Testing dark energy as a function of scale

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Seminar at AIMS by Dr. Ignacy Sawicki, 15 November 2013

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Testing dark energy as a function of scale

  1. 1. Ignacy Sawicki AIMS arXiv:1305.008, 1210.0439 (PRD) + 1208.4855 (JCAP) Together with: L. Amendola, M. Kunz, M. Motta, I.Saltas.
  2. 2. The Bygone Era of Easy Choices ฮ› โ€ข ๐‘ค = โˆ’1 Dark Energy โ€ข ๐‘ค โ‰  โˆ’1 โ€œModified gravityโ€ โ€ข โ€ข โ€ข k-essence ๐‘ค =/โ‰  โˆ’1 2 ๐‘s = 1 ๐œ‚โ‰ 1 15 November 2013 AIMS, Muizenberg โ€ข โ€ข โ€ข ๐‘ค =/โ‰  โˆ’1 2 ๐‘s โ‰  1 ๐œ‚=1
  3. 3. Managing the Model Bestiary ๏‚ž ๏‚ž ๏‚ž ๏‚ž Acceleration effectively from ฮ› 2 ๐‘s = 1 Non-minimal coupling gives fifth force Chameleon screening & Compton scale ๏‚ž ๏‚ž ๏‚ž ๏‚ž ๏‚ž ๏‚ž (coupled) Quintessence, ๐’‡ ๐‘น , Brans-Dicke Slow-Rolling ๐“๐Ÿ โ‰ช ๐›€๐‘ฟ ๐‘ฏ๐Ÿ 15 November 2013 ๏‚ž Acceleration from kinetic condensate Can describe hydrodynamics (incl. imperfect corrections) Realistically should be nearly shift-symmetric Non-trivial acoustic metric Screening through Vainstein mechanism k-essence, KGB, galileons, shift-symmetric Horndeski Fast-Rolling ๐“๐Ÿ โˆผ ๐›€๐‘ฟ ๐‘ฏ๐Ÿ AIMS, Muizenberg
  4. 4. What you get depends on what you put in Planck Ade et al. (2013) SDSS-III DR9 Anderson et al. (2012) 15 November 2013 AIMS, Muizenberg
  5. 5. In this talkโ€ฆ ๏‚ž What properties can we actually observe without having assumed a model first? ๏‚— Only ๐ป(๐‘ง) not ๐‘ค ๏‚— Only potentials ฮฆ, ฮจ, not e.g. DM growth rate ๏‚ž Can we measure properties of DE in a model-independent way? ๏‚— Not all, but can form null tests from data which can eliminate model classes ๏‚ž Fundamental reason: dark degeneracy between dark matter and dark energy ๏‚— All cosmological probes are only sensitive to geodesics 15 November 2013 AIMS, Muizenberg
  6. 6. 15 November 2013 AIMS, Muizenberg
  7. 7. Our Limited Eyes Supernovae: ๐‘‘L 15 November 2013 Galaxies P(k): BAO/RSD AIMS, Muizenberg Galaxy Shapes: Lensing
  8. 8. The Best-Case Scenario Assume โ€ข โ€ข โ€ข โ€ข as little as feasible FRW + (scalar) linear perturbations Matter & light move on geodesics of some metric Linear density bias ๐›ฟgal = ๐‘(๐‘˜, ๐‘Ž)๐›ฟm (Equivalence principle/Universality of couplings) Infinite โ‚ฌ$ยฃยฅ build Super-Euclid โ€ข Desired precision for position and redshift โ€ข SNe โ€ข lensing โ€ข counting galaxies 15 November 2013 AIMS, Muizenberg
  9. 9. LSS: Galaxy Power Spectrum ๏‚ž Baryon Acoustic Oscillations is a fixed ruler ๏‚— use to measure distance if same physical size SDSS III, Anderson et al. (2012) 15 November 2013 AIMS, Muizenberg
  10. 10. Background SNe, โŠฅ BAO, CMB peak โ€ข ๐ป0 ๐ท ๐‘ง = โˆฅ BAO โ€ข ๐ป ๐‘ง = In principle 15 November 2013 1 โˆ’ฮฉ ๐‘˜0 sinh โˆ’ฮฉ ๐‘˜0 ๐ป0 d๐‘ง ๐ป(๐‘ง) ฮ”๐‘ง ๐‘  ๐‘ง โ€ข Observables are ๐ป(๐‘ง)/๐ป0 , ฮฉ ๐‘˜0 โ€ข Not ๐‘ค ๐‘ง or ฮฉm AIMS, Muizenberg
  11. 11. Dark Degeneracy 2 ๐ป0 ฮฉ ๐‘‹ = 1 โˆ’ 2 ฮฉ ๐‘˜0 ๐‘Žโˆ’2 + ฮฉm0 ๐‘Žโˆ’3 ๐ป ๏‚ž In principle no way of measuring split between DE and DM ๏‚ž Only choice of parameterisation breaks degeneracy ๏‚— e.g. constant ๐‘ค 15 November 2013 Anderson et al. (2012) AIMS, Muizenberg Kunz (2007)
  12. 12. Huterer and Peiris (2006) Natural EoS for Quintessence ๐‘ค = ๐‘ค0 + ๐‘ค ๐‘Ž 1 โˆ’ ๐‘Ž 15 November 2013 AIMS, Muizenberg ?
  13. 13. Perturbations d๐‘  2 = โˆ’ 1 + 2ฮจ d๐‘ก 2 + ๐‘Ž2 1 + 2ฮฆ d๐’™ ๐Ÿ โ€ฒ 2 3 ฮฉ ๐›ฟ 2 m m 3 ฮฆ โˆ’ฮจ + ๐‘˜ ฮฆ= ฮฆ + ฮจ = ๐œน๐… = ๐œŽฮฉ ๐‘‹ ๐›ฟ ๐‘‹ + ๐Ÿ‘ ๐Ÿ ๐›€๐‘ฟ ๐œน๐‘ฟ ๏‚ž ๏‚ž Want to measure ๐บeff and ๐œ‚ to determine DE model Can we actually do this? 3 ๐‘˜ 2 ฮจ = โˆ’ ๐‘ฎ ๐ž๐Ÿ๐Ÿ ๐’Œ, ๐’‚ ฮฉm ๐›ฟm 2 ฮฆ + ฮจ = 1 โˆ’ ๐œผ(๐’Œ, ๐’‚) ฮจ ๏‚ž Remember: ๐บeff and ๐œ‚ hide dynamics ๏‚— No reason for them to be โ€ฒโ€ฒ ๐›ฟm ๐ปโ€ฒ + 2+ ๐ป 15 November 2013 โ€ฒ ๐›ฟm 3 โˆ’ ๐‘ฎ ๐ž๐Ÿ๐Ÿ ๐’Œ, ๐’‚ ๐œน ๐ฆ = 0 2 AIMS, Muizenberg simple
  14. 14. Is dark energy smooth? โ€ข ๐œ‚=1 โ€ข ๐บeff = 1 ฮ›: of course 2 โ€ข ๐‘s = 1 โ€ข ๐œ‚=1 โ€ข ๐บeff โ†’ 1 + 2 โ€ข ๐‘s = 1 ๐›ผ 2 ๐‘s ๐‘˜ 2 Quintessence: more or less โ€ข ๐œ‚= 1 2 โ€ข ๐บeff = 4 3 ๐‘“(๐‘…): not at all 1 ๐›ฟ๐œŒ ๐‘‹ = โˆ’ ๐›ฟ๐œŒm 3 15 November 2013 AIMS, Muizenberg
  15. 15. LSS: Measure Galaxy Shapes ๏‚ž Weak lensing ๏‚— Gravity from DM and DE changes path of light, distorting galaxy shapes ๏‚— Can invert this shear to measure the gravitational potential ๏‚ž 15 November 2013 AIMS, Muizenberg ๐ฟ = ๐‘˜2 ฮฆ โˆ’ ฮจ Measure distribution of potential not of DM
  16. 16. LSS: Measure Galaxy Shapes ๏‚ž Weak lensing ๏‚— Gravity from DM and DE changes path of light, distorting galaxy shapes ๏‚— Can invert this shear to measure the gravitational potential ๏‚ž 15 November 2013 AIMS, Muizenberg ๐ฟ = ๐‘˜2 ฮฆ โˆ’ ฮจ Measure distribution of potential not of DM
  17. 17. LSS: Galaxy Power Spectrum ๏‚ž Amplitude: related to dark matter through bias ๐›ฟgal = ๐‘ ๐‘˜, ๐‘ง ๐›ฟm ๏‚— ๐‘ can only be measured when you know what DE is ๏‚— ๐œŽ8 is not an observable SDSS III, Anderson et al. (2012) 15 November 2013 AIMS, Muizenberg
  18. 18. LSS: Redshift-Space Distortions Hawkins et al (2002) ๏‚ž ๏‚ž 15 November 2013 ๐‘˜, ๐‘ง, cos 2 ๐›ผ = ๐›ฟgal ๐‘˜, ๐‘ง โˆ’ AIMS, Muizenberg Redshift Space ๏‚ž ๐‘ง ๐›ฟgal Real Space Measure peculiar velocity of galaxies, ๐œƒgal cos 2 ๐œƒgal ๐‘˜, ๐‘ง ๐›ผ ๐ป
  19. 19. How are RSD (ab)used? ๏‚— Continuity for DM โ€ฒ ๐›ฟm + ๐œƒm โ‰ˆ 0 โ€ข If ๐œƒm = ๐œƒgal then can measure dark matter growth rate โ€ฒ ๐›ฟm โ‰ก ๐‘“๐›ฟm = ๐‘“๐œŽ8 โ€ข โ€ข BOSS DR9 + WiggleZ, SDSS LRG, 2dFRGS Samushia et al. (2012) 15 November 2013 AIMS, Muizenberg Only measuring velocities of galaxiesโ€ฆ everything else is our interpretation Non-linearity important at early times. How do you set the initial conditions?
  20. 20. From acceleration measure force ๐‘ง ๐›ฟgal ๐‘˜, ๐‘ง, cos 2 ๐›ผ = ๐›ฟgal ๐‘˜, ๐‘ง โˆ’ cos 2 ๐ด(๐‘˜, ๐‘ง) ๏‚ž ๐œƒgal ๐‘˜, ๐‘ง ๐›ผ ๐ป ๐‘…(๐‘˜, ๐‘ง) Galaxies move on geodesics 2 (๐‘Ž ๐œƒgal )โ€ฒ = ๐‘˜2 ฮจ ๐ป ๐ปโ€ฒ ๐‘˜ 2 ฮจ = โˆ’๐‘…โ€ฒ โˆ’ ๐‘… 2 + ๐ป ๐‘˜2 ฮฆ โˆ’ ฮจ = ๐ฟ 15 November 2013 AIMS, Muizenberg
  21. 21. Reconstruction of Metric ๏‚ž Ratios of potentials always observable ฮฆ โˆ’ = ๐œ‚ ฮจ ๏‚ž ฮจโ€ฒ =1+ฮ“ ฮจ We measure power spectra of potentials, not dark matter 15 November 2013 AIMS, Muizenberg
  22. 22. What about ๐บeff ? โ€ฒ ๐บeff ฮฉm0 1 + ๐œ‚ + ๐บeff =ฮ“ ๐บeff ๐ฟ/๐‘… ๏‚ž Dark degeneracy strikes back ๏‚ž No way of measuring ๐บeff without a model ๏‚— Would somehow need to weigh DM and separated from DE 15 November 2013 AIMS, Muizenberg
  23. 23. So what? ๏‚ž Full constraints on particular models of course are perfectly fine ๏‚— Expensive and non-generic: how to anoint the particular model? ๏‚— Initial conditions? ๏‚ž In practice, we use parameterisations which represent parts of model space ๏‚— Are they consistent? ๏‚— Do they say anything about my model? ๏‚— Do they allow us to unambiguously see the things my model canโ€™t do? 15 November 2013 AIMS, Muizenberg
  24. 24. 15 November 2013 AIMS, Muizenberg
  25. 25. Horndeski (1974) Nicolis, Ratazzi, Tricherini (2009 Deffayet, Gao, Steer, Zahariade (2011) The model space โ„’ โˆผ ๐พ ๐‘‹, ๐œ™ + ๐บ3 ๐‘‹, ๐œ™ โง ๐œ™ + +๐บ4 ๐‘‹, ๐œ™ ๏‚ž ๐›ป๐œ‡ ๐›ป ๐œˆ ๐œ™ 2 + ๐บ5 ๐‘‹, ๐œ™ ๐›ป๐œ‡ ๐›ป ๐œˆ ๐œ™ If ๐‘‹ small, then nothing new Quintessence โ„’ โ‰ˆ ๐‘‹ + ๐‘‰ ๐œ™ + ๐‘“(๐œ™)๐‘… ๐‘“ ๐‘… Brans-Dicke ๏‚ž If ๐‘‹ large, then any term can be important ๏‚ž The background is a path across the 4D operator space 15 November 2013 AIMS, Muizenberg 3 + grav 2๐‘‹ โ‰ก ๐œ•๐œ‡ ๐œ™ 2
  26. 26. What can we actually say? d๐‘ก๐‘Ž3 ๐‘†2 (๐‘˜) = Creminelli, Luty, Nicolis, Senatore (2006) IS, Saltas, Amendola, Kunz (2012) Gleyzes, Piazza, Vernizzi (2013) ๐œ…perf ๐‘ก ๐’ชperf ๐‘ก, ๐‘˜ 2 + ๐œ…3 ๐‘ก ๐’ช3 ๐‘ก, ๐‘˜ 2 + +๐œ…4 ๐‘ก ๐’ช4 ๐‘ก, ๐‘˜ 2 + ๐œ…5 (๐‘ก)๐’ช5 (๐‘ก, ๐‘˜ 2 ) On FRW, get corrections to perfect fluid that go as ๐‘˜ 2 ๐œ™ ๐‘‡ ๐œ‡๐œˆ = perf ๐‘‡ ๐œ‡๐œˆ Jeans + ๐œ…3 ๐‘˜ 2 + ๐œ…4 ๐‘˜ 2 ๐œ‡๐œˆ ๐บeff ๐œ‡๐œˆ ๐œ‚, ๐บeff Alternative: ๏‚— e.g. braneworld models: corrections go as ๐‘˜ ๏‚— Lorentz-violating: higher powers of ๐‘˜ Measure DE properties from scale dependence on the realised background 15 November 2013 AIMS, Muizenberg Amin, Wagoner, Blandford (2007) Blas, Sibiryakov (2011)
  27. 27. Is it any scalar at all? 0 ๐›ฟ๐‘‡0 โŠƒ ๐›ฟ๐œ™, ๐›ฟ๐œ™, ๐›ฟm ๐›ฟ๐‘‡๐‘– ๐‘– โŠƒ ๐›ฟ๐œ™ , ๐›ฟ๐œ™, ๐œน๐“ ๐›ฟ๐‘‡๐‘–0 โŠƒ ๐›ฟ๐œ™, ๐œน๐“, ๐œƒm ๐›ฟ๐œ™ = EoM ฮฆโ€ฒโ€ฒ ฮฆโ€ฒ ฮจโ€ฒ ฮฆ + ๐›ผ1 + ๐›ผ2 + ๐›ผ3 + ๐›ผ4 ๐‘˜ 2 + ๐›ผ5 + ๐›ผ6 ๐‘˜ 2 ฮจ ฮจ ฮจ ฮจ ฮ“(๐‘˜, ๐‘ง) ๐œ‚(๐‘˜, ๐‘ง) ฮจ = ฮฉm ๐›ผ7 ๐œƒm ๐‘…โ€ฒ /๐‘… Fix ๐›ผ ๐‘– (๐‘ง) ๐‘“(๐‘…): one param ๐‘šC (๐‘ง) 2 October2013 ๐›ฟ๐‘‡๐‘— ๐‘– โŠƒ ๐œน๐“ NYU Abu Dhabi
  28. 28. The Takeaway ๏‚ž In principle, we can reconstruct the evolution of the metric ๏‚— We cannot get the split between DE and DM without assuming some class of models ๏‚ž Generically, DE models predict a change in the power law for ฮจ as a function of scale ๏‚— Different frameworks give you different scale dependence: could potentially eliminate scalars completely ๏‚ž If I told you today that the background was inconsistent with ๐‘ค = โˆ’1, what have you learned? ๏‚— If that happens, weโ€™ll have to be more sophisticated about interpreting the data 15 November 2013 AIMS, Muizenberg

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