Constraining the Dark Universe

5 Pages·0.19 MB·

by  Rachel Bean

1
Constraining the Dark Universe
Rachel Beana, Steen H. Hansenb, Alessandro Melchiorrib
aTheoretical Physics, The Blackett Laboratory,Imperial College, Prince Consort Road, London, U.K.
bNAPL, University of Oxford, Keble road, OX1 3RH, Oxford, UK
We combine complementary datasets to constrain dark energy. Using standard Big Bang Nucleosynthesis and the
observed abundances of primordial nuclides to put constraints on ΩQ at temperatures near T ∼ 1MeV, we find the
strong constraint ΩQ(MeV)<0.045 at 2σ c.l.. Under the assumption of flatness, using results from Cosmic Microwave
Background(CMB)anisotropymeasurements,highredshiftsupernovae(SN-Ia)observationsanddatafromlocalcluster
2 abundanceswe put a new constraint on the equation of state parameter wQ <−0.85 at 68% c.l..
0
0
2 Introduction. The discovery that the universe’s Ia) to put constraints on the dark energy equation

n evolution may be dominated by an effective cosmo- of state parameterized by a redshift independent
a logical constant [1], is one of the most remarkable quintessence-field pressure-to-density ratio w . We
Q
J
cosmologicalfindingsofrecentyears. Anexceptional also made use of the Hubble Space Telescope (HST)
0 opportunity is now opening up to decipher the na- constraint on the Hubble parameter h=0.72±0.08
1
tureofdarkmatter[2],totesttheveracityoftheories [19].

2 andreconstructthedarkmattersprofileusingawide Wewillbrieflyreviewtheresultsobtainedinthose
v variety of observations over a broad redshift range. paper in the next sections.
7 One candidate that could possibly explainthe ob-
2 Early-Universe Constraints from BBN. Inthe last
servationsisadynamicalscalar“quintessence”field.
1 few years important experimental progress has been
One of the strong aspects of quintessence theories
1 made in the measurement of light element primor-
0 is that they go some way explaining the fine-tuning
dial abundances. For the 4He mass fraction, Y ,
2 problem, why the energy density producing the ac- He
0 celerationis ∼10−120M4. A vastrangeof“tracker” two marginally compatible measurements have been
/ pl obtained from regression against zero metallicity in
h (see for example [3,11]) and “scaling” (for example
blue compact galaxies. A low value Y = 0.234±
p [12]-[15]) quintessence models exist which approach He
- attractor solutions, giving the required energy den- 0.003 [5] and a high one YHe = 0.244± 0.002 [6]
o give realistic bounds. We use the high value in our
r sity, independent of initial conditions. The common
t characteristic of quintessence models is that their analysis;if one instead consideredthe low value, the
s
bounds obtained would be even stronger.
a equationsofstate,w =p/ρ,varywithtimewhilsta
Q
: Observations in different quasar absorption line
v cosmological constant remains fixed at wQ=Λ = −1.
systems give a relative abundance of deuterium,
i Observationally distinguishing a time variation in
X which is critical in fixing the baryon fraction, of
the equation of state or finding w different from
r Q D/H =(3.0±0.4)·10−5 [7].
a −1 will therefore be a success for the quintessential
In the standard BBN scenario, the primordial
scenario.
abundances are a function of the baryon density
We will here discuss observational constraints on
η ∼ Ω h2 only. In order to put constraints on the
general quintessence models. b
energy density of a primordial field a T ∼ MeV, we
In [23] we used standard big bang nucleosynthe-
modifiedthestandardBBNcode [4]byincludingthe
sis and the observed abundances of primordial nu-
quintessence energy component Ω . We then per-
clides to put constraints on the amplitude of the en- Q
formed a likelihood analysis in the parameter space
ergy density, Ω , at temperatures near T ∼ 1MeV.
Q (Ω h2,ΩBBN) using the observed abundances Y
The inclusion of a scaling field increases the expan- b Q He
and D/H. In Fig. 1 we plot the 1,2 and 3σ likeli-
sion rate of the universe, and changes the ratio of
hood contours in the (Ω h2,ΩBBN) plane.
neutrons to protons at freeze-outandhence the pre- b Q
Our main result is that the experimental data for
dicted abundances of light elements.
4He and D does not favour the presence of a dark
In [24] we have then combined the latest observa-
energy component, providing the strong constraint
tions of the Cosmic Microwave Background (CMB)
Ω (MeV)<0.045at2σ (corresponding to λ>9 for
anisotropies provided by the Boomerang [16], DASI Q
the exponential potential scenario), strengthening
[17] and Maxima [18] experiments and the informa-
significantlythepreviouslimitof [8,15]Ω (MeV)<
tion from Large Scale Structure (LSS) with the lu- Q
0.2. The reason for the difference is due to the
minosity distance of high redshift supernovae (SN-
improvement in the measurements of the observed
2
degenerate in the interplay between w and Ω .
Q Q
Furthermore, it does not add any new features be-
yond those produced by the presence of a cosmolog-
ical constant [25], and it is not particularly sensitive
to further time dependencies of w .
Q
CMB Degeneracy

6000
Ω=0.30 Ω=0.050 h=0.65 w= -1.0
m b Q
5000 Ω=0.44 Ω=0.073 h=0.54 w= -0.6
m b Q
2K Ωk=0
µ 4000
π
2
C/l
Figure 1. 1,2 and 3σ likelihood contours in the 1) 3000
(Ωbh2,ΩQ(1MeV)) parameter space derived from ll(+
4He and D abundances. 2000
1000
abundances,especiallyforthedeuterium,whichnow
0
corresponds to approximately∆N <0.2−0.3 ad- 10 100 1000
eff
ditional effective neutrinos (see, e.g. [9]), whereas Multipole l
Ref. [8,15] used the conservative value ∆N < 1.5.
eff
One could worry about the effect of any underesti-
matedsystematicerrors,andwethereforemultiplied
the error-bars of the observed abundances by a fac- Figure2. CMBpowerspectraandtheangulardiam-
tor of 2. Even taking this into account, there is still eter distance degeneracy. The models are computed
a strong constraint ΩQ(MeV) < 0.09 (λ > 6.5) at assuming flatness, Ωk = 1−ΩM −ΩQ = 0). The
2σ. Integrated Sachs Wolfe effect on large angular scale
Constraints on the Dark energy equation of state. slightly breaks the degeneracy. The degeneracy can
be brokenwith a strong prior on h, in this paper we
Theimportanceofcombiningdifferentdatasetsin
use the results from the HST.
order to obtain reliable constraints on w has been
Q
stressed by many authors (see e.g. [20], [21],[22]),
since eachdatasetsuffersfromdegeneraciesbetween
the various cosmological parameters and w . Even Secondly, the time-varying Newtonian potential
Q
if one restricts consideration to flat universes and after decoupling will produce anisotropies at large
to a value of w constant in time then the SN-Ia angular scales through the Integrated Sachs-Wolfe
Q
luminosity distance and position of the first CMB (ISW) effect. The curve in the CMB angular spec-
peakarehighlydegenerateinw andΩ ,theenergy trumonlargeangularscalesdependsnotonlyonthe
Q Q
density in quintessence. valueofwQbutalsoitsvariationwithredshift. How-
The effects of varying w on the angular power ever, this effect will be difficult to disentangle from
Q
spectrumoftheCMBanisotropiescanbereducedto thesameeffectgeneratedbyacosmologicalconstant,
just two . Firstly, since the inclusion of quintessence especially in view of the affect of cosmic variance
changes the overall content of matter and energy, and/orgravitywavesonthe largescale anisotropies.
theangulardiameterdistanceoftheacoustichorizon In order to emphasize the importance of degen-
size at recombination will be altered. In flat models eraciesbetweenalltheseparameterswhile analyzing
(i.e. where the energy density in matter is equal the CMB data, we plot in Figure 2 some degener-
to Ω = 1−Ω ), this creates a shift in the peaks ate spectra,obtainedkeepingthe physicaldensity in
M Q
positions of the angular spectrum as matter ΩMh2, the physical density in baryons Ωbh2
andRfixed. Aswecanseefromtheplot,modelsde-
R = (1−Ω )y, (1) generate in w can easily be constructed. However
Q Q
q
the combination of CMB data with other different
zdec
y = [(1−Ω )(1+z)3 datasets can break the mentioned degeneracies.
Z Q
0
+Ω (1+z)3(1+wQ)]−1/2dz. Type Ia supernovae, in particular, can be ex-
Q
tremely useful in this. Evidence that the universe’s
It is important to note that the effect is completely expansionratewasacceleratingwasfirstprovidedby
3
-0.5 Table 1
Constraints on w and Ω = 1−Ω using differ-
Q M Q
ent priors and datasets. We always assume flatness
B
-0.6 M and t > 10 Gyr. The 1σ limits are found from
C 0
S the 16% and 84% integrals of the marginalized like-
N
-Ia lihood. The HST prior is h = 0.72 ± 0.08 while
-0.7 for the BBN prior we use the conservative bound
Q
W Ω h2 =0.020±0.005.
b
-0.8
CMB+HST w <−0.62
Q
-0.9 0.15<ΩM <0.45
CMB+HST+BBN −0.95<w <−0.62
Q
0.15<Ω <0.42
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 M
Ω
M CMB+HST+SN-Ia −0.94<wQ <−0.74
0.16<Ω <0.34
M
CMB+HST+SN-Ia+LSS w <−0.85
Q
Figure 3. Contours of constant R (CMB) and 0.28<Ω <0.43
M
SN −Ia luminosity distance in the w -Ω plane.
Q M
The degeneracy between the two distance measures
can be broken by combining the two sets of com-
plementary information. The luminosity distance is
chosentobe equalto dl atz =1forafiducialmodel ter marginalizing over all remaining nuisance pa-
withΩ =0.7,Ω =0.3,h=0.65. (Wenotethatas rameters. The analysis is restricted to flat uni-
Λ M
ΩQ =1−ΩM goes to zero the dependence of R and verses. One can see that wQ is poorly constrained
d upon w also become zero, as there is no dark from CMB data alone, even when the strong HST
L Q
energy present.) Figure taken from [24] prior on the Hubble parameter, h = 0.72 ± 0.08,
is assumed. Adding a Big Bang Nucleosynthesis
prior, Ω h2 = 0.020 ± 0.005, has small effect on
b
the CMB+HST result. Adding SN-Ia breaks the
two groups, the SCP and High-Z Search Team([1])
CMB Ω −w degeneracy and improves the upper
Q Q
usingtypeIasupernovae(SN-Ia)toprobethenearby
limit on w , with w < −0.74. Finally, including
Q Q
expansion dynamics. SN-Ia seem to be good stan-
information from local cluster abundances through
dard candles, as they exhibit a strong phenomeno- σ = (0.55±0.1)Ω−0.5, where σ is the rms mass
logicalcorrelationbetweenthedeclinerateandpeak flu8ctuation in spherMes of 8h−1 M8pc, further breaks
magnitude of the luminosity. The observed appar-
the quintessential-degeneracy,giving w <−0.85 at
Q
ent bolometric luminosity is related to the lumi-
1-σ. Also reportedin Table I, are the constraints on
nosity distance, measured in Mpc, by m = M +
B Ω . As we can see, the combined data suggests the
M
5logd (z) + 25, where M is the absolute bolomet-
L presence of dark energy with high significance, even
ric magnitude. The luminosity distance is sensi-
in the case CMB+HST. It is interesting to project
tive to the cosmological evolution through an inte-
ourlikelihoodintheΩ −w plane. Proceedingasin
Q Q
gral dependence on the Hubble factor d = (1 +
l [27],we attribute alikelihoodto apointinthe (Ω ,
z ′ ′ M
z) (dz /H(z ,Ω ,w ), and can therefore be used
0 Q q wQ) plane by finding the remaining parametersthat
toRconstrain the scalar equation of state. As can be
maximize it. We then define our 68%, 95%and 99%
seen in Figure 3 there is an inherent degeneracy in
contourstobewherethelikelihoodfallsto0.32,0.05
theluminositydistanceintheΩ /w plane;onecan
M Q and0.01ofits peakvalue,aswouldbe thecasefora
seethatlittlecanbesaidabouttheequationofstate
two dimensional multivariate Gaussian. In Figure 4
from luminosity distance data alone. However, the
weplotlikelihoodcontoursinthe(Ω ,w )planefor
M Q
degeneraciesofCMBandSN1adatacomplementone
the joint analyses of CMB+SN-Ia+HST+LSS data
another so that together they offer a more powerful
together with the contours from the SN-Ia dataset
approachfor constraining w .
Q only. As we can see, the combination of the data
breaks the luminosity distance degeneracy.
Table I shows the 1-σ constraints on w for dif-
Q
ferent combinations of priors, obtained in [24] af- Conclusions.
4
and datasets), our analysis is compatible with other
-0.6 recent analysis on w ([30]). Our final result is per-
Q
fectly in agreement with the w = −1 cosmological
Q
constant case and gives no support to a quintessen-
-0.7
tial field scenario with w > −1. A frustrated net-
Q
wQ-0.8 Supernovae 95% c.l.99% c.l. wfiaeonlrdukmaorbfeedreoxmocfaluqindueiwndtaelalstsseohnritgaihaplsumigreonldiyfiecelsaxnpacoreen.ehnIitgnihaallydsdcdaiitlsiifonang-
vored, e.g. power law potentials with p ≥ 1 and the
66
-0.9 88%% cc..ll.. CMB+SN-Ia+LSS+HST oscIitllwatiollrybeptohteendtiuatly, toofnhaigmheerarfeedws.hift datasets, for
examplefromclusteringobservations[29]topointto
-1.0 a variation in w that might place quintessence in a
0.2 0.4 0.6 0.8 1.0
more favorable light.
Ω The result obtained here, however, could be
M
plagued by some of the theoretical assumptions
we made. The CMB and LSS constraints can be
weakened by the inclusion of additional relativis-
tic degrees of freedom [33], by a background of
gravity waves, of isocurvature perturbations or by
Figure 4. The likelihood contours in the (Ω , w )
M Q adding features in the primordialperturbationspec-
plane, with the remaining parameters taking their
tra. These modifications are not expected in the
best-fitting values for the joint CMB+SN-Ia+LSS
most basic and simplified inflationary scenario but
analysis described in the text. The contours corre-
they are still compatible with the present data. The
spondto 0.32,0.05and0.01ofthe peak value of the
SN-Ia result has been obtained under the assump-
likelihood, which are the 68%, 95% and 99% confi- tion of a constant-with-time w > −1. Inclusion of
Q
dence levels respectively. theregionwithw <−1couldaffectourconstraints
Q
([32]). In[24]wehaveshownthatingeneralw isa
eff
rathergoodapproximationfordynamicalquintessen-
tialmodelssincethe luminositydistancedepends on
We haveprovidednew constraintsonthe darken- wQ through a multiple integral that smears its red-
ergy by combining different cosmological data. We shift dependence, and our results are therefore valid
have examined BBN abundances in a cosmological forawideclassofquintessentialmodels. This‘numb-
scenariowith a scaling field. We have quantitatively ing’ofsensitivitytowQ,firstnoticedby[31],implies
discussed how large values of the fractional density thatmaybeaneffective equationofstateis themost
inthescalingfieldΩ atT ∼1MeVcanbeinagree- tangible parameter able to be extracted from super-
Q
mentwiththeobservedvaluesof4HeandD,assum- novae. However with the promise of large data sets
ingstandardBigBangNucleosynthesis. The2σlimit fromPlanckandSNAPsatellites,opportunitiesmay
Ω (1MeV) < 0.045 severely constrains a wide class yet still be open to reconstructa time varying equa-
Q
ofquintessentialscenarios,likethosebasedonanex- tion of state [22].
ponentialpotential. For example,for the pure expo-
Acknowledgements It is a pleasure to thank Ruth
nential potential the total energy today is restricted
Durrer, Pedro Ferreira, Massimo Hansen and Matts
to Ω = 3Ω (1MeV)≤0.04. This result put strong
Q 4 Q Roosforcommentsandsuggestions. RBandAMare
constraints on the presence of quintessence during
supportedby PPARC.SHH is supportedby a Marie
recombination.
CurieFellowshipofthe EuropeanCommunityunder
We have then provided constraints on the equa-
thecontractHPMFCT-2000-00607. Weacknowledge
tion of state parameter w . The new CMB results
Q the use of CMBFAST [26].
provided by Boomerang and DASI improve the con-
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