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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 62 , Issue 12 : 120411(2019) https://doi.org/10.1007/s11433-019-9439-8

Models of vacuum energy interacting with cold dark matter: Constraints and comparison

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  • ReceivedMay 18, 2019
  • AcceptedMay 23, 2019
  • PublishedJun 18, 2019
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Abstract


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11875102, 11835009, 11522540, and 11690021), the National Program for Support of Top-Notch Young Professionals, and Doctoral Research Project of Shenyang Normal University (Grant Nos. BS201844, and BS201702).


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  • Figure 1

    (Color online) Graphical representation of the results of $\Delta$AIC and $\Delta$BIC for the I$\Lambda$CDM models.

  • Figure 2

    (Color online) The SN+CMB+BAO+$H_0$ constraints on the I$\Lambda$CDM models. The 68.3% and 95.4% confidence level contours are shown in the $\Omega_{\rm{m0}}$-$\beta$ plane. The red dashed line denotes the case of $\beta=0$.

  • Figure 3

    (Color online) The SN+CMB+BAO+$H_0$ constraints on the I$\Lambda$CDM models. The 68.3% and 95.4% confidence level contours are shown in the $\beta$-$h$ plane. The red dashed line denotes the case of $\beta=0$.

  • Figure 4

    (Color online) One-dimensional marginalized posterior distributions of the parameter $\beta$ for the I$\Lambda$CDM models, from the SN + CMB + BAO + $H_0$ data. The pink dashed line denotes the case of $\beta=0$.

  • Figure 5

    (Color online) The two-dimensional marginalized contours (1$\sigma$ and 2$\sigma$) in the $\Omega_{\rm~m}$–$\beta$ plane and the one-dimensional marginalized distributions of $\beta$ for the I$\Lambda$CDM model with $Q=-\beta~H\rho_{\rm~c}$ by using the Planck+BSH and Planck+BSH+LSS data. The red dashed line denotes the case of $\beta=0$.

  • Figure 6

    (Color online) The two-dimensional marginalized contours (1$\sigma$ and 2$\sigma$) in the $\Omega_{\rm~m}$-$\beta$ plane and the one-dimensional marginalized distributions of $\beta$ for the I$\Lambda$CDM model with $Q=-\beta~H\rho_{\rm~vac}$ by using the Planck+BSH and Planck+BSH+LSS data. The red dashed line denotes the case of $\beta=0$.

  • Table 1   Summary of the information criteria results
    Model $\chi^2_{\rm~min}$ $\Delta$AIC $\Delta$BIC
    $\Lambda$CDM$699.3776$$0$$0$
    I$\Lambda$CDM1$699.1004$$1.7228$$6.3402$
    I$\Lambda$CDM2$699.0236$$1.6460$$6.2634$
    I$\Lambda$CDM3$699.0638$$1.6862$$6.3036$
    I$\Lambda$CDM4$699.0656$$1.6880$$6.3054$
    I$\Lambda$CDM5$699.1012$$1.7236$$6.3410$
    I$\Lambda$CDM6$698.5856$$1.2080$$5.8254$
    I$\Lambda$CDM7$698.7272$$1.3496$$5.9670$
    I$\Lambda$CDM8$699.0852$$1.7076$$6.3250$
  • Table 2   Fitting results of the $\Lambda$CDM model and the I$\Lambda$CDM models with $Q=\beta~H_{0}\rho$.Best-fit values with $\pm1\sigma$ errors are presented
    Parameter $\Lambda$CDM I$\Lambda$CDM1 I$\Lambda$CDM2 I$\Lambda$CDM3 I$\Lambda$CDM4
    $\Omega_{\rm{m0}}$ $0.3236^{+0.0074}_{-0.0080}$$0.3203^{+0.0072}_{-0.0082}$$0.3189^{+0.0089}_{-0.0066}$$0.3201^{+0.0077}_{-0.0080}$$0.3197^{+0.0077}_{-0.0074}$
    $\Omega_{\rm{b0}}$ $0.0498^{+0.0007}_{-0.0007}$$0.0498^{+0.0008}_{-0.0009}$$0.0495^{+0.0009}_{-0.0006}$$0.0498^{+0.0007}_{-0.0009}$$0.0498^{+0.0008}_{-0.0008}$
    $\beta$$-0.0110^{+0.0186}_{-0.0179}$$-0.0098^{+0.0152}_{-0.0151}$$-0.0063^{+0.0091}_{-0.0070}$$-0.0270^{+0.0429}_{-0.0385}$
    $h$$0.6673^{+0.0059}_{-0.0051}$$0.6691^{+0.0061}_{-0.0054}$$0.6706^{+0.0048}_{-0.0061}$$0.6696^{+0.0060}_{-0.0055}$$0.6696^{+0.0056}_{-0.0056}$
  • Table 3   Fitting results of the $\Lambda$CDM model and the I$\Lambda$CDM modelswith $Q=\beta~H\rho$. Best-fit values with $\pm1\sigma$ errors are presented
    Parameter $\Lambda$CDM I$\Lambda$CDM5I$\Lambda$CDM6I$\Lambda$CDM7I$\Lambda$CDM8
    $\Omega_{\rm{m0}}$ $0.3236^{+0.0074}_{-0.0080}$$0.3205^{+0.0072}_{-0.0084}$$0.3197^{+0.0086}_{-0.0072}$$0.3204^{+0.0073}_{-0.0080}$$0.3201^{+0.0076}_{-0.0081}$
    $\Omega_{\rm{b0}}$ $0.0498^{+0.0007}_{-0.0007}$$0.0498^{+0.0008}_{-0.0009}$$0.0484^{+0.0013}_{-0.0009}$$0.0490^{+0.0009}_{-0.0008}$$0.0498^{+0.0008}_{-0.0009}$
    $\beta$$-0.0091^{+0.0151}_{-0.0157}$$-0.0064^{+0.0066}_{-0.0045}$$-0.0038^{+0.0044}_{-0.0039}$$-0.0202^{+0.0323}_{-0.0309}$
    $h$$0.6673^{+0.0059}_{-0.0051}$$0.6692^{+0.0064}_{-0.0052}$$0.6796^{+0.0079}_{-0.0112}$$0.6748^{+0.0074}_{-0.0071}$$0.6697^{+0.0058}_{-0.0057}$
  • Table 4   Fitting results of the I$\Lambda$CDM models with $Q=\beta~H\rho_{\rm~vac}$ from different datasets. Best-fit values with $\pm1\sigma$ errors are presented
    Parameter CMB BAOSN$H_{0}$
    $\Omega_{\rm{m0}}$ $0.5256^{+0.0791}_{-0.3107}$$0.4577^{+0.0691}_{-0.3326}$$0.3713^{+0.0539}_{-0.0957}$$0.8918^{+0.7060}_{-0.8806}$
    $\Omega_{\rm{b0}}$ $0.0710^{+0.0072}_{-0.0340}$$0.1091^{+0.1216}_{-0.0991}$$0.2594^{+0.1521}_{-0.2494}$$0.5960^{+0.4040}_{-0.5859}$
    $\beta$$-0.5461^{+0.6280}_{-0.4539}$$0.9671^{+0.0328}_{-1.9671}$$0.7202^{+0.2798}_{-0.8374}$$0.2719^{+0.7281}_{-1.2719}$
    $h$$0.5603^{+0.2134}_{-0.0276}$$0.6532^{+0.3468}_{-0.2655}$$0.4881^{+0.5119}_{-0.1881}$$0.7060^{+0.0330}_{-0.0330}$
  • Table 5   Fitting results of the I$\Lambda$CDM models with $Q=\beta~H\rho_{\rm~c}$ from different datasets.Best-fit values with $\pm1\sigma$ errors are presented
    Parameter CMB BAOSN$H_{0}$
    $\Omega_{\rm{m0}}$ $0.3044^{+0.3188}_{-0.1188}$$0.4266^{+0.1192}_{-0.1617}$$0.3538^{+0.0458}_{-0.0729}$$0.8683^{+0.7307}_{-0.8574}$
    $\Omega_{\rm{b0}}$ $0.0490^{+0.0010}_{-0.0263}$$0.0449^{+0.1254}_{-0.0349}$$0.0224^{+0.2829}_{-0.0124}$$0.5786^{+0.4214}_{-0.5684}$
    $\beta$$0.0051^{+0.0850}_{-0.0955}$$0.8252^{+0.1748}_{-0.9324}$$0.8651^{+0.1349}_{-1.18544}$$-0.4657^{+1.4657}_{-0.5343}$
    $h$$0.6742^{+0.3174}_{-0.0088}$$0.3804^{+0.6196}_{-0.0633}$$0.8290^{+0.1710}_{-0.5290}$$0.7060^{+0.0330}_{-0.0330}$
qqqq

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