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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 - PowerPoint PPT Presentation
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OBSERVING DARK ENERGYPRESENT STATUS AND FUTURE
PROSPECTS
STEEN HANNESTAD UNIVERSITY OF AARHUS
RINGBERG, 28 APRIL 2005
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THE EVOLUTION EQUATIONS FOR THE SCALE FACTOR INSTANDARD FRW COSMOLOGY
THE CONDITION FOR ACCELERATION IS
ANY COMPONENT OF THE PRESENT ENERGY DENSITY SATISFYING THIS IS CALLED DARK ENERGY
)1(3 wa
IN GENERAL THE EQUATION OF STATE IS
)(fP
HOWEVER, IN MANY CASES THE PRESSURE IS PROPORTIONALTO ENERGY DENSITY
)(awP
PROVIDED w IS CONSTANT, THE BEHAVIOUR IS PARTICULARLYSIMPLE
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1
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Energy density and pressure
A SINGLE SCALAR FIELD MODEL
THE EQUATION OF STATE IS THEN
)(2/
)(2/2
2
V
Vw
DURING SLOW-ROLL w ~ -1KINETICALLY DOMINATED w ~ 1
AN EXAMPLE OF AN EVOLVING EQUATION OF STATE
See Wetterich ’88, Peebles & Ratra ’88Zlatev, Wang & Steinhardt ’98Perotta, Baccigalupi & Matarrese ’99Amendola ’00Barreiro, Copeland & Nunes ’00Bludman & Ross ’01and MANY more(see for instance hep-th/0212290)
WHAT ABOUT w < -1?
VIOLATES P > 0 AND SIGNALS VACUUM INSTABILITY
FURTHERMORE, THERE WILL BE A SINGULARITY (”BIG RIP”) WHERE THE SCALE FACTOR BLOWS UP AT
2/10
0 )1(
1
1
11
3
2~
mwHtt
(CALDWELL, KAMIONKOWSKI & WEINBERG 2003)
HOWEVER, THERE ARE MODELS IN WHICH w < -1 DURING SOMEFINITE EPOCH
MULTIPLE FIELDS, EXTRA DIMENSIONS,...
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MODELS WITH MODIFIED LARGE SCALE GRAVITY
DVALI & TURNER (2003) CONSIDERED GENERIC MODELS WITHMODIFIED LARGE SCALE GRAVITY
THIS CAN BE REWRITTEN AS
THE ASYMPTOTIC BEHAVIOUR IS
This includes models suchas DGP (2000). However, many of these models are Strongly disfavoured because of anomalous growth of perturbations (SH & Mersini, hep-ph/0405218)
THE OBSERVATIONAL SIDE
MEASUREMENTS OF DISTANT TYPE I-A SUPERNOVAE (SINCE 1998)
PERLMUTTER ET AL. 1999, RIESS ET AL. 1998
SINCE 1998 THE SAMPLE HAS BEEN INCREASED. THE MOST RECENT IS THE RIESS ET AL. ”GOLD” SAMPLE OF 157 SUPERNOVAE(RIESS ET AL. 2004)
z
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0 )'(
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0
z
z
zwdzzf
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)'(1'3exp)(
SUPERNOVAE MEASURE THE LUMINOSITY DISTANCE
KdMm L log5
IN A FLAT UNIVERSE, THIS IS DEFINED AS
SUPERNOVA MEASUREMENTS ARE SENSITIVE TO w VIA f (z)
az /1
WHAT ARE THE SUPERNOVA OBSERVATIONS ACTUALLY MEASURING?
THE DECELERATION PARAMETER
0
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USING THE FRIEDMANN EQUATION THIS CAN BECAST AS
)2(2
10 mq
A SIMILAR EXPRESSION CANBE FOUND FOR MORE GENERAL DARK ENERGY
2
00
)1(2
11~ zqz
HdL
THE LUMINOSITY DISTANCE CAN BE RELATED TO THE DECELERATION PARAMETER BY THE FOLLOWING RELATION
RESULTS FROM PERLMUTTER ET AL.1998
RESULTS ARE ASSUMING A CONSTANTw
MUCH MORE ABOUT THIS IN THE NEXT TALK!
OTHER OBSERVATIONAL PROBES
WMAP PROJECT, PUBLISHED RESULTS ON THECOSMIC MICROWAVE BACKGROUND FEBRUARY 2003
THE CMB SPECTRUM DEPENDS ON THE DARK ENERGY EOSIN TWO WAYS:
A) THERE IS A GEOMETRIC SHIFT OF THE SPECTRUM. THE ANGULAR SCALE OF THE CMB IS PROPORTIONAL TO THEINTEGRAL
reczzw
MMM dzzzF0
2/1))(1(332/1 )1)(1()1(
w = -0.5
w = -1
w = -2
w = -5
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B) THE LATE INTEGRATED SACHS WOLFE EFFECT
w = -0.5
w = -1
w = -2
w = -5
SDSS SURVEY
SDSS POWER SPECTRUM
IN GENERAL, THE DENSITY PERTURBATIONS IN CDM GROW ACCORDINGTO
0)(2
3))(1)((1
2
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aawa mm
IN THE LINEAR REGIME (IN A FLAT UNIVERSE).
SINCE THE LARGE SCALE STRUCTURE SURVEYS MEASURE THEMATTER FLUCTUATIONS THEY ARE SENSITIVE TO DARK ENERGY
NEW TYPE Ia SUPERNOVA DATA KNOP ET AL. ASTRO-PH/0309368 (SCP)
09.005.1 15.020.0
w
FOR A CONSTANT EQUATION OF STATE THE COMBINED CONSTRAINTSARE QUITE STRONG
SH & E MORTSELL, ASTRO-PH/0407259 (JCAP)
C.L. 95% @ 79.034.1 w
INCLUDES THE RIESS ET AL. 2004 DATA
CMB+LSS+SNI-A
CMB+LSS
WHAT ABOUT TIME EVOLUTION OF w?
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 THEREFORESOME EFFECTIVE PARAMETRIZATION SHOULD BE USED
MANY MODELS PREDICT A STRONG EVOLUTION OF wWITH TIME (QUINTESSENCE, EXTRA DIMENSIONS, ETC)
FOR THE SUPERNOVA DATA THE TYPICAL CHOICE IS
...10 zwww
HOWEVER, THIS IS BAD BECAUSE IT DIVERGES AT HIGH zSO THAT COMBINATION WITH CMB IS IMPOSSIBLE
ALAM ET AL. (ASTRO-PH/0311364) USE THE PARAMETRIZATION
))1()1(( 22100 zAzAA
THEY FIND THAT THERE IS AN INDICATION OF A TIME EVOLUTIONAT ROUGHLY 2.7
NOTE THAT FOR A FLAT UNIVERSE THERE ARE ONLY TWO FREE PARAMETERS SINCE
mAAA 1210
MANY DIFFERENT GROUPS HAVE STUDIED THIS CLAIM,ADDING OTHER DATA.
A DIFFERENT PARAMETRIZATION IS NECESSARY SINCETHE SERIES EXPANSION BREAKS DOWN AT HIGH z
SH & MORTSELL (JCAP 0409, 001 – ASTRO-PH/0407259) USED
qs
q
qs
q
awaw
aawwaw
0110)(
THIS ASSUMES A SMOOTH CROSSOVER BETWEEN TWOASYMPTOTIC LIMITS OF w
aw
aww
for
0for
0
1
(SEE UPADHYE, ISHAK & STEINHARDT (ASTRO-PH/0411803) FOR ADISCUSSION OF VARIOUS RECENT PARAMETRIZATIONS)
THE TRANSITION OCCURS ROUGHLY AT a = as
THE WIDTH IS DETERMINED BY q
q = 0.5, 1, 2, 5, 10
COMBINING ALL AVAILABLE DATA THERE DOES AT FIRST SIGHTSEEM TO BE SOME TENTATIVE INDICATION OF A TIME EVOLUTIONWITH A STEEP GRADIENT TOWARDS MORE NEGATIVE VALUES OFw AT PRESENT
THE BEST FIT MODEL HAS
41.350.08.14.0 01 qaww s
THIS FINDING IS IN ACCORDANCE WITH ALAM ET AL. (AND SEVERALOTHER STUDIES)
WHAT IS THE STATISTICAL SIGNIFICANCE OF THE RESULT?
1626.91623.1ALL
177.1173.8A-SNI
1447.31446.7LSSCMB
CDMVARYING
HOWEVER, SINCE THERE ARE FOUR MORE PARAMETERS, THEEVOLVING MODELS ACTUALLY HAVE A SMALLER GOODNESS OF FIT.
THERE IS NO EVIDENCE FOR ANY EVOLUTION OF THE EQUATIONOF STATE!!!
WHAT IS IN STORE FOR THE FUTURE?
LARGE SCALE STRUCTURE SURVEYS2dF (completed) 250.000 galaxies SDSS (ongoing) 1.000.000 galaxies
COSMOLOGICAL SUPERNOVA SURVEYSESSENCE, DARK ENERGY CAMERA, SNAP
WEAK LENSING SURVEYS
BETTER CMBR TEMPERATURE MEASUREMENTS
Satellites Balloons InterferometersWMAP (ongoing) Boomerang (ongoing) CBI (ongoing)Planck (2007) TopHat (ongoing) DASI (ongoing)
CMBR POLARIZATION MEASUREMENTS
Satellites Balloons GroundWMAP (ongoing) Boomerang (2002-3) Polatron (ongoing)Planck (2007) DASI
SNAP SATELLITE
http://snap.lbl.gov
THE SUPERNOVAACCELERATIONPROBE (SNAP) WILLOBSERVE ROUGHLY2000 TYPEI-a SN OUTTO REDSHIFTS OFORDER 1.5, STARTINGFROM ~ 2012?
SNAP ALONE WILL BE ABLE TO MEASURE w AS WELL AS THEPRESENT BOUND WITHOUT ANY ADDITIONAL DATA
Distortion of background images by foreground matter
Unlensed Lensed
WEAK LENSING – A POWERFUL PROBE FOR THE FUTURE
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FROM A WEAK LENSING SURVEY THE ANGULAR POWER SPECTRUMCAN BE CONSTRUCTED, JUST LIKE IN THE CASE OF CMB
),/( rP MATTER POWER SPECTRUM (NON-LINEAR)
WEIGHT FUNCTION DESCRIBING LENSINGPROBABILITY
(SEE FOR INSTANCE JAIN & SELJAK ’96, ABAZAJIAN & DODELSON ’03,SIMPSON & BRIDLE ’04)
Non-linear physics
Wide survey
WEAK LENSING POWER SPECTRUM
SNe
PROJECTED ERRORS FOR A WEAK LENSING SURVEY
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 TOCALCULATE AND INCLUDE.
HOWEVER, IN MANY CASES IT IS IMPOSSIBLE!
IF ”DARK ENERGY” IS DUE TO A MODIFICATION OF GRAVITY THEN IT ISMEANINGLESS TO TALK ABOUT FLUCTUATIONS IN THE DARK ENERGY
IF DARK ENERGY IS A FLUID IT SHOULD BE CHARACTERIZED BY BOTHTHE EOS AND THE SPEED OF SOUND
P
w
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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 SETOF PERTURBATION EQUATIONS
CHANGING THE SPEED OF SOUND OF DARK ENERGY AFFECTSPERTURBATION GROWTH, BUT ONLY WHEN DARK ENERGY ISA SIGNIFICANT PART OF THE ENERGY DENSITY
w = -0.2 w = -0.8
c2 = 0
c2 = 1c2 = 1
c2 = 0
PRESENT CONSTRAINTS ON THE SPEED OF SOUND OF THEDARK ENERGY FROM ALL AVAILABLE DATA
STH, ASTRO-PH/0504017(see also Corasaniti, Giannantonio & Melchiorri, astro-ph/0504115)
NOTICE THAT THERE IS A SLIGHT BIAS OF THE ALLOWED REGIONFOR w, DEPENDING ON WHETHER DARK ENERGY PERTURBATIONSARE ASSUMED.
ALSO, THE GLOBAL BEST FIT CHANGES SLIGHTLY.
2 d.o.f. 2/d.o.f
NO PERTURBATIONS 1626.1 1515 1.073FLUID 1625.5 1516 1.073
HOWEVER, AT PRESENT THERE IS NO EVIDENCE FOR OR AGAINSTDARK ENERGY PERTURBATIONS.
FUTURE CONSTRAINTS ON THE SPEED OF SOUND OF DARK ENERGY(STH, ASTRO-PH/0504017)
DATA c2)
CMB 6.26
CMB+LSS1 (SDSS) 5.67
CMB+LSS2 5.66
CMB+LSS2+WL 3.03
THERE ARE STRONG BOUNDS ON THE DARK ENERGY EQUATIONOF STATE, PROVIDED THAT w IS CONSTANT.THE PRESENT BOUND IS (JCAP 0409, 001)
FAVOURING A COSMOLOGICAL CONSTANT
CONCLUSIONS
THERE IS AT PRESENT NO EVIDENCE FOR ANY EVOLUTION OF THEDARK ENERGY EQUATION OF STATE, CONTRARY TO SOME CLAIMS
FUTURE DATA WILL ALLOW FOR AT LEAST A FACTOR FEW IMPROVEMENT IN THE DETERMINATION OF w, BUT ARE NOTLIKELY TO MEASURE THE FLUID PROPERTIES OF DARK ENERGY
C.L. 95% @ 79.034.1 w
THERE IS NO INDICATION OF PERTURBATIONS IN THE DARK ENERGY
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