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Constraining the Lattice Fluid Dark Energy from SNe Ia, BAO and OHD

2012年两岸粒子物理与宇宙学研讨会. Constraining the Lattice Fluid Dark Energy from SNe Ia, BAO and OHD. 报告人： 段效贤 中国科学院国家天文台. Outline . Lattice Fluid Dark Energy Model Constraint from SNe Ia Constraint from BAO Constraint from OHD Result Conclusions and Discussions.

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Constraining the Lattice Fluid Dark Energy from SNe Ia, BAO and OHD

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  1. 2012年两岸粒子物理与宇宙学研讨会 Constraining the Lattice Fluid Dark Energy from SNe Ia, BAO and OHD 报告人： 段效贤 中国科学院国家天文台

  2. Outline • Lattice Fluid Dark Energy Model • Constraint from SNe Ia • Constraint from BAO • Constraint from OHD • Result • Conclusions and Discussions

  3. Lattice Fluid Dark Energy Model The equation of state of Lattice Fluid Dark Energy can be written as whereρXandpXare the energy density and pressure ofthe fluid, respectively. Ais a dimensionless constant, ρ0is the present-day cosmic energy density defined byρ0 =3H02/8π withH0the present- day Hubble parameter.

  4. "Statistical Thermodynamics of Polymer Solutions", by Isaac C. Sanchez, Robert H. Lacombe, Macromolecules (1978), Volume: 11, Issue: 6, Pages: 1145-1156.

  5. Now we study the evolution of the Universe filled withmatter (includes baryon matter and dark matter), radiation and LFDE. The metric of FRW Universe is givenby: wherea(t) is the scale factor andK= +1, 0, -1 describethe topology of the Universe which correspond to closed,flat and open Universe, respectively.

  6. The scale factor evolves according to the Friedmannequation: whereρtotalis the total energy density of the Universe. Observations reveal that the Universe is highly flat inspace. So we put K= 0 in the following. Then theFriedmann equation can be written as whereρm/a3andρr/a4are the energy density of matter andradiation, respectively; ρmandρrare respectively theenergy density of matter and radiation in the present-day Universe.

  7. In order to obtain ρX, we substitute the equation ofstate for LFDE Eq. (1) into the energy conservation equation: Keeping in mind the relation1/a= 1 +z and definingΩX≡ρX/ρ0, we obtain the energy conservation equation asfollows This ordinary differential equation could not be solvedanalytically. So we are going to study the numerical solution by using the observational data from SNeIa, BAO and OHD.

  8. Constraint from SNe Ia The luminosity distancedLof SNe Ia is defined by wherecis the speed of light. The function E(z) is definedby where Ωr ≡ρr/ρ0, is the sum of photons and relativisticneutrinos whereNeffis the effective number of neutrino species(the standard value of Neffis 3.04), Ωγ= 2.469×10−5h−2for TCMB= 2.725K.

  9. The theoretical distance modulus is defined by The observed distance modulus is listed in the dataset of Union 2.1. Then we can calculate theχ2SNeIa whereCSNis the contravariant matrix which includesthe systematical errors for the SNe Ia data, could be found in the dataset of Union 2.1.

  10. where cs(z) is the sound speed, cs(z)= and = 3Ωb/4Ωγ。 Constraint from BAO We used the measurements derived from observationdata of the 6dFGS, the distribution of galaxies fromthe Sloan Digital Sky Survey Data(SDSS) Release 7Galaxy Sampleand the WiggleZ Dark Energy Survey. The BAO relevant distance measure is modelled byvolume distance, which is defined by The comoving sound horizon is defined by

  11. We could get the distance ratio wherezdis the drag redshift defined in D.J. Eisenstein et. al., Astrophys. J. 496,605 (1998). Beutleret al. derived the measurement from 6dFGS that the observed dobsz=0.106= 0.336±0.015. Percivalet al. measured the distance ratio at two redshifts:dobsz=0.2= 0.1905±0.0061,dobsz=0.35= 0.1097±0.0036. The acoustic parameter is defined by

  12. From the WiggleZ Dark Energy Survey, Blakeet al.measured the acoustic parameter at three redshifts, Aobs(z = 0.44) = 0.474±0.034, Aobs(z = 0.6) = 0.442±0.020, Aobs(z = 0.73) =0.424±0.021. Then we could get theχ2BAO

  13. Constraint from OHD Relative Galaxy Ages can also be used to constrain cos-mological parameters. Given the measurement of theage difference of two passively-evolving galaxies formednearly at the same time,δt, and the small redshift intervalδz by which they are separated, the ratioδz/δtcould becalculated. Then we can infer the derivative:dz/dt. The quantity measured in the method above is directlyrelated to the Hubble parameter:

  14. we take the observational data at 15 different redshifts in J. Xu, and Y. Wang, JCAP. 1006, 002 (2010):12 of them are fromGemini Deep Survey (GDDS), SPICES, VVDS, and KeckObservations; 3 more available data in where the authors obtained : H(z = 0.24) =79.69±2.32, H(z = 0.34) = 83.8±2.96, and H(z =0.43) = 86.45±3.27, by using the BAO peak positionas a standard ruler in the radial direction. The theoretical value ofH(z) could be obtainedfrom Eq. (8). Thereforeχ2for Hubble data is Then the totalχ2is:

  15. Result The marginalized probability contoursat 1σ, 2σand 3σCL in theA-Ωmplane of the resultof combined constraint of SN, BAO and OHD:

  16. The evolution of the equation of statew=pX/ρX. Whenz >2.0,wis approaching -1. As the redshift decreases to 0,wincrease slightly to w= -0.937.

  17. Age of the Universe For our model, the age of the Universe is found to be 13.35 Gyr.

  18. Conclusions and Discussions We constrain the model with current cosmological observational data,find the best fit value ofparameters:A=-0.3, Ωm= 0.30. Taking the best values ofAand Ωm, we investigatethe comic implications of the model. We find the equation of state is almost the same as the ΛCDMmodel atthe redshifts greater than 2.0. For the present-day Universe, we have w=-0.937 whichis consistent with many otherobservations. The age of Universe is estimated to be 13.35 Gyr inour LFDE model. Finally, the statefinder r andsof theLFDE model evolve fromr = 1.0, s = 0 (which is thevalue of ΛCDM Universe) at high redshifts to the presentvalues:r= 0.572,s= 0.144.

  19. Thank you!

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