A global fit study on the new agegraphic dark energy model

0.36 MB·English

by  Jing-Fei Zhang

A globalfit study onthe new agegraphic darkenergy model
Jing-Fei Zhang,1 Yun-He Li,1 and Xin Zhang 1,2,
∗ †
1Department ofPhysics, Collegeof Sciences, NortheasternUniversity, Shenyang 110004, China
2Center for High Energy Physics, Peking University, Beijing100080, China
We perform a global fit study on the new agegraphic dark energy (NADE) model in a non-flat universe
by using the MCMC method withthe full CMB power spectra data from the WMAP 7-yr observations, the
SNIadatafromUnion2.1sample,BAOdatafromSDSSDR7andWiggleZDarkEnergySurvey,andthelatest
measurementsofH fromHST.WefindthatthevalueofΩ isgreaterthan0atleastatthe3σconfidencelevels
0 k0
(CLs),whichimpliesthattheNADEmodeldistinctlyfavorsanopenuniverse. Besides,ourresultsshowthat
thevalueofthekeyparameterofNADEmodel, n = 2.673+0.053+0.127+0.199,atthe1–3σCLs,whereitsbest-fit
3 0.077 0.151 0.222
valueissignificantlysmallerthanthoseobtainedinpreviou−swo−rks. −Wefindthatthereasonleadingtosucha
1
changecomesfromthedifferentSNIasamplesused. Ourfurthertestindicatesthatthereisadistincttension
0
betweentheUnion2sampleofSNIaandotherobservations,andthetensionwillberelievedoncetheUnion2
2
sampleisreplacedbytheUnion2.1sample. So,thenewconstraintresultoftheNADEmodelobtainedinthis

n workismorereasonablethanbefore.
a
J PACSnumbers:95.36.+x,98.80.Es,98.80.-k

2
2
I. INTRODUCTION background(CMB). For the CMB information, to save time

] and power, one often uses the CMB “distance priors” (R,
O
l , z ) whose information is extracted from the temperature
Darkenergyhasbecomeoneofthemostimportantresearch A
C powe∗rspectrumofCMB basedona ΛCDM scenario. How-
areasincosmologysincethecosmicaccelerationwasdiscov-
. ever,itshouldbenotedthatusingtheCMB“distancepriors”
h eredbytheobservationsoftypeIasupernovae(SNIa)[1].The
to constrain other dark energy modelswill lead to a circular
p cosmologicalconstant, Λ, introducedbyEinsteinin 1917,is
- a natural candidate for dark energy, which fits the observa- problem, since the values of the CMB “distance priors” de-
o pend on a specific cosmological model, namely, the ΛCDM
r tional data best to date. However, the model of Λ plus cold
model.Besides,the“distancepriors”donotcapturetheinfor-
t darkmatter,knownastheΛCDMmodel,alwayssuffersfrom
s mationconcerningthegrowthofstructureprobedbythelate-
a the two well-knowntheoreticaldifficulties, namely, the fine-
[ tuningandcosmiccoincidenceproblems[2]. Thus, dynami- time ISW effect which is sensitive to the properties of dark
3 caldarkenergymodelsbecomepopular,becausetheymayal- energy.Inthepast,theNADEmodelwasconstrainedonlyby
theCMB“distancepriors”data.Inthisstudy,weshallusethe
v leviatethetheoreticalchallengesfacedbytheΛCDMmodel.
fullCMBdatafromthe7-yrWMAPobservationstoexplore
0 Forarecentreviewofdarkenergy,seeRef.[3].
theparameterspaceofthecosmologicalmodelinvolvingthe
0
Among the many dynamical dark energy models, a class
3 NADE.Suchanexplorationisbelievedtocompletethestudy
withfeatureofquantumgravity,embodyingholographicprin-
0 oftheNADEmodel.
. ciple, looks very special and attractive. Such class of mod-
2 In the previous studies, the spatial curvature, Ω , is usu-
els, usually called “holographic dark energy”, has been in- k0
1 ally neglected. So, we do not know if a flat universe is still
vestigated in detail [4] and constrained by the observational
2 favored by current data in the NADE model. Moreover, the
data[5]. Inthispaper,wefocusonthe“newagegraphicdark
1
initial condition of the NADE model [6] is only applicable
: energy”(NADE)model[6]inthisclass,whichtakesintoac-
v fora flatuniversecontainingonlydarkenergyand pressure-
counttheuncertaintyrelationofquantummechanicstogether
i less matter. In Ref. [7], a new, updated initial condition is
X with the gravitationaleffect in generalrelativity. The reason
proposed,whichisapplicableforanon-flatuniversewithvar-
thatthe NADE modelis fairly attractiveis also owingto the
r
a factthatthismodelhasthesamenumberofparameterstothe ious components. We shall apply this new initial condition
in the present work. In such an application, for employing
ΛCDM model, less than other dynamical dark energy mod-
the “CosmoMC” package, one may treat the parameter n as
els. The NADE model has been proven to fit the data well.
aderivedparameterandusetheNewton’siterationalgorithm
However, it should be noticed that the global fit analysis on
to determine its value. In addition, in a global fit analysis,
theNADEmodelhasneverbeendone.
thecosmologicalperturbationsofdarkenergyshouldalsobe
The global fit analysis is very important for the study
considered. Thanks to the quintessence-like property of the
of a cosmological model. To determine the parameters of
NADE,thereisnow = 1-crossingbehaviorandsothecor-
dark energy models, one often has them constrained by us- −
responding gravity instability is absent. In the holographic
ing some important observational data sets, such as SNIa,
darkenergymodel,thew = 1-crossinghappens,soonehas
baryon acoustic oscillation (BAO) and cosmic microwave −
toemploytheparameterizedpost-Friedmann(PPF)approach
totreatthegravityinstabilityoftheperturbationsina global
fit analysis; for details see Ref. [8]. For the NADE model,
however,wehavenoneedtoemploythePPFapproach.
∗Correspondingauthor
Electronicaddress:[email protected] Our paper is organized as follows. In Sec. II, we derive
†
2
the backgroundand perturbation evolution equations for the Forsolvingthedifferentialequation(6),weadopttheinitial
NADEmodelinanon-flatuniverse. InSec.III,weintroduce condition,Ω (z ) = n2(1+zini)−2 1+ √F(z ) 2 atz = 2000
the fit method and the observational data, and then give the de ini 4 ini ini
withF(z)= Ωr0(1+z) ,givenin(cid:16)Ref.[7],wh(cid:17)ichhelpsreduce
global fit results. Concluding remarks are given in Sec. IV. Ωm0+Ωr0(1+z)
In this work, we assume today’s scale factor a = 1, and so onefreeparameterfortheNADEmodel.Thisinitialcondition
0
the redshift z satisfies z = a 1 1; the subscript“0” always is an updated version of the original one, Ωde(zini) = n2(1+
−
− z ) 2/4atz = 2000,giveninRef.[9]. Theonlydifference
indicatesthepresentvalueofthecorrespondingquantity,and ini − ini
theunitswithc=~=1areused. betweenthemisthatthenewoneisvalidwhentheradiation
is considered as a non-ignorable component. Note that the
initialconditionisalsoapplicableinanon-flatuniverse,since
thespatialcurvatureΩ ismuchsmallerthanΩ orΩ atz=
II. BRIEFDESCRIPTIONOFTHENADEMODEL k m r
2000.Formoredetailsaboutthederivationandapplicationof
thenewinitialcondition,seeRef.[7].
TheNADEmodelisconstructedinlightoftheKa´rolyha´zy
Inourwork,forsimplicity,wefixΩ =2.469 10 5h 2(1+
relationandcorrespondingenergyfluctuationsofspace-time. r0 × − −
0.2271N ) according to the WMAP 7-yr observations[10],
TheenergydensityofNADE,ρ ,hastheform[6] eff
de whereN =3.04isthestandardvalueoftheeffectivenumber
eff
ofneutrinospeciesandhistheHubbleconstantH inunitsof
3n2M2 0
ρ = Pl, (1) 100km/s/Mpc.
de η2 It should be noted that the parameters n, Ω , Ω and
dm0 b0
Ω are not independent. One of them can be derived from
where nisanumericalparameter, M isthereducedPlanck k0
Pl the others. For example, we can treat the parameter n as
mass,andηistheconformalageoftheuniverse,
the derivedparameter. In thiscase, oncethe valuesof Ω ,
dm0
t dt˜ a da˜ Ωb0 and Ωk0 are given, one can impose an initial value of n
η = , (2) and then obtain the true value of n by using the Newton it-
≡Z a Z Ha˜2
0 0 eration algorithm, n = n f(n )/f (n ), where f(n ) =
k+1 k k ′ k k
−
1 Ω Ω Ω Ω Ω (0) withΩ (0) thekth
where a is the scale factor and H a˙/a is the Hubble pa- − dm0− b0− r0− k0− de |nk de |nk
≡ ordernumericalsolution(atz=0)ofEq.(6)withthenewini-
rameter. Hereadotdenotesthederivativewithrespecttothe
tialcondition,and f (n )isthenumericalderivativeof f(n)at
cosmictimet. ′ k
thepointn=n . Ofcourse,onecanalsotreatΩ orΩ or
The background evolution of a non-flat universe is de- k dm0 b0
Ω asaderivedparameterandgetitsvaluebyusingasimilar
scribedbytheFriedmannequation, k0
method.
For our global fit analysis, it is convenient to modify the
Ω =1, (3)
i
“CosmoMC” package [11] if n is set as a derived parame-
X
ter. Thus, wewilluse theNewtonmethodmentionedabove,
where Ω is defined as the ratio of the energy density ρ to
i i which is provedto be convergent,to get the true value of n.
the critical energydensity ρ 3M2 H2 with i = de, dm, b,
c ≡ Pl Wechoosetheinitialvaluen =2.7andsetaterminationcon-
r and k which denotes the dark energy, dark matter, baryon, 0
ditionfortheiteration,suchas n n ǫ withǫ asmall
radiation and spatial curvature, respectively. Note that here | k+1− k| ≤
quantity. Once Eq. (6) is solved, the Hubble expansion rate
ρ 3M2k/a2.
k ≡− Pl canbeobtainedby
Theenergyconservationequationsforthevariouscompo-
nentstaketheform Ω (1+z)3+Ω (1+z)4+Ω (1+z)2 1/2
H(z)= H m0 r0 k0 .
ρ˙i+3H(1+wi)ρi =0, (4) 0" 1−Ωde(z) #
(7)
where w is the equation-of-state parameter (EOS) of a spe- With the backgroundevolution of the NADE model com-
i
cificcomponentdenotedbysubscripti,suchasw =w =0, pleted, we now consider how to handle the perturbation of
dm b
w =1/3andw = 1/3.FortheEOSofNADE,onecanob- NADE. Since the EOS of NADE is always greater than 1,
tarin k − wecaneasilyhandleitsperturbation.WetakeNADEasap−er-
fectfluidwiththeEOSgivenbyEq.(5). Inthesynchronous
2(1+z) gauge,theconservationofenergy-momentumtensorTµ =0
w = 1+ Ω , (5) ν;µ
de de
− 3n givestheperturbationequationsofdensitycontrastandveloc-
p
itydivergencefortheNADEintheFourierspace,
from Eqs. (1), (2) and (4). Furthermore, using Eqs. (1)–(4),
eonnteiaclaenqaulastoioena,silygettheequationofmotionofΩde,adiffer- δ′ = −(1+wde)(θ+ h2′)−3aH(c2s−wde)δ, (8)
c2
dΩdzde = −1Ω+dze (1−Ωde)"3+G(z)− 2(1n+z) Ωde#, (6) θ′ = −aH(1−3c2s)θ+ 1+swdek2δ−k2σ. (9)
p
Here d/dη, H and w are given by Eqs. (7) and
de
whereG(z)= Ωm0(1Ω+rz0)(+1Ω+zr0)2(1−+Ωzk)02+Ωk0 withΩm0 =Ωdm0+Ωb0. (5). O′th≡er notation is consistent with the work of Ma and
3
Bertschinger[12]. For the gauge ready formalism about the
TABLEI:Globalfitresultsofthenewagegraphicdarkenergymodel.
perturbationtheory,seeRef.[13]. FortheNADE,weassume
theshearperturbationσ=0.Inourcalculations,theadiabatic
initialconditionswillbetaken. Class Parameter Bestfitwitherrors
Primary Ω h2 0.113+0.006+0.011+0.015
Finally,wefeelthatitmaybenecessarytomakesomead- dm0 0.005 0.009 0.014
100Ω h2 2.262−+0.064−+0.114−+0.158
ditionalcommentson thetreatmentofdarkenergyperturba- b0 0.045 0.103 0.156
Ω 0.020−+0.006−+0.010−+0.016
tions in the NADE model. Actually, it is fairly difficult to k0 0.005 0.012 0.016
τ 0.085−+0.015−+0.032−+0.049
calculatethecosmologicalperturbationsofdarkenergyinthe 0.011 0.023 0.036
Θ 1.040+−0.002+−0.005+−0.008
holographic-typedark energymodels, because there is some n 0.970+−00..001032+−00..002055+−00..003067
non-local effect that makes the perturbation mechanism ex- log[10s10A ] 3.181−+00..001410−+00..002830−+00..013272
s 0.033 0.075 0.113
tremelyobscureandhardtohandle.Thisisthereasonwhyfor Derived n 2.673−+0.053−+0.127−+0.199
0.077 0.151 0.222
alongtimenooneaddressedtheissueofdarkenergypertur- H (km/s/Mpc) 69.−2+1.2−+2.6+3−.9
0 1.4 2.9 4.2
bationsinacompletemannerintheholographic-typemodels. Ω 0.697+0−.011+−0.02−5+0.037
de0 0.015 0.031 0.046
Bethatasitmay,Li, Lin,andWang[14]madeacalculation Ωm0 0.284+−00..001104+−00..002229+−00..003433
for the perturbations in the holographic dark energy model, Age(Gyr) 13.125−+0.202−+0.457−+0.657
0.220 0.414 0.580
in which some approximations are used in dealing with the zre 10.531−+01..828348−+22..045885−+33..268966
− − −
non-local integrals in the equations governing the evolution
ofmetricperturbations,andtheyprovedthattheperturbations
arestableforbothsuper-horizonandsub-horizonscales. But
Thesoundspeedofdarkenergy,c2 δp /δρ ,isusually
a complete analysis of the cosmologicalperturbationsin the s ≡ de de
treatedasaphenomenologicalparameterforafluidmodelof
holographic dark energy model is still absent. Thus, in the
darkenergy.Itmustberealandnon-negativetoavoidunphys-
past,toavoidtheinclusionofdarkenergyperturbationprob-
icalinstabilities. Infact,ifwetreatthedarkenergystrictlyas
lem, one only used the CMB “distance priors” data, instead
an adiabatic fluid, then the sound speed c would be imag-
of the full CMB data, to constrain the holographicand age- s
inary (in this case, the physical sound speed is equal to the
graphicdarkenergymodels.
adiabatic sound speed, c2 = c2 < 0), leading to instabilities
However, recently, it was realized that, in order to make s a
indarkenergy. Inordertofixthisproblem,itisnecessaryto
progress, one should first ignore the non-local effect in the
assume that dark energy is a non-adiabatic fluid and impose
holographic-type models and directly calculate dark energy
c2 > 0by hand[16]. Ouranalysisisinsensitiveto thevalue
perturbationsinthesemodelsasiftheyareusualperfectflu- s
of c . As long as c is close to 1, the dark energy does not
ids.Alonethisline,globalfitanalysesontheholographicdark s s
clustersignificantlyon sub-Hubblescales. Therefore,in our
energymodelwere performed[8, 15]. Itshould be stressed,
analysis, we set c to be1; the adiabaticsoundspeedcan be
however,thatsuchatreatmentisonlyanexpedientmeasure, s
imaginary, c2 dp /dρ < 0. This is what is done in the
in the case that we are not capable of completely handling a ≡ de de
CAMB and CMBFAST codes. Of course, one can also take
thenon-localeffectinthecalculationofdarkenergyperturba-
c asaparameter,butthefitresultswouldnotbeaffectedby
tionsinthesemodels. But, ontheotherhand,sincethenon- s
thistreatment[17].
localeffectisnotadominantfactor,itisbelievedthatthefluid
Forthedata,besidestheCMBdata(includingtheWMAP
approximationintheholographic-typedarkenergymodelsis
7-yr temperature and polarization power spectra [10]), the
reasonable.
mainotherastrophysicalresultsthatweshalluseinthispaper
forthejointcosmologicalanalysisarethefollowingdistance-
scaleindicators:
III. GLOBALFITRESULTS
The Union2.1sample of 580 SNIa with systematic er-
In our global fit analysis, the parameter n of the NADE • rorsconsidered[18].
modelis treated as a derivedparameter, whose value can be
obtainedbytheparametersΩ ,Ω andΩ viatheNewton The BAO data, including the measurements of
b0 dm0 k0 •
iterationalgorithm,asmentionedinSec.II.The“CosmoMC” r (z )/D (0.2) and r (z )/D (0.35) from the SDSS
s d V s d V
package uses the physical densities of baryon ω Ω h2 DR7 [19] and the measurements of A parameter at
b b0
andcolddarkmatterω Ω h2 insteadofΩ a≡ndΩ . z=0.44, 0.6, 0.73fromtheWiggleZDarkEnergySur-
dm dm0 b0 dm0
≡
Thus,ourmostgeneralparameterspacevectoris: vey[20].
P (ω ,ω ,Θ,τ,Ω ,n ,A ), (10) The Hubble constant measurement H = 73.8
b dm k0 s s 0
≡ • ±
2.4km/s/MpcfromtheWFC3ontheHST[21].
whereΘistheratio(multipliedby100)ofthesoundhorizon
to the angular diameter distance at decoupling, τ is the op- OurglobalfitresultsaresummarizedinTableIandFig.1.
tical depth to re-ionization, A and n are the amplitude and We notice two remarkable results: (i) the value of Ω is
s s k0
thespectralindexoftheprimordialscalarperturbationpower greaterthan0atleastatthe3σconfidencelevels(CLs),which
spectrum. For the pivot scale, we set k = 0.002Mpc 1 to implies that the NADE model distinctly favors an open uni-
s0 −
be consistentwith the WMAP team [10]. Notethatwe have verse; (ii) the best-fit value of n is evidently less than those
assumedpurelyadiabaticinitialconditions. obtainedinthepreviouswork.
4
Likelihood
0.0215 0.0235
2hm00.12
Wd 0.1
0.0215 0.0235 0.1 0.12
1.045 1.045
Q
1.035 1.035
0.0215 0.0235 0.1 0.12 1.035 1.045
0.12 0.12 0.12
Τ 0.09 0.09 0.09
0.06 0.06 0.06
0.0215 0.0235 0.1 0.12 1.035 1.045 0.060.090.12
0.03 0.03 0.03 0.03
Wk000..0012 00..0012 00..0012 00..0012
0.0215 0.0235 0.1 0.12 1.035 1.045 0.060.090.12 0.010.020.03
72 72 72 72 72
H06780 6780 6780 6780 6780
66 66 66 66 66
0.0215 0.0235 0.1 0.12 1.035 1.045 0.060.090.12 0.010.020.03 66687072
2.9 2.9 2.9 2.9 2.9 2.9
2.7 2.7 2.7 2.7 2.7 2.7
n
2.5 2.5 2.5 2.5 2.5 2.5
0.0215 0.0235 0.1 0.12 1.035 1.045 0.060.090.12 0.010.020.03 66687072 2.5 2.7 2.9
Wb0h2 Wdm0h2 Q Τ Wk0 H0 n
FIG.1: The1Dmarginalizeddistributionsofindividualparametersand2Dcontoursatthe1–3σconfidencelevelsfromtheglobalfitusing
theCMB+BAO+SNIa+H data.
0

6000
WMAP data
NADE
Union2.1+CMB+BAO+H0 5000 CDM
2mk)4000
TTC/2p(l3000
+1)
l(l2000
1000
0
1 10 100 1000
l
FIG.2: ParameterspacesintheΩ –Ω planeconstrainedbydif- FIG. 3: The CMB CTT power spectra for the NADE and ΛCDM
de0 m0 l
ferent joint data sets. The cyan, orange and red regions denote modelswiththebest-fitparametervalues. Theblackdotswitherror
the constraint results from the joint CMB, BAO and H observa- bars denote the observational data from the WMAP 7-yr observa-
0
tionswithoutSNIadata,withUnion2sampleofSNIadataandwith tions.
Union2.1sampleofSNIadata,respectively. NotethattheUnion2.1
sampleisusedwiththesystematicerrorswhiletheUnion2sample
isn’t,soitisnowonderwhytheUnion2sampleslightlyconstrains The fit result of n is n = 2.673+0.053+0.127+0.199 at the 1–
0.077 0.151 0.222
theparametersmoretightlythantheUnion2.1sample. 3σ CLs. We find that the best-fit v−alue−of n−is significantly
different from the results obtained in the previous work [7,
9, 22–25]. For example, Refs. [7], [22], [24] and [25] gave
The result of the spatial curvature we obtained is still at n = 2.810, 2.807, 2.887, and 2.886, respectively. What can
thelevelof10 2, consistentwiththeotherresultsaboutdark thischangetellus? Next,weshallexplorewhatthefactoris
−
energyintheliterature.However,itshouldbepointedoutthat thatismakingthischange.
ourworkisthefirsttoshowthattheNADEmodeldistinctly To doso, andwithoutlossof generality,we take the most
favorsanopenuniverseundercurrentdata. recentworkinRef.[7]asanexampletomakeacomparison.
5
Welistherefourdifferentpointsbetweenthem:(1)thespatial thedifferentialequationofΩ ,whichcanreduceonefreepa-
de
curvatureis consideredin thisworkwhileit isn’tconsidered rameter for the NADE model. In order to easily modify the
inRef.[7];(2)theHubbleconstantH measurementandthe “CosmoMC”package,wesetΩ ,Ω , andΩ asfreepa-
0 dm0 b0 k0
BAO measurement of A parameter from the WiggleZ Dark rameters and n as a derived parameter, and use the Newton
EnergySurveyare usedin this workwhiletheyare notused iterationalgorithmtoobtainthetruevalueofn.
inRef.[7];(3)theSNIadatasetusedinthisworkisUnion2.1 OurglobalfitresultsshowthattheNADEmodeldistinctly
sample while it is Union2 sample in Ref. [7]; (4) this paper favorsanopenuniverse,sincethevalueofΩ isgreaterthan
k0
performs a global fit where the full CMB information from 0 at the 3σ CLs. Besides, we find that the value of the key
WMAP-7yrobservationsisusedwhiletheCMBinformation parameteroftheNADEmodeln = 2.673+0.053+0.127+0.199sig-
usedinRef.[7]comesonlyfrom7-yrWMAP“distancepri- nificantlydifferentfromthoseobtainedin−t0h.0e77p−r0e.1v5i1o−u0.s22w2ork.
ors”. After testing these four items one by one by varying Wefindthatthemainreasonleadingtosuchachangecomes
oneconditionandsettingtheothersthesame,wefindthatthe fromthedifferentSNIasamplesused. Namely,theUnion2.1
changeismainlyduetothedifferentSNIadataused. sampleandtheUnion2samplegivefairlydifferentconstraint
Toseeclearly,weplotthetestresultsofdifferentSNIadata results for the NADE model. Our further test indicates that
used for the NADE model in Fig. 2. The cyan, orange and thereisadistincttensionbetweentheUnion2sampleofSNIa
redregionsdenotetheparameterspacesconstrainedbyusing andotherobservations,andthetensionwillberemovedonce
thejointCMB,BAOandH0 observationswithoutSNIadata, theUnion2sampleisreplacedbytheUnion2.1sample.Thus,
withUnion2sampleofSNIadata,andwithUnion2.1sample weconcludethatthenewconstraintresultoftheNADEmodel
ofSNIadata,respectively. NotethattheCMBdatausedhere obtained in this paper is more reasonable than the previous
are the 7-yr WMAP “distance priors” for simplicity. Com- ones.
paringthecyanregion(withoutSNIa)withtheorangeregion
We also plot the CMB power spectra for the NADE and
(with Union2), one can easily find that their overlappingre-
ΛCDMmodelsbyusingthebest-fitresultsoftheglobalfits.It
gion is very small, which implies that there is a tension be-
isshownthattheNADEmodelandtheΛCDMmodelproduce
tween the Union2 sample of SNIa and the joint CMB, BAO
slightlydifferentfeaturesin thelow lregions. Since the low
and H observations. However, the tension between SNIa
0 l data are rather rare and rough, the two models cannot be
andCMB+BAO+H willbegreatlyrelievedoncetheUnion2
0 discriminatedbythelate-timeISWeffectsyet.Weexpectthat
sampleisreplacedbytheUnion2.1sampleofSNIa,sincethe
thefuturehighlyaccuratedatacandothisjob.
overlap between cyan and red regions is very large. Thus,
If dark energy is truly dynamical, as hinted by recent
we can concludethat the new constraintresultof the NADE
work[26],thepossiblenon-gravitationalinteractionbetween
modelobtainedinthisworkismorereasonablethanbefore.
dark energy and dark matter may deserve deeper investiga-
In addition, by using the globalfit results obtained in this
tions. In this work the interaction between dark energy and
work (best-fitvalues), we plotthe CMB powerspectrum for
darkmatterisnotconsidered. Ifsuchaninteractionexists in
the NADE modelin Fig.3. To make a comparison,we also
plot the corresponding curve of the ΛCDM model with the theNADEmodel,thecalculationsoftheperturbationsofdark
energyand dark matterwill becomemore complicated. The
best-fit parameters given by the same data sets. The 7-yr
global fit analysis on the interacting agegraphic dark energy
WMAP observationaldata points with uncertaintiesare also
modelis fairly attractive. In addition, the comparisonof the
markedinthefigure.WecanclearlyseethattheNADEmodel
producesadifferentfeaturecomparedwiththeΛCDMmodel various holographic models of dark energy under a uniform
globalfitisalsonecessary. Weleavethesesubjectsinthefu-
inthelowlregions.However,sincethelowldataarerareand
turework.
rough, the two models cannot be discriminated by the late-
timeISWeffectsbyfar.
IV. CONCLUDINGREMARKS Acknowledgments
Inthiswork, ourmaintask isto performa globalfitanal- This work was supported by the National Science Foun-
ysis on the NADE model in a non-flat universe by using a dation of China under Grant Nos. 10705041, 10975032,
MCMC method with the joint data of the full CMB spectra, 11047112 and 11175042, and by the National Ministry
BAO,SNIaandH0observations.Weusetheinitialcondition, of Education of China under Grant Nos. NCET-09-0276,
Ω (z ) = n2(1+zini)−2 1+ √F(z ) 2 at z = 2000, to solve N100505001,N090305003,andN110405011.
de ini 4 ini ini
(cid:16) (cid:17)
[1] A.G.Riessetal.[SupernovaSearchTeamCollaboration],As- A.A.Starobinsky,Int.J.Mod.Phys.D9(2000)373;S.M.Car-
tron.J.116,1009(1998);S.Perlmutteretal.[SupernovaCos- roll,LivingRev.Rel.4(2001)1;T.Padmanabhan,Phys.Rept.
mologyProjectCollaboration],Astrophys.J.517,565(1999). 380(2003)235;P.J.E.PeeblesandB.Ratra,Rev.Mod.Phys.
[2] S. Weinberg, Rev. Mod. Phys. 61 (1989) 1; V. Sahni and 75(2003)559;E.J.Copeland,M.SamiandS.Tsujikawa,Int.
6
J. Mod. Phys. D 15 (2006) 1753; J. Frieman, M. Turner and [11] A.LewisandS.Bridle,Phys.Rev.D66,103511(2002).
D.Huterer,Ann.Rev.Astron.Astrophys.46,385(2008). [12] C.P.MaandE.Bertschinger,Astrophys.J.455,7(1995).
[3] M.Li,X.D.Li,S.WangandY.Wang,Commun.Theor.Phys. [13] J.c.HwangandH.r.Noh,Phys.Rev.D65,023512(2002).
56,525(2011). [14] M.Li,C.LinandY.Wang,JCAP0805,023(2008).
[4] M.Li,Phys.Lett.B603,1(2004);X.Zhang,Int.J.Mod.Phys. [15] L.Xu,Phys.Rev.D85,123505(2012).
D14,1597(2005); B.Chen, M.LiandY.Wang, Nucl.Phys. [16] C. Gordon and W. Hu, Phys. Rev. D 70, 083003
B 774, 256 (2007); X. Zhang, Phys. Lett. B 648, 1 (2007); (2004);J.Valiviita,E.MajerottoandR.Maartens,JCAP0807,
X. Zhang, Phys. Rev. D 74, 103505 (2006); C. Gao, F. Wu, 020(2008).
X. Chen and Y. G. Shen, Phys. Rev. D 79, 043511 (2009); [17] H. Li and J. Q. Xia, JCAP 1004, 026 (2010); H. Li and
J.Zhang,X.ZhangandH.Liu,Eur.Phys.J.C52,693(2007); X.Zhang,Phys.Lett.B713,160(2012)
X.Zhang,Phys.Lett.B683,81(2010);M.LiandR.X.Miao, [18] N.Suzuki, D.RubinandC.Lidmanetal.,Astrophys.J. 746,
arXiv:1210.0966[hep-th]. 85(2012).
[5] X. Zhang and F. Q. Wu, Phys. Rev. D 72, 043524 (2005); [19] B.A.Reidetal.[SDSSCollaboration],Mon.Not.Roy.Astron.
X. Zhang and F. Q. Wu, Phys. Rev. D 76, 023502 (2007); Soc.401,2148(2010).
Q. G. Huang and Y. G. Gong, JCAP 0408, 006 (2004); [20] C.Blake,E.KazinandF.Beutleretal.,Mon.Not.Roy.Astron.
Z.Chang,F.Q.WuandX.Zhang,Phys.Lett.B633,14(2006); Soc.418,1707(2011).
J.Y.Shen,B.Wang,E.AbdallaandR.K.Su,Phys.Lett.B609, [21] A.G.Riess,L.MacriandS.Casertanoetal.,Astrophys.J.730,
200(2005); Z.L.YiandT.J.Zhang, Mod. Phys.Lett.A22, 119(2011).
41(2007); X.Zhang,Phys.Rev.D79,103509(2009); M.Li, [22] M.Li,X.D.Li,S.WangandX.Zhang,JCAP0906,036(2009).
X.D.Li,S.Wang,Y.WangandX.Zhang,JCAP0912(2009) [23] M.Li,X.LiandX.Zhang,Sci.ChinaPhys.Mech.Astron.53,
014;Z.Zhang,S.Li,X.D.Li,X.ZhangandM.Li,JCAP1206, 1631(2010).
009(2012). [24] H.Wei,JCAP1008,020(2010).
[6] H.WeiandR.G.Cai,Phys.Lett.B660,113(2008). [25] Y.Li,J.Ma, J.Cui, Z.WangandX.Zhang, Sci.ChinaPhys.
[7] Y. H. Li, J. F. Zhang and X. Zhang, Chin. Phys. B, in press, Mech.Astron.54,1367(2011).
arXiv:1201.5446[gr-qc]. [26] G. B. Zhao, R. G. Crittenden, L.Pogosian and X. M. Zhang,
[8] S. Wang, Y. H. Li, X. D. Li and X. Zhang, arXiv:1207.6679 Phys. Rev.Lett.109, 171301 (2012); J.Z.MaandX. Zhang,
[astro-ph.CO]. Phys.Lett.B699,233(2011);H.LiandX.Zhang,Phys.Lett.
[9] H.WeiandR.G.Cai,Phys.Lett.B663,1(2008). B703,119(2011);X.D.Li,S.Wang,Q.G.Huang,X.Zhang
[10] E.Komatsuetal.[WMAPCollaboration],Astrophys.J.Suppl. andM.Li,Sci.ChinaPhys.Mech.Astron.55,1330(2012).
192,18(2011).