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OBSERVING DARK ENERGY PRESENT STATUS AND FUTURE PROSPECTS

OBSERVING DARK ENERGY PRESENT STATUS AND FUTURE PROSPECTS. STEEN HANNESTAD UNIVERSITY OF AARHUS RINGBERG, 28 APRIL 2005. THE EVOLUTION EQUATIONS FOR THE SCALE FACTOR IN STANDARD FRW COSMOLOGY. THE CONDITION FOR ACCELERATION IS. ANY COMPONENT OF THE PRESENT ENERGY DENSITY

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OBSERVING DARK ENERGY PRESENT STATUS AND FUTURE PROSPECTS

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  1. OBSERVING DARK ENERGY PRESENT STATUS AND FUTURE PROSPECTS STEEN HANNESTAD UNIVERSITY OF AARHUS RINGBERG, 28 APRIL 2005

  2. THE EVOLUTION EQUATIONS FOR THE SCALE FACTOR IN STANDARD FRW COSMOLOGY THE CONDITION FOR ACCELERATION IS ANY COMPONENT OF THE PRESENT ENERGY DENSITY SATISFYING THIS IS CALLED DARK ENERGY

  3. IN GENERAL THE EQUATION OF STATE IS HOWEVER, IN MANY CASES THE PRESSURE IS PROPORTIONAL TO ENERGY DENSITY PROVIDED w IS CONSTANT, THE BEHAVIOUR IS PARTICULARLY SIMPLE

  4. AN EXAMPLE OF AN EVOLVING EQUATION OF STATE A SINGLE SCALAR FIELD MODEL Energy density and pressure THE EQUATION OF STATE IS THEN See Wetterich ’88, Peebles & Ratra ’88 Zlatev, Wang & Steinhardt ’98 Perotta, Baccigalupi & Matarrese ’99 Amendola ’00 Barreiro, Copeland & Nunes ’00 Bludman & Ross ’01 and MANY more (see for instance hep-th/0212290) DURING SLOW-ROLL w ~ -1 KINETICALLY DOMINATED w ~ 1

  5. WHAT ABOUT w < -1? VIOLATES r + 3P > 0 AND SIGNALS VACUUM INSTABILITY FURTHERMORE, THERE WILL BE A SINGULARITY (”BIG RIP”) WHERE THE SCALE FACTOR BLOWS UP AT (CALDWELL, KAMIONKOWSKI & WEINBERG 2003) HOWEVER, THERE ARE MODELS IN WHICH w < -1 DURING SOME FINITE EPOCH MULTIPLE FIELDS, EXTRA DIMENSIONS,...

  6. MODELS WITH MODIFIED LARGE SCALE GRAVITY DVALI & TURNER (2003) CONSIDERED GENERIC MODELS WITH MODIFIED LARGE SCALE GRAVITY This includes models such as DGP (2000). However, many of these models are Strongly disfavoured because of anomalous growth of perturbations (SH & Mersini, hep-ph/0405218) THIS CAN BE REWRITTEN AS THE ASYMPTOTIC BEHAVIOUR IS

  7. a = 3/2 a = -3/2

  8. THE OBSERVATIONAL SIDE

  9. MEASUREMENTS OF DISTANT TYPE I-A SUPERNOVAE (SINCE 1998) PERLMUTTER ET AL. 1999, RIESS ET AL. 1998

  10. SINCE 1998 THE SAMPLE HAS BEEN INCREASED. THE MOST RECENT IS THE RIESS ET AL. ”GOLD” SAMPLE OF 157 SUPERNOVAE (RIESS ET AL. 2004)

  11. SUPERNOVAE MEASURE THE LUMINOSITY DISTANCE IN A FLAT UNIVERSE, THIS IS DEFINED AS SUPERNOVA MEASUREMENTS ARE SENSITIVE TO w VIA f (z)

  12. WHAT ARE THE SUPERNOVA OBSERVATIONS ACTUALLY MEASURING? THE DECELERATION PARAMETER USING THE FRIEDMANN EQUATION THIS CAN BE CAST AS A SIMILAR EXPRESSION CAN BE FOUND FOR MORE GENERAL DARK ENERGY

  13. THE LUMINOSITY DISTANCE CAN BE RELATED TO THE DECELERATION PARAMETER BY THE FOLLOWING RELATION

  14. RESULTS FROM PERLMUTTER ET AL. 1998 RESULTS ARE ASSUMING A CONSTANT w MUCH MORE ABOUT THIS IN THE NEXT TALK!

  15. OTHER OBSERVATIONAL PROBES

  16. WMAP PROJECT, PUBLISHED RESULTS ON THE COSMIC MICROWAVE BACKGROUND FEBRUARY 2003

  17. THE CMB SPECTRUM DEPENDS ON THE DARK ENERGY EOS IN TWO WAYS: A) THERE IS A GEOMETRIC SHIFT OF THE SPECTRUM. THE ANGULAR SCALE OF THE CMB IS PROPORTIONAL TO THE INTEGRAL w = -0.5 w = -1 w = -2 w = -5

  18. B) THE LATE INTEGRATED SACHS WOLFE EFFECT w = -0.5 w = -1 w = -2 w = -5

  19. SDSS SURVEY

  20. SDSS POWER SPECTRUM

  21. IN GENERAL, THE DENSITY PERTURBATIONS IN CDM GROW ACCORDING TO IN THE LINEAR REGIME (IN A FLAT UNIVERSE). SINCE THE LARGE SCALE STRUCTURE SURVEYS MEASURE THE MATTER FLUCTUATIONS THEY ARE SENSITIVE TO DARK ENERGY

  22. FOR A CONSTANT EQUATION OF STATE THE COMBINED CONSTRAINTS ARE QUITE STRONG NEW TYPE Ia SUPERNOVA DATA KNOP ET AL. ASTRO-PH/0309368 (SCP)

  23. SH & E MORTSELL, ASTRO-PH/0407259 (JCAP) CMB+LSS CMB+LSS+SNI-A INCLUDES THE RIESS ET AL. 2004 DATA

  24. WHAT ABOUT TIME EVOLUTION OF w? MANY MODELS PREDICT A STRONG EVOLUTION OF w WITH TIME (QUINTESSENCE, EXTRA DIMENSIONS, ETC) HOW SHOULD A TIME EVOLUTION BE PARAMETRIZED? LUMINOSITY DISTANCE, ANGULAR DISTANCE AND GROWTH FACTOR ARE ALL INTEGRAL QUANTITIES A DIRECT MAPPING OF w(z) IS DIFFICULT AND THEREFORE SOME EFFECTIVE PARAMETRIZATION SHOULD BE USED FOR THE SUPERNOVA DATA THE TYPICAL CHOICE IS HOWEVER, THIS IS BAD BECAUSE IT DIVERGES AT HIGH z SO THAT COMBINATION WITH CMB IS IMPOSSIBLE

  25. ALAM ET AL. (ASTRO-PH/0311364) USE THE PARAMETRIZATION NOTE THAT FOR A FLAT UNIVERSE THERE ARE ONLY TWO FREE PARAMETERS SINCE THEY FIND THAT THERE IS AN INDICATION OF A TIME EVOLUTION AT ROUGHLY 2.7s

  26. MANY DIFFERENT GROUPS HAVE STUDIED THIS CLAIM, ADDING OTHER DATA. A DIFFERENT PARAMETRIZATION IS NECESSARY SINCE THE SERIES EXPANSION BREAKS DOWN AT HIGH z SH & MORTSELL (JCAP 0409, 001 – ASTRO-PH/0407259) USED THIS ASSUMES A SMOOTH CROSSOVER BETWEEN TWO ASYMPTOTIC LIMITS OF w (SEE UPADHYE, ISHAK & STEINHARDT (ASTRO-PH/0411803) FOR A DISCUSSION OF VARIOUS RECENT PARAMETRIZATIONS)

  27. THE TRANSITION OCCURS ROUGHLY AT a = as THE WIDTH IS DETERMINED BY q q = 0.5, 1, 2, 5, 10

  28. COMBINING ALL AVAILABLE DATA THERE DOES AT FIRST SIGHT SEEM TO BE SOME TENTATIVE INDICATION OF A TIME EVOLUTION WITH A STEEP GRADIENT TOWARDS MORE NEGATIVE VALUES OF w AT PRESENT

  29. THE BEST FIT MODEL HAS THIS FINDING IS IN ACCORDANCE WITH ALAM ET AL. (AND SEVERAL OTHER STUDIES)

  30. WHAT IS THE STATISTICAL SIGNIFICANCE OF THE RESULT? c2 VARYING LCDM HOWEVER, SINCE THERE ARE FOUR MORE PARAMETERS, THE EVOLVING MODELS ACTUALLY HAVE A SMALLER GOODNESS OF FIT. THERE IS NO EVIDENCE FOR ANY EVOLUTION OF THE EQUATION OF STATE!!!

  31. WHAT IS IN STORE FOR THE FUTURE? BETTER CMBR TEMPERATURE MEASUREMENTS Satellites Balloons Interferometers WMAP (ongoing)Boomerang (ongoing)CBI (ongoing) Planck (2007) TopHat (ongoing)DASI (ongoing) CMBR POLARIZATION MEASUREMENTS Satellites Balloons Ground WMAP (ongoing)Boomerang (2002-3)Polatron (ongoing) Planck (2007) DASI LARGE SCALE STRUCTURE SURVEYS 2dF (completed) 250.000 galaxies SDSS (ongoing) 1.000.000 galaxies COSMOLOGICAL SUPERNOVA SURVEYS ESSENCE, DARK ENERGY CAMERA, SNAP WEAK LENSING SURVEYS

  32. SNAP SATELLITE THE SUPERNOVA ACCELERATION PROBE (SNAP) WILL OBSERVE ROUGHLY 2000 TYPEI-a SN OUT TO REDSHIFTS OF ORDER 1.5, STARTING FROM ~ 2012? http://snap.lbl.gov

  33. SNAP ALONE WILL BE ABLE TO MEASURE w AS WELL AS THE PRESENT BOUND WITHOUT ANY ADDITIONAL DATA

  34. WEAK LENSING – A POWERFUL PROBE FOR THE FUTURE Distortion of background images by foreground matter Unlensed Lensed

  35. FROM A WEAK LENSING SURVEY THE ANGULAR POWER SPECTRUM CAN BE CONSTRUCTED, JUST LIKE IN THE CASE OF CMB MATTER POWER SPECTRUM (NON-LINEAR) WEIGHT FUNCTION DESCRIBING LENSING PROBABILITY (SEE FOR INSTANCE JAIN & SELJAK ’96, ABAZAJIAN & DODELSON ’03, SIMPSON & BRIDLE ’04)

  36. WEAK LENSING POWER SPECTRUM Wide survey Non-linear physics

  37. PROJECTED ERRORS FOR A WEAK LENSING SURVEY SNe

  38. WHAT ABOUT PERTURBATIONS IN THE DARK ENERGY? IF THE DARK ENERGY IS A FLUID (I.E. A PHYSICAL COMPONENT WITH ENERGY DENSITY AND PRESSURE) IT CAN HAVE FLUCTUATIONS. IN SOME CASES (E.G. A SINGLE SCALAR FIELD) THESE ARE EASY TO CALCULATE AND INCLUDE. HOWEVER, IN MANY CASES IT IS IMPOSSIBLE! IF ”DARK ENERGY” IS DUE TO A MODIFICATION OF GRAVITY THEN IT IS MEANINGLESS TO TALK ABOUT FLUCTUATIONS IN THE DARK ENERGY IF DARK ENERGY IS A FLUID IT SHOULD BE CHARACTERIZED BY BOTH THE EOS AND THE SPEED OF SOUND

  39. EQUATION OF STATE PARAMETER FOR A PERFECT FLUID THE SOUND SPEED IS THEN HOWEVER, FOR AN IMPERFECT FLUID IT CAN BE WRITTEN AS IN SYNCHRONOUS GAUGE THIS LEADS TO THE FOLLOWING SET OF PERTURBATION EQUATIONS

  40. CHANGING THE SPEED OF SOUND OF DARK ENERGY AFFECTS PERTURBATION GROWTH, BUT ONLY WHEN DARK ENERGY IS A SIGNIFICANT PART OF THE ENERGY DENSITY w = -0.2 w = -0.8 c2 = 1 c2 = 1 c2 = 0 c2 = 0

  41. PRESENT CONSTRAINTS ON THE SPEED OF SOUND OF THE DARK ENERGY FROM ALL AVAILABLE DATA STH, ASTRO-PH/0504017 (see also Corasaniti, Giannantonio & Melchiorri, astro-ph/0504115)

  42. NOTICE THAT THERE IS A SLIGHT BIAS OF THE ALLOWED REGION FOR w, DEPENDING ON WHETHER DARK ENERGY PERTURBATIONS ARE ASSUMED. ALSO, THE GLOBAL BEST FIT CHANGES SLIGHTLY. c2 d.o.f. c2/d.o.f NO PERTURBATIONS 1626.1 1515 1.073 FLUID 1625.5 1516 1.073 HOWEVER, AT PRESENT THERE IS NO EVIDENCE FOR OR AGAINST DARK ENERGY PERTURBATIONS.

  43. FUTURE CONSTRAINTS ON THE SPEED OF SOUND OF DARK ENERGY (STH, ASTRO-PH/0504017)

  44. CONCLUSIONS THERE ARE STRONG BOUNDS ON THE DARK ENERGY EQUATION OF STATE, PROVIDED THAT w IS CONSTANT. THE PRESENT BOUND IS (JCAP 0409, 001) FAVOURING A COSMOLOGICAL CONSTANT THERE IS AT PRESENT NO EVIDENCE FOR ANY EVOLUTION OF THE DARK ENERGY EQUATION OF STATE, CONTRARY TO SOME CLAIMS THERE IS NO INDICATION OF PERTURBATIONS IN THE DARK ENERGY FUTURE DATA WILL ALLOW FOR AT LEAST A FACTOR FEW IMPROVEMENT IN THE DETERMINATION OF w, BUT ARE NOT LIKELY TO MEASURE THE FLUID PROPERTIES OF DARK ENERGY

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