OBSERVING DARK ENERGY

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 lt -1? VIOLATES r 3P gt 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 lt -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
(No Transcript)
18
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
19
B) THE LATE INTEGRATED SACHS WOLFE EFFECT
w -0.5
w -1
w -2
w -5
20
SDSS SURVEY
21
(No Transcript)
22
SDSS POWER SPECTRUM
23
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
24
FOR A CONSTANT EQUATION OF STATE THE COMBINED
CONSTRAINTS ARE QUITE STRONG
NEW TYPE Ia SUPERNOVA DATA KNOP ET AL.
ASTRO-PH/0309368 (SCP)
25
SH E MORTSELL, ASTRO-PH/0407259 (JCAP)
CMBLSS
CMBLSSSNI-A
INCLUDES THE RIESS ET AL. 2004 DATA
26
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? LUMI
NOSITY 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
27
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
28
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)
29
THE TRANSITION OCCURS ROUGHLY AT a as
THE WIDTH IS DETERMINED BY q
q 0.5, 1, 2, 5, 10
30
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
31
THE BEST FIT MODEL HAS
THIS FINDING IS IN ACCORDANCE WITH ALAM ET AL.
(AND SEVERAL OTHER STUDIES)
32
WHAT IS THE STATISTICAL SIGNIFICANCE OF THE
RESULT?
c2
LCDM
VARYING
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!!!
33
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
34
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
35
SNAP ALONE WILL BE ABLE TO MEASURE w AS WELL AS
THE PRESENT BOUND WITHOUT ANY ADDITIONAL DATA
36
WEAK LENSING A POWERFUL PROBE FOR THE FUTURE
Distortion of background images by foreground
matter

Unlensed Lensed
37
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)
38
WEAK LENSING POWER SPECTRUM
Wide survey
Non-linear physics
39
PROJECTED ERRORS FOR A WEAK LENSING SURVEY
SNe
40
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
41
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
42
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
43
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)
44
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.
45
FUTURE CONSTRAINTS ON THE SPEED OF SOUND OF DARK
ENERGY (STH, ASTRO-PH/0504017)
46
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