Constraints on the generalized tachyon field models from latest observational data
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Constraints on the generalized tachyon ?eld models from latest observational data Rong-Jia Yang 1?,Shuang Nan Zhang 1,2,3,and Yuan Liu 11Department of Physics and Tsinghua Center for Astrophysics,Tsinghua University,Beijing 100084,China 2Key Laboratory of Particle Astrophysics,Institute of High Energy Physics,Chinese Academy of Sciences,P.O.Box 918-3,Beijing 100049,China,3Physics Department,University of Alabama in Huntsville,Huntsville,AL 35899,USA Abstract We consider constraints on generalized tachyon ?eld (GTF)models from latest observational data (including 182gold SNIa data,the shift parameter,and the acoustic scale).We obtain at 68.3%con?dence level ?m =0.37±0.01,k 0=0.09+0.04?0.03,α=1.8+7.4?0.7(the best-?t values of the parameters)and z q =0～0.47?0.51(the transitional redshift)for GTF as dark energy component only;k 0=0.21+0.20?0.18,α=0.57±0.01and z q =0～0.49?0.68for GTF as uni?cation of dark energy and dark matter.In both cases,GTF evolves like dark matter in the early universe.By applying model-comparison statistics and test with independent H (z )data,we ?nd GTF dark energy scenario is favored over the ΛCDM model,and the ΛCDM model is favored over GTF uni?ed dark matter by the combined data.For GTF as dark energy component,the ?uctuations of matter density is consistent with the growth of linear density perturbations.For GTF uni?ed dark matter,the growth of GTF density ?uctuations grow more slowly for a →1,meaning GTF
do not behave as classical ΛCDM scenarios.
PACS numbers:95.36.+x,98.80.-k,98.80.Es
I.INTRODUCTION
Tachyon?eld can be seen as special cases of k-essence[1]and has been explored exten-sively[2,3,4,5,6,7,8,9,10,11,12,13,14].For a constant potential,the tachyon?eld can be generalized as
F(X)=?V0(1?2X n)1
,(2)
1+2k2α0(1+z)6α
c2s=?(2α?1)w k,(3)
whereα=n/(2n?1)and k0is a constant(?∞
There have been a number of papers considering observational constraints on GCG model, such as Refs.[24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44, 45,46,47,48,49,50,51,52].As the scalar?eld realization of GCG,GTF with Lagrangian (1)yet has not been fully analyzed with observational data currently available.This is necessary if such exotic types of matter are to be considered as serious alternatives to the ΛCDM scenario.Cosmological models that include(generalized)Chaplygin gas component can be divided into two classes:models with and without a signi?cant CDM component.
It now appears increasingly likely from both theoretical stability issues and observational constraints(e.g.[24,50,51,52])from matter clustering properties(dark matter is very clumpy while dark energy is quite smooth out to the Hubble scale)that dark matter and dark energy are not the same substance.Also it appears rather di?cult to unify dark matter and dark energy into a single scalar?eld in the context of the string landscape[53].
Nevertheless,in this paper we will consider these two cases:GTF as dark energy only and as uni?cation of dark matter and dark energy,without loss of generality.The data sets used here include the recently released182gold supernova(SNIa)data[54],the shift parameter R and the acoustic scale l a from observations of CMB[55].Our results show that GTF dark energy scenario is favored over theΛCDM model,and theΛCDM model is favored over GTF as uni?cation of dark matter and dark energy by the combined data.
II.THE LUMINOSITY DISTANCE OF THE GTF MODEL
For a?at and homogeneous Friedmann-Robertson-Walker(FRW)space,the Einstein’s ?eld equations take the forms:
H2:= ˙a
(1+
a′
w k(a′))].For GTF as uni?cation of dark matter and dark energy
E(k0,α)=[?b(1+z)3+?r(1+z)4+(1??b??r)f(z)]1/2,(6) where?b is the present dimensionless density parameter of baryonic matter.The Hubble-parameter free luminosity distance is expressed as
D L(z)=H0(1+z) z′0dz′
III.OBSER V ATIONAL CONSTRAINTS AND THE EVOLUTION OF THE GTF
To consider the best?t values of the parameters,we study observational bounds on the GTF models for a?at universe.Our constraints come from combinations of182gold supernova data[54]and the CMB observation[55].
The SNIa data which provide the main evidence for the existence of dark energy in the framework of standard cosmology[56].Here we use a recently published dataset consisting of 182SNIa with23SNIa at z 1obtained by imposing constraints A v<0.5(excluding high extinction)[54].Each data point at redshift z i includes the Hubble-parameter free distance modulusμobs(z i)(≡m obs?M,where M is the absolute magnitude)and the corresponding errorσ2(z i).The resulting theoretical distance modulusμth(z)is de?ned as
μth(z)≡5log10D L(z)+μ0,(8)
whereμ0≡5log10h?42.38is the nuisance parameter which can be marginalized over[57]. FittingΛCDM model with these182SNIa data,the best-?t value of parameter is?m=0.34;?tting GCG as dark energy component,it is?m=0.39[27].
In order to break the degeneracies among the parameters,we consider the shift parameter R and the acoustic scale l a[58]which are nearly uncorrelated with each other and de?ned as
R≡?1/2m z CMB0dz
a CMB0c s da/(a˙a).(10) For the case of GTF as dark energy only,?r/?m=1/(1+z eq)(z eq=2.5×104?m h2(T CMB/2.7K)?4)with the redshift of recombination z CMB=1089(a CMB=1/[1+ z CMB]).The sound speed is c s=1/
The shift parameter R is a geometrical measure as it measures the size of apparent sound horizon at the epoch of recombination.Keeping the sound horizon size?xed,di?erent cosmological models lead to di?erent background expansion and hence the shift parameter can be used to compare and constrain di?erent models.However,the sound horizon size also changes when varying cosmological parameters,most notably changing the matter density ?m.Hence in general the shift parameter will not be an accurate substitute for CMB dada, but the combination of the shift parameter R and the acoustic scale l a has been proved to be a good and e?cient approximation to the full CMB data to probe cosmological models [55,61,62].
Since the SNIa,the shift parameter R,and the acoustic scale l a are e?ectively independent measurements,we can simply minimize their totalχ2value given by[63,64,65]
χ2(?m,k0,α)=χ2SNIa+χ2R+χ2l
a
,(11)
where
χ2SNIa=
N
i=1(μobs L(z i)?μth L(z i))2
0.03 2,(13)
and
χ2l
a
= l a?302.2
(AIC)[66]and the Bayesian Information Criterion(BIC)[67](see also[68]and reference therein)to select the best-?t https://www.sodocs.net/doc/f12661879.html,paring with theΛCDM case,the di?erence of the Akaike Information Criterion(AIC)is?AIC=?5.29,supporting GTF dark energy scenario;the Bayesian Information Criterion(BIC)is?BIC=1.14,less supporting GTF dark energy scenario.
Because model-comparison statistics can not discriminate between GTF dark energy scenario and theΛCDM model.We carry out another independent observational test with 9H(z)data points[69,70]in the range0 z 1.8obtained by using the di?erential ages of passively evolving galaxies determined from the Gemini Deep Deep Survey(GDDS)[71]and archival data[72,73].We compare these observational H(z)data with the predicted values of the Hubble parameter H of the GTF dark energy scenario for the case of(?m=0.37, k0=0.09,α=1.8)and the case of(?m=0.39,k0=0)respectively.We?ndχ2=11.87 (p(χ2>11.86)=0.22)for the former case andχ2=12.66(p(χ2>12.66)=0.18)for the latter case,both with9degrees of freedom because no?tting is done with the H(z)data. This serves as an independent evidence that the GTF dark energy scenario is favored over the ΛCDM model by these H(z)data.The predicted values of the Hubble parameter H of the GTF dark energy scenario in68.3%con?dence level limits compared with the observational H(z)data is shown in?gure1;theΛCDM case is also presented for comparison.
Figures2,3,4show the68.3%,95.4%and99.7%joint con?dence contours in the?m-k0 plane withαat its best?t value of1.8,the?m-αplane with k0at its best?t value of0.09, and theα-k0plane with?m at its best?t value of0.37respectively.The dot-dashed lines, dotted lines,dashed lines represent the results from the182gold SNIa sample,the acoustic scale l a and the shift parameter R respectively.The colored areas show the results from the combination of these three data sets.Obviously the current observational bounds on the indexαare considerably weak.
B.The case of GTF as uni?cation of dark matter and dark energy
For the case of GTF as uni?cation of dark matter and dark energy,we?nd the best?t
andα=0.57±0.01with values of the parameters at68%con?dence level:k0=0.21+0.2
?0.18
χ2k,min=167.27(p(χ2>χ2k,min)=0.78).
For GTF as uni?cation of dark matter and dark energy,k0=0dose not correspond to
FIG.1:The predicted values of the Hubble parameter H of the GTF as dark energy only in68.3% con?dence level limits from?tting the combined data,compared with the observational H(z)data
case(the dash-dot line).
with error bars and theΛCDM
FIG.2:The68.3%,95.4%and99.7%con?dence regions in the k0-?m plane withαat its best-?t value of1.8,for the case of GTF as dark energy only.The dot-dashed lines,dotted lines,dashed lines represent the results from the182gold SNIa sample,the acoustic scale and the shift parameter respectively.The colored areas show the results from the combination of these three data sets.
FIG.3:The same con?dence regions as in Fig
2in the α-?m plane with k 0at its best-?t value of 0.09,for the FIG.4:The same con?dence regions as in Fig 2in the α-k 0plane with ?m at its best-?t value of 0.37,for the case of GTF as dark energy only.
the ΛCDM case,so we can not apply F-test [74]for model selection,but we can still apply AIC and https://www.sodocs.net/doc/f12661879.html,paring with the ΛCDM case,we ?nd ?AIC=0.68and ?BIC=https://www.sodocs.net/doc/f12661879.html,paring with the case of GTF as dark energy,we ?nd ?AIC=5.97and ?BIC=2.8.These results of model-comparison statistics indicate that the case of GTF as uni?cation of
FIG.5:The predicted values of the Hubble parameter H of GTF uni?cation of dark matter and dark energy in68.3%con?dence level limits from?tting the combined data,compared with the observational H(z)data with error bars.
dark matter and dark energy is not favored by the combined data.
To con?rm this result,we also carry out the independent9H(z)data points[69,70]test. We?ndχ2=16.60(p(χ2>11.86)=0.06),meaning that GTF as uni?cation of dark matter and dark energy is also not favored by these H(z)data as shown in?gure5.
Figure6shows the68.3%,95.4%and99.7%joint con?dence contours in theα-k0plane. The dot-dashed lines,dotted lines,dashed lines represent the results from the182gold SNIa sample,the shift parameter R and the acoustic scale l a respectively.The colored areas show the results from the combination of these three data sets.Obviously the current observational bounds on the index k0are considerably weak.
C.The evolution of the GTF
To study the evolution of the GTF,we investigate the deceleration parameter q(z),the EoS parameter w k(z),and the energy densityρk(z).For GTF as dark energy component alone,the deceleration parameter q(z)is de?ned as
q(z)=?a¨a/˙a2=1
2
?k(z),(15)
FIG.6:The68.3%,95.4%and99.7%con?dence regions in theα-k0plane,for the case of GTF as uni?cation of dark matter and dark energy.The dot-dashed lines,dotted lines,dashed lines represent the results from the182gold SNIa sample,the shift parameter,and the acoustic scale respectively.The colored areas show the results from the combination of these three data sets.
where?k is energy density parameter of GTF.For GTF as uni?cation of dark matter and dark energy,the deceleration parameter q(z)is given by
q(z)=1
2
?k(z),(16)
Because we only consider the evolution of the deceleration parameter at low redshift,the radiation is ignored here.
For the case of GTF as dark energy component only,the present value of the deceleration parameter q(z)is found to be?q z=0～0.44?0.48.The phase transition from deceleration to acceleration of the Universe occurs at the redshift z q=0～0.47?0.51in68.3%con?dence level limits,as shown in?gure7.For GTF as uni?cation of dark matter and dark energy,?q z=0～0.50?0.61and z q=0～0.49?0.68in68.3%con?dence level limits as shown in ?gure8.All these results are comparable with that estimated from157gold data(z t?0.46±0.13)[75],but less than that obtained from gold+SNLS SNIa data for DGP brane (z q=0～0.8?0.93)[76].
For the case of GTF as dark energy component only,?gure9and10show the evolution of the EoS parameter and the energy density ratio of GTF dark energy at low or high
FIG.7:The deceleration parameter as a function of redshift in68.3%con?dence level limits from ?tting the combined data,compared with theΛCDM case(the dash-dot line),for GTF as dark energy component only.
redshift,compared with the vacuum energy in both cases.For z 2,the EoS parameter runs closely to?0,meaning the negative pressure of the GTF dark energy approaches to zero rapidly,compared with the cases of the radiation and the dark matter.Such behavior can,to a certain degree,solve the?ne-tuning problem[22,23].For GTF as uni?cation of dark matter and dark energy,?gure11and12show the evolution of the EoS parameter and the energy density ratio at low or high redshift,compared with the cases of the radiation and the vacuum energy.All these results at low redshift are consistent with that obtained in Ref.[55]by model-independent methods in68.3%con?dence level limits.
IV.GROWTH OF LINEAR DENSITY PERTURBATIONS
Stability properties of some perfect?uid cosmological models are studied extensively[77], such as Refs.[16,50,51,52,78,79]concentrated on the stability of GCG as uni?cation of dark matter and dark energy,Refs.[24,27,80]on the stability of GCG as dark energy component only,and Refs.[17,81,82]on the stability of tachyon?eld dark energy.
FIG.8:The deceleration parameter as a function of redshift in68.3%con?dence level limits from ?tting the combined data,for GTF as uni?cation of dark matter and dark energy.
A.The case of GTF as dark energy only
In this subsection,we study the growth of density perturbations for the mixture of a matter?uid and a GTF dark energy?uid in the linear regime on subhorizon scales.Assuming the GTF dark energy to be a smooth,unclustered component(the only e?ect of the GTF evolution is to alter the growth of matter perturbations through the the e?ect of the GTF energy density on the expansion of the universe),the growth equation for the linear matter density perturbation,δ≡δρm/ρm,is given by[27,80]
δ′′+ 2+˙H
?m
2
FIG.9:The evolution of the equation of state parameter of GTF as dark energy component only in68.3%con?dence level limits from?tting the combined data,compared with theΛCDM case (the dash-dot line).
FIG.10:The evolution of the energy density ratio of the GTF as dark energy component only in68.3%con?dence level limits from?tting the combined data,compared with the cases of the radiation(the dash line),the dark matter(the dot line),and the vacuum energy(the dash-dot line).
FIG.11:The evolution of the equation of state parameter of GTF as uni?cation of dark matter and dark energy in68.3%con?dence level limits from?tting the combined data.
a=1for some selected values of the parameters(k0andα)in68%con?dence level.Figure 13shows the behavior ofδas a function of the scale https://www.sodocs.net/doc/f12661879.html,pared to theΛCDM universe,?uctuations grow more slowly in a universe where GTF dark energy plays a role. For parameters(k0andα)changing in68%con?dence level,δdeviates slightly,consistent with the growth of linear density perturbations.The behavior ofδin Fig.13agrees with the result obtained in Ref.[27]in the framework of GCG dark energy.
B.The case of GTF as uni?cation of dark matter and dark energy
Because baryons play a crucial role in the context of uni?ed dark matter/dark energy models[83,84],here we study the growth of density perturbations for the mixture of a baryonic?uid and a GTF?uid unifying dark matter and dark energy.In the comoving synchronous gauge the relativistic equations governing the evolution of perturbations in a two?uid(baryon and GTF)system are[83,85]
δ′′b+ 2+˙H2[?bδb+(1?3(2α?1)w k)?kδk]=0,(19)
δ′k+(1+w k)[θk/aH?δ′b]?6αw kδk=0,(20)
(2α?1)w k k2
θ′k+[1+3(2α?1)w k]θk+
FIG.12:The evolution of the energy density ratio of the GTF as uni?cation of dark matter and dark energy in68.3%con?dence level limits from?tting the combined data,compared with the cases of the radiation(the dash line)and the vacuum energy(the dash-dot line).
FIG.13:The evolution of the matter density perturbationδas a function of the scale factor a (normalized to a=1at the present)for some selected values of the parameters(k0andα)of the GTF as dark energy in68%con?dence level with?m=0.37.
FIG.14:The evolution of the GTF(uni?ed dark matter)density perturbationδk as a function of the scale factor a(normalized to a=1at the present)for some selected values of the parameters (k0andα)in68%con?dence level,compared with the evolution of the matter density perturbation δin the case ofΛCDM.
whereδ′′i is the density contrast of the i th?uid obeying p i=w iρi,θk is element velocity divergence.Given w k and H as functions of a we can easily transform this set of equations into four?rst order di?erential equations and integrate them using numerical method.Since in the linear regime and deep into the matter eraδi∝a implyingδ′i∝a with normalized initial conditions[δb,δ′b,δk,θ]=[0.001,0.001,0.001,0]for a=0.001and a prior k=100h Mpc?1which corresponds to a scale of order50h?1kpc.Figure14shows the behavior ofδk as a function of the scale factor.The?uctuations of GTF density grow more slowly for a→1, meaning GTF does not behave as classicalΛCDM scenarios.The reason is that baryons can carry over gravitational clustering when the GTF?uid starts behaving di?erently from CDM[83].
V.CONCLUSIONS AND DISCUSSIONS
Assuming that the Universe is spatially?at,we place observational constraints on GTF scenario with182gold SNIa data and two cosmic microwave background parameters(the shift parameter and the acoustic scale).For GTF as dark energy component only,the best-?t
values of the parameters at68.3%con?dence level are:?m=0.37±0.01,k0=0.09+0.04
and
?0.03
α=1.8+7.4
withχ2k,min=159.30(p(χ2>χ2k,min)=0.88),comparing withχ2Λmin=168.59?0.7
(p(χ2>χ2Λ,min)=0.77)in theΛCDM case.For GTF as uni?cation of dark matter and dark
and energy,the best?t values of the parameters at68%con?dence level are:k0=0.21+0.2
?0.18
α=0.57±0.01,withχ2k,min=167.27(p(χ2>χ2k,min)=0.78).In both cases,GTF evolves like dark matter in the early universe.
To consider the best-?t models,we apply model-comparison https://www.sodocs.net/doc/f12661879.html,paring with GTF dark energy scenario,the combined data do not support theΛCDM case according to F-test and AIC,but possibly support theΛCDM case according to BIC.Similarly the case of GTF as uni?cation of dark matter and dark energy is not supported according to F-test, AIC and BIC.Tested with independent9H(z)data points,GTF dark energy scenario is favored over theΛCDM model,and theΛCDM model is favored over GTF as uni?cation of dark matter and dark energy.This supports theoretical arguments against unifying dark matter and dark energy into one scalar?eld.Of course,new and better data are still needed to further discriminate between these models.
By investigating the deceleration parameter,we?nd that the present value of the de-celeration parameter q(z)is?q z=0～0.44?0.48,the phase transition from deceleration to acceleration of the Universe occurs at the redshift z q=0～0.47?0.51in68.3%con?-dence level limits for GTF as dark energy component only;and?q z=0～0.50?0.61and z q=0～0.49?0.68in68.3%con?dence level limits for GTF as uni?cation of dark matter and dark energy.These results can be tested with future cosmological observations.If assumed to be a smooth component,GTF as dark energy component is consistent with the growth of linear density perturbations.If GTF uni?es dark matter and dark energy,because baryons can carry over gravitational clustering when the GTF?uid starts behaving di?erently from CDM,the growth of GTF density?uctuations grow more slowly for a→1,meaning GTF do not behave as classicalΛCDM scenarios.
Acknowledgments
We thank Yun Wang,Zu-Hui Fan,Hao Wei,Pu-Xun Wu,Yan Wu,Wei-Ke Xiao,Jian-Feng Zhou,Zhi-Xing Ling,and Bi-Zhu Jiang for discussions.The anonymous referee is thanked for his/her patience in reviewing this manuscript several times,as well as providing
insightful and constructive criticisms and suggestions,which allowed us to improve the manuscript signi?cantly.This study is supported in part by the Ministry of Education of China,Directional Research Project of the Chinese Academy of Sciences under project No. KJCX2-YW-T03and by the National Natural Science Foundation of China under project no.10521001,10733010and10725313.
[1]Sen A2002Mod.Phys.Lett.A171797;2005Int.J.Mod.Phys.A205513
[2]Padmanabhan T and Choudhury T R2002Phys.Rev.D66,081301
[3]Gorini V,Kamenshchik A,Moschella U and Pasquier V2004Phys.Rev.D69,123512
[4]Shao Y,Gui Y.-X.and Wang W2007MPLA221175
[5]Choudhury D,Ghoshal D,Jatkar D P and Panda S2002Phys.Lett.B544,231.
[6]Hao J and Li X2002Phys.Rev.D66,087301
[7]Bagla J S,Jassal H K and Padmanabhan T2003Phys.Rev.D67,063504
[8]Calcagni G and Liddle A R2006Phys.Rev.D74,043528
[9]Garousi M R,Sami M and Tsujikawa S2004Phys.Rev.D70,043536
[10]Copeland E J,Garousi M R,Sami M and Tsujikawa S2005Phys.Rev.D71,043003
[11]Cardenas V H2006Phys.Rev.D73,103512
[12]Shiu G and Wasserman I2002Phys.Lett.B541,6
[13]Wang Y and Mukherjee P2006Astrophys.J.650,1
[14]Koshelev A S2007Journal of High Energy Physics,04,029
[15]Chimento L P2004Phys.Rev.D6*******
[16]Gorini V,Kamenshchik A,Moschella U,Pasquier V and Starobinsky A2005Phys.Rev.D
72,103518
[17]Frolov A,Kofman L and Starobinsky A2002Phys.Lett.B545,8
[18]Kamenshchik A,Moschella U and Pasquier V2001Phys.Lett.B511,265
[19]Scherrer R J2004Phys.Rev.Lett.93011301
[20]Yang R J and Zhang S N2008Chin.Phys.Lett.25344
[21]Garriga J and Mukhanov V F1999Phys.Lett.B458219
[22]Armend′a riz-Pic′o n C,Mukhanov V,and Steinhardt P J2000Phys.Rev.Lett.854438;2001
Phys.Rev.D6*******.
[23]Chiba T,Okabe T,and Yamaguchi M2000Phys.Rev.D6*******
[24]Bean R and Dor′e O2003Phys.Rev.D6*******.
[25]Gorini V,Kamenshchik A and Moschella U2003Phys.Rev.D67,063509
Gorini V,Moschella U,Kamenshchik A and Pasquier V2005AIP Conf.Proc.751108 [26]Colistete R Jr,Fabris J C,Gonalves S V B and de Souza P E2003Int.J.Mod.Phys.D13
669
[27]Sen A A and Scherrer R J2005Phys.Rev.D7*******
[28]Multam¨a ki T,Manera M and Gaztanaga E2004Phys.Rev.D6*******
[29]Makler M,Oliveira S Q and Waga I2003Phys.Lett.B5551
[30]Silva P T and Bertolami O2003Astrophys.J.599829
[31]Cunha J V,Lima J A S and Alcaniz J S2004Phys.Rev.D6*******
[32]Bertolami O,Sen A A,Sen S and Silva P T2004Mon.Not.R.Astron.Soc.353329
[33]Zhu Z-H2004Astron.Astrophys.423421
[34]Zhang X,Wang F-Q and Zhang J-F2006J.Cosmol.Astropart.Phys.JCAP01(2006)003
[35]Bouhmadi-Lopez M and Jimenez Madrid J A2005J.Cosmol.Astropart.Phys.
JCAP05(2005)005
[36]Gong Y-G2005J.Cosmol.Astropart.Phys.JCAP03(2005)007
[37]Giannantonio T and Melchiorri A2006Class.Quantum Grav.234125
[38]Biesiada M,Godlowski W and Szydlowski M2005Astrophys.J.62228
[39]Jimeez Madrid J2006Phys.Lett.B634106
[40]Ghosh S,Kulkarni S and Banerjee R2007Phys.Rev.D7*******
[41]Lobo F S N2006Phys.Rev.D7*******
[42]Wu P and Yu H2007J.Cosmol.Astropart.Phys.JCAP03(2007)015;2007Astrophys.J.658,
663
[43]Bento M C,Bertolami O and Sen A A2003Phys.Rev.D67,063003
[44]Alcaniz J,Jain D and Dev A2003Phys.Rev.D6*******
[45]Bertolami O and Silva P T2006Mon.Not.R.Astron.Soc.3651149
[46]Dev A,Jain D and Alcaniz J S2003Phys.Rev.D6*******
[47]Chen D M2003Astrophys.J.587L55;2003Astron.Astrophys.397415
[48]Bilic N,Tupper G B and Viollier R D2002Phys.Lett.B53517
[49]Alcaniz J S,Jain D and Dev A2003Phys.Rev.D6*******
[50]Sandvik H,Tegmark M,Zaldarriaga M and Waga I2004Phys.Rev.D6*******
[51]Perrotta F,Matarrese S and Torki M2004Phys.Rev.D7*******
[52]Amendola L,Waga I and Finelli F2005J.Cosmol.Astropart.Phys.JCAP11(2005)009
[53]Liddle A R and Ure?n a-L′o pez L A2006Phys.Rev.Lett.97161301
[54]Riess A G et al2007Astrophys.J.65998
[55]Wang Y and Mukherjee P2007astro-ph/0703780v1
Wang Y2006Astrophys.J.6501
[56]Riess A G et al1998Astron.J.1161009
Perlmutter S et al1999Astrophys.J.517565
[57]Perivolaropoulos L2005Phys.Rev.D7106350
Pietro E Di and Claeskens J F2003Mon.Not.Roy.Astron.Soc.3411299
Gao C J and2004Phys.Rev.D7*******
Yang R J and Jing J L2004Chin.Phys.513;2004Chin.Phys.Lett.321
Wei H and Zhang S N2007Phys.Rev.D7*******
[58]Page L et al2003Astrophys.J.Suppl.148233
[59]Fixsen D J1996Astrophys.J.473576
[60]Sandage A et al2006Astrophys.J.653,843
[61]Elgar?y O and Multam¨a ki T2007Astron.Astrophys.47165
[62]Wright E L2007Astrophys.J.664633
[63]Movahed M S and Rahvar S2006Phys.Rev.D7*******
Nesseris S and Perivolaropoulos L2004Phys.Rev.D7*******
[64]Wu P and Yu H2007Phys.Lett.B64416
[65]Wei H and Zhang S N2007Phys.Rev.D7*******;2007Phys.Lett.B6447;2007Phys.
Lett.B654139
[66]Akaike H1974IEEE Transactions on Automatic Control19716
[67]Schwarz G1978The Annals of Statistics6461
[68]Liddle A R2004MNRAS351L49
[69]Jimenez R,Verde L,Treu T and Stern D2003Astrophys.J.593622
[70]Simon J,Verde L and Jimenez R2005Phys.Rev.D7*******
[71]Abraham R G et al2004Astron J1272455
[72]Treu T,Stiavelli M,Casertano S,Moller P and Bertin G1999Mon.Not.Roy.Astron.Soc.
黄自艺术歌曲钢琴伴奏及艺术成就
【摘要】黄自先生是我国杰出的音乐家，他以艺术歌曲的创作最为代表。而黄自先生特别强调了钢琴伴奏对于艺术歌曲组成的重要性。本文是以黄自先生创作的具有爱国主义和人道主义的艺术歌曲《天伦歌》为研究对象，通过对作品分析，归纳钢琴伴奏的弹奏方法与特点，并总结黄自先生的艺术成就与贡献。 【关键词】艺术歌曲；和声；伴奏织体；弹奏技巧 一、黄自艺术歌曲《天伦歌》的分析 （一）《天伦歌》的人文及创作背景。黄自的艺术歌曲《天伦歌》是一首具有教育意义和人道主义精神的作品。同时，它也具有民族性的特点。这首作品是根据联华公司的影片《天伦》而创作的主题曲，也是我国近代音乐史上第一首为电影谱写的艺术歌曲。作品创作于我国政治动荡、经济不稳定的30年代，这个时期，这种文化思潮冲击着我国各个领域，连音乐艺术领域也未幸免――以《毛毛雨》为代表的黄色歌曲流传广泛，对人民大众，尤其是青少年的不良影响极其深刻，黄自为此担忧，创作了大量艺术修养和文化水平较高的艺术歌曲。《天伦歌》就是在这样的历史背景下创作的，作品以孤儿失去亲人的苦痛为起点，发展到人民的发愤图强，最后升华到博爱、奋起的民族志向，对青少年的爱国主义教育有着重要的影响。 （二）《天伦歌》曲式与和声。《天伦歌》是并列三部曲式，为a+b+c，最后扩充并达到全曲的高潮。作品中引子和coda所使用的音乐材料相同，前后呼应，合头合尾。这首艺术歌曲结构规整，乐句进行的较为清晰，所使用的节拍韵律符合歌词的特点，如三连音紧密连接，为突出歌词中号召的力量等。 和声上，充分体现了中西方作曲技法融合的创作特性。使用了很多七和弦。其中，一部分是西方的和声，一部分是将我国传统的五声调式中的五个音纵向的结合，构成五声性和弦。与前两首作品相比，《天伦歌》的民族性因素增强，这也与它本身的歌词内容和要弘扬的爱国主义精神相对应。 （三）《天伦歌》的伴奏织体分析。《天伦歌》的前奏使用了a段进唱的旋律发展而来的，具有五声调性特点，增添了民族性的色彩。在作品的第10小节转调入近关系调，调性的转换使歌曲增添抒情的情绪。这时的伴奏加强和弦力度，采用切分节奏，节拍重音突出，与a段形成强弱的明显对比，突出悲壮情绪。 c段的伴奏采用进行曲的风格，右手以和弦为主，表现铿锵有力的进行。右手为上行进行，把全曲推向最高潮。左手仍以柱式和弦为主，保持节奏稳定。在作品的扩展乐段，左手的节拍低音上行与右手的八度和弦与音程对应，推动音乐朝向宏伟、壮丽的方向进行。coda 处，与引子材料相同，首尾呼应。 二、《天伦歌》实践研究 《天伦歌》是具有很强民族性因素的作品。所谓民族性，体现在所使用的五声性和声、传统歌词韵律以及歌曲段落发展等方面上。 作品的整个发展过程可以用伤感――悲壮――兴奋――宏达四个过程来表述。在钢琴伴奏弹奏的时候，要以演唱者的歌唱状态为中心，选择合适的伴奏音量、音色和音质来配合，做到对演唱者的演唱同步，并起到连接、补充、修饰等辅助作用。 作品分为三段，即a+b+c+扩充段落。第一段以五声音阶的进行为主，表现儿童失去父母的悲伤和痛苦，前奏进入时要弹奏的使用稍凄楚的音色，左手低音重复进行，在弹奏完第一个低音后，要迅速的找到下一个跨音区的音符；右手弹奏的要有棱角，在前奏结束的时候第四小节的t方向的延音处，要给演唱者留有准备。演唱者进入后，左手整体的踏板使用的要连贯。随着作品发展，伴奏与旋律声部出现轮唱的形式，要弹奏的流动性强，稍突出一些。后以mf力度出现的具有转调性质的琶音奏法，要弹奏的如流水般连贯。在重复段落，即“小
我国艺术歌曲钢琴伴奏-精
我国艺术歌曲钢琴伴奏-精 2020-12-12 【关键字】传统、作风、整体、现代、快速、统一、发展、建立、了解、研究、特点、突出、关键、内涵、情绪、力量、地位、需要、氛围、重点、需求、特色、作用、结构、关系、增强、塑造、借鉴、把握、形成、丰富、满足、帮助、发挥、提高、内心 【摘要】艺术歌曲中，伴奏、旋律、诗歌三者是不可分割的重 要因素，它们三个共同构成一个统一体，伴奏声部与声乐演唱处于 同样的重要地位。形成了人声与器乐的巧妙的结合，即钢琴和歌唱 的二重奏。钢琴部分的音乐使歌曲紧密的联系起来，组成形象变化 丰富而且不中断的套曲，把音乐表达的淋漓尽致。 【关键词】艺术歌曲；钢琴伴奏；中国艺术歌曲 艺术歌曲中，钢琴伴奏不是简单、辅助的衬托，而是根据音乐 作品的内容为表现音乐形象的需要来进行创作的重要部分。准确了 解钢琴伴奏与艺术歌曲之间的关系,深层次地了解其钢琴伴奏的风 格特点,能帮助我们更为准确地把握钢琴伴奏在艺术歌曲中的作用 和地位，从而在演奏实践中为歌曲的演唱起到更好的烘托作用。 一、中国艺术歌曲与钢琴伴奏 “中西结合”是中国艺术歌曲中钢琴伴奏的主要特征之一，作 曲家们将西洋作曲技法同中国的传统文化相结合，从开始的借鉴古 典乐派和浪漫主义时期的创作风格，到尝试接近民族乐派及印象主 义乐派的风格，在融入中国风格的钢琴伴奏写作，都是对中国艺术 歌曲中钢琴写作技法的进一步尝试和提高。也为后来的艺术歌曲写 作提供了更多宝贵的经验，在长期发展中，我国艺术歌曲的钢琴伴 奏也逐渐呈现出多姿多彩的音乐风格和特色。中国艺术歌曲的钢琴
写作中，不可忽略的是钢琴伴奏织体的作用，因此作曲家们通常都以丰富的伴奏织体来烘托歌曲的意境，铺垫音乐背景，增强音乐感染力。和声织体，复调织体都在许多作品中使用，较为常见的是综合织体。这些不同的伴奏织体的歌曲，极大限度的发挥了钢琴的艺术表现力，起到了渲染歌曲氛围，揭示内心情感，塑造歌曲背景的重要作用。钢琴伴奏成为整体乐思不可缺少的部分。优秀的钢琴伴奏织体，对发掘歌曲内涵，表现音乐形象，构架诗词与音乐之间的桥梁等方面具有很大的意义。在不断发展和探索中，也将许多伴奏织体使用得非常娴熟精确。 二、青主艺术歌曲《我住长江头》中钢琴伴奏的特点 《我住长江头》原词模仿民歌风格，抒写一个女子怀念其爱人的深情。青主以清新悠远的音乐体现了原词的意境，而又别有寄寓。歌调悠长，但有别于民间的山歌小曲；句尾经常出现下行或向上的拖腔，听起来更接近于吟哦古诗的意味，却又比吟诗更具激情。钢琴伴奏以江水般流动的音型贯穿全曲，衬托着气息宽广的歌唱，象征着绵绵不断的情思。由于运用了自然调式的旋律与和声，显得自由舒畅，富于浪漫气息，并具有民族风味。最有新意的是，歌曲突破了“卜算子”词牌双调上、下两阕一般应取平行反复结构的惯例，而把下阕单独反复了三次，并且一次比一次激动，最后在全曲的高音区以ff结束。这样的处理突出了思念之情的真切和执著，并具有单纯的情歌所没有的昂奋力量。这是因为作者当年是大革命的参加者，正被反动派通缉，才不得不以破格的音乐处理，假借古代的