ~ 15 – 20 days Decay time: many months Bright: M B ~ – 19.5 at peak No hydrogen in the spectra Early spectra: Si, Ca, Mg,...(absorption) Late spectra: Fe, Ni,…(emission) Very high velocities (~10,000 km/s) SN Ia found in all types of galaxies, including ellipticals Progenitor systems must have long lifetimes *luminosity, color, spectra at max. light

31. SN Ia Spectral Homogeneity (to lowest order) from SDSS Supernova Survey

32. 32 Spectral Homogeneity at fixed epoch

33. 33 SN2004ar z = 0.06 from SDSS galaxy spectrum Galaxy-subtracted Spectrum SN Ia template

34. How similar to one another? Some real variations: absorption-line shapes at maximum Connections to luminosity? Matheson, etal, CfA sample

35. 35 Hsiao etal Supernova Ia Spectral Evolution Late times Early times

36. 36 Layered Chemical Structure provides clues to Explosion physics

37. 37 SN1998bu Type Ia Multi-band Light curve Extremely few light-curves are this well sampled Suntzeff, etal Jha, etal Hernandez, etal

38. Luminosity Time  m 15 15 days Empirical Correlation: Brighter SNe Ia decline more slowly and are bluer Phillips 1993

39. SN Ia Peak Luminosity Empirically correlated with Light-Curve Decline Rate Brighter  Slower Use to reduce Peak Luminosity Dispersion Phillips 1993 Peak Luminosity Rate of decline Garnavich, etal

40. 40 Type Ia SN Peak Brightness as calibrated Standard Candle Peak brightness correlates with decline rate Variety of algorithms for modeling these correlations: corrected dist. modulus After correction,  ~ 0.16 mag (~8% distance error) Luminosity Time

41. 41 Published Light Curves for Nearby Supernovae Low-z SNe: Anchor Hubble diagram Train Light- curve fitters Need well- sampled, well- calibrated, multi-band light curves

42. Low-z Data 42

43. 43 Carnegie Supernova Project Nearby Optical+ NIR LCs

44. 44 Correction for Brightness-Decline relation reduces scatter in nearby SN Ia Hubble Diagram Distance modulus for z<<1: Corrected distance modulus is not a direct observable: estimated from a model for light-curve shape Riess etal 1996

45. 45 Acceleration Discovery Data: High-z SN Team 10 of 16 shown; transformed to SN rest-frame Riess etal Schmidt etal V B+1

46. Riess, etal High-z Data (1998) 46

47. High-z Supernova Team data (1998) 47

48. Likelihood Analysis This assume 48 Goliath etal 2001

49. 49

50. Exercise 5 Carry out a likelihood analysis of using the High-Z Supernova Data of Riess, etal 1998: use Table 10 above for low-z data and the High-z table above for high-z SNe. Assume a fixed Hubble parameter for the first part of this exercise. 2 nd part: repeat the exercise, but marginalizing over H 0 with a flat prior, either numerically or using the analytic method of Goliath etal. Errors: assume intrinsic dispersion of and fit dispersions from the tables and dispersion due to peculiar velocity from Kessler etal (0908.4274), Eqn. 28, with 50