f. finelli et al- observing dark energy through cmb anisotropies

8/3/2019 F. Finelli et al- Observing Dark Energy through CMB anisotropies

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Mem. S.A.It. Suppl. Vol. 5, 339c SAIt 2004

Memorie della

Supplementi

Observing Dark Energy through CMBanisotropies

F. Finelli, C. Burigana, R C. Butler, F. Cuttaia, E. Franceschi, A. Gruppuso,

M. Malaspina, N. Mandolesi, G. Morgante, G. Morigi, L. Popa, M. Sandri, L. Terenzi,

L. Valenziano and F. Villa

IASF, Istituto di Astrofisica Spaziale e Fisica Cosmica, Sezione di Bologna, CNR-INAF,

via Gobetti, 101 I-40129 Bologna Italy

e-mail: [email protected]

Abstract. It is still unclear if the recent acceleration of the universe is fueled by a cosmo-logical constant (whose energy density is constant and acts as a simple parameter in the

Einstein equations) or by a new dynamical component (which fluctuates in time and space).

While both of these possibilities are not completely satisfactory theoretically, a cosmologi-

cal constant plus cold dark matter (CDM model) provide the best fit to CMB anisotropies

data. Here we present the signatures of dark energy perturbations on the CMB anisotropy

pattern, as a possibility to discriminate between a new dynamical component (uncoupled to

the rest of matter) and a cosmological constant or to test if the dark sector can be unified.

Key words. Cosmology - dark energy - CMB anisotropies

1. Introduction

Evidence for a recent acceleration of the uni-verse has been independently found in theSNIa data by two groups (Perlmutter et al.1996; Riess et al. 1996). Such possibility wasalso favored by other observational data, lead-ing to a cosmic concordance model.

A positive cosmological constant wouldbe the simplest way to model this accelera-tion, but its value is completely unexplainedon theoretical grounds. is indeed related to

the zero-point energy of quantum fluctuations:already with one of the lowest scales in par-ticle physics, the QCD scale, the magnitudeof the vacuum energy is 1041GeV2,which is much larger than the observed value

1094GeV2. Anthropic arguments have thenbeen advocated to explain such a small value(Weinberg 1989).

However, a cosmological constant doesnot exhaust all the possibilities in explainingthe recent acceleration of the universe (seeSahni & Starobinsky 2000; Peebles & Ratra2003 for reviews). A component with a suf-ficiently negative equation of state (wX pX/X 1/3) goes under the generic nameof Dark Energy (DE henceforth). If DE isnot a parameter in the Einstein equations, it

may affect cosmological observations not onlythrough its imprint in the expansion rate, butalso by its fluctuations. In this latter case,a host of cosmological observations - CMBanisotropies, LSS, ... - may result complemen-


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340 F. Finelli et al.: Observing Dark Energy through CMB anisotropies

tary and, sometimes, more important with re-spect to SNIa data, as we shall see. This obser-vational chance to reveal DE shoud be takenvery seriously, given the enormous difficulty to

directly detect DE quanta.In this contribution we give the details for

the treatment of DE perturbations and theirimprint on CMB anisotropies. These imprintsare on top of the DE background evolution,which alters the position of the peaks and pro-duce a non-negligible Integrated Sachs-Wolfe(ISW henceforth) effect. In the CDM case,this latter effect (first studied by Kofman &Starobinsky 1985) is due to the damping ofgravitational fluctuations induced by a non-vanishing and enhances the value of theobserved temperature anisotropies in the low-multipole tails up to a factor 2 with respect tothe sCDM case.

2. DE perturbations

By considering DE uncoupled to the rest ofmatter and isotropic DE pressure perturba-tions, the equations of motion for DE pertur-bations are similar to the ones for the other de-grees of freedom (CDM, baryons, photons, seeMa & Bertschinger 1995):

X = (1 + wX)

X

h

2

+3H(wXX pX

X)

X = H(1 3c2X) X+

c2X

1 + wXk2X (1)

where X X/X is the density contrast, Xis the velocity potential, H = a/a is the con-formal Hubble parameter and h is the trace ofmetric perturbations in the synchronous gauge.The isotropic pressure perturbation pX can bewritten as (Abramo et al. 2004):

pX = c2XX

+ 3H(1 + wX)XX

k2

c2X pX

X

(2)

where the last piece vanishes if pX is just afunction of X. From the above equations weunderstand how it is not sufficient to specify

wX(t) (and X at the present time) to study DEin the context of structure formation, but it isalso necessary to specify its pressure pertur-bations (and therefore the speed of sound c2

X).

The present contribution is devoted to brieflyillustrate the impact of DE perturbations on theCMB power spectrum.

3. DE models

The most popular idea is to model dark energyas a scalar field with a small effective mass(Ratra & Peebles 1988) - dubbed quintessence(Caldwell et al. 1998). The standard scenario(a canonical scalar field described by a Klein-Gordon (KG) Lagrangian for which c2X = 1 inEqs. (1,2)) is a minimal modification toCDM

because of the relative unimportance of scalarfield perturbations on scales smaller than theHubble radius. All the information containedin the scalar potential V() is encoded in wXin that case. The low- tail is however differ-ent from a CDM scenario because of the im-portance of quintessence perturbation on largescales (Abramo & Finelli 2001).

In order to investigate the impact of the DEsound speed it is necessary to study a differ-ent class of models, based on a Born-Infeld(BI) Lagrangian, in which c2X = wX (Abramo& Finelli 2003, 2001; see also DeDeo et al.2003). In Fig. 1 we show the comparison of

two different theories for scalar fields. The im-pact of the sound speed is marginal for scalarfield theories, but important at low multipoles.For the WMAP (Bennett et al. 2003) con-straints on these two theories see Abramo etal. (2004).

The simplest DE model (even if it has notbeen historically the first to be analyzed) is aperfect fluid with pressure pX = A/

X

and

speed of sound c2X = pX/ X = wX (calledGeneralized Chaplygin Gas, for brevity GCG,Kamenshchik et al. 2001). In absence of exper-imental evidence for scalar fields, this model isvery important in order to check if DE might

be described by a perfect fluid. In these GCGmodels DE is not a smooth component andtherefore its perturbations are important alsoat larger multipoles (Carturan & Finelli 2003;Amendola et al. 2003). In Fig. 2 we show the


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F. Finelli et al.: Observing Dark Energy through CMB anisotropies 341

Fig. 1. Upper panel: background quantities fortwo similar BI (dashed lines) and KG (solidlines) dark energy models as a function of red-shift. The upper curves denote r and M (=b + CDM), and the lower wX: for each curveanother one is nearly superimposed to it, sincethe two models are designed to be very similar.

The cosmological parameters are b 0 = 0.04,CDM0 = 0.26, h = 0.72 (in the radiationdominated era the sound speed for BI is zero).Lower panel: CMB TT power spectra for KGmodel (solid line), BI model (dashed line) anda fiducial CDM (dotted line), all normalizedat the amplitude of their first acoustic peak.Only for comparison we also show the (wrong)power spectrum of the BI model obtained with-out considering the scalar field perturbations(dot-dashed line). There are no appreciable dif-ferences in the power spectrum for the E-modepolarization.

difference between a GCG (perfect fluid) and ascalar field BI as a candidate for DE.

4. Unified Dark Models

The study of DE perturbations becomes de-cisive for a model in which dark energy anddark matter are described in a unified way.Different scenarios which aim at unifying thedark sector (96 % of the current total energydensity) have been recently proposed: the GCGis one among these. In these unified dark mod-els (UDM for brevity), the difficulty is not

to have a (homogeneous) cosmological modelwhich reproduce vacuum energy and dust; thereal challenge is to obtain density perturba-tions which behave according to the data (andtherefore similarly to CDM). In this sense, the

Fig. 2. A comparison of the GCG model (with = 1) and the BI model. As in Fig. 1, in theupper panel the background (BI solid, GCGdotted) and in the lower the CMB TT powerspectrum (BI dotted, GCG dashed). The differ-ent equations of state explain the peaks posi-tion, but the different shape of the plateau isdue to the different pressure in the two models(although c2X = wX in both).

comparison of the CMB and LSS predictionsof UDM based on the GCG with observa-tions has been much more selective than the

SNIa test (Carturan & Finelli 2003; Amendolaet al. 2003), as it can be seen from Fig. 3.It was found that the better agreement withWMAP data is in the region of parameterswhere the CDM and a UDM are almost iden-tical (Amendola et al. 2003).

5. Conclusions

Although the acceleration of the universe hasbeen found in samples of SNIa data, the fun-damental or effective degree of freedom re-sponsible for such acceleration may fluctu-ate in space and time, if it is not simply a

cosmological constant. In this case a detailedstudy of DE perturbations is needed in orderto fully investigate the DE imprints on CMBanisotropies and structure formation. By tak-ing this approach, we have studied and con-


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342 F. Finelli et al.: Observing Dark Energy through CMB anisotropies

Fig. 3. The importance of CMB constraintsfor GCG models. The thick lines are the SNIaconstraints and the three dashed lines are theCMB constraints from WMAP (in both cases65% , 95% , 99% CL from left to right respec-

tively). The combined constraints are the greylines (65% , 95% CL respectively): as can beseen, the SNIa constraints add little informa-tion (Amendola et al. 2003).

strained the macroscopic properties of DE.This study is important in the perspective ofbetter CMB data as those coming from P(http://astro.estec.esa.nl/ , see Burigana et al.this issue). With the same techniques the mat-ter power spectrum may be studied and com-pared with LSS data.

Acknowledgements. We would like to thank R.Abramo, L. Amendola, D. Carturan and T. Pereira

for discussions and an enjoyable collaboration.

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