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

)(2

1

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1

2

2

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V

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

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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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aaq

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

32

aa

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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ww

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w

ccH s

s

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