Unified dark fluid with fast transition: Including entropic perturbations

In this paper, we investigate a unified dark fluid model with a fast transition and entropic perturbations. An effective sound speed is designated as an additional free model parameter when the entropic perturbations are included, and, if the entropic perturbations are zero, the effective sound speed will decrease to the adiabatic sound speed. In order to analyze the viability of the unified model, we calculate the squared Jeans wave number with the entropic perturbations. Furthermore, by using the Markov Chain Monte Carlo method, we perform a global fitting for the unified dark fluid model from the type Ia supernova Union 2.1, baryon acoustic oscillation, and the full information of the cosmic microwave background measurement given by the WMAP 7 yr data points. The constrained results favor a small effective sound speed. Compared to the cosmological constant and cold dark matter, it is found that the cosmic observations do not favor the phenomenon of a fast transition for the unified dark fluid model.

Figure 1

The evolutional curves of the EoS for the UDF model when the parameter $a_t=0.68$. The red dotted, green dotted-dashed, blue dashed, and black solid lines correspond to the cases of $\beta =0.5$, 0.1, 0.05, and 0.02, respectively. The thick orange solid line is the critical state between the slow and fast transition.

Figure 2

The evolutional curves of $|1+8w_u-3w_u^2-6c_{s,ad}^2|$ for the UDF model on the interval [0.67, 0.69] when the parameter $a_t=0.68$. The red dotted, green dotted-dashed, blue dashed, and black solid lines correspond to the cases of $\beta =0.5$, 0.1, 0.05 and 0.02, respectively.

Figure 3

The effects on CMB temperature power spectra of the model parameter $\beta$. The dotted red, green dotted-dashed, blue dashed, and solid black lines are for $\beta =0.02$, 0.1, 0.3, and 0.5, respectively; the other relevant parameters are fixed with the mean values as shown in Table .

Figure 4

The evolutional curves for the radio of dark fluid and radiation ${\Omega }_u/{\Omega }_r$ when the parameter $\beta$ is varied. The dotted red, green dotted-dashed, blue dashed, and solid black lines are for $\beta =0.02$, 0.1, 0.3, and 0.5, respectively; the horizontal orange thick line responds to the case of ${\Omega }_u={\Omega }_r$, and the other relevant parameters are fixed with the mean values as shown in Table . In the early epoch, ${\Omega }_u={\Omega }_{dm}$.

Figure 5

The effects on CMB temperature power spectra of the model parameter $a_t$. The dotted red, green dotted-dashed, blue dashed, and solid black lines are for $a_t=0.5$, 0.6, 0.7, and 0.8, respectively; the other relevant parameters are fixed with the mean values as shown in Table .

Figure 6

The evolutional curves for the radio of dark fluid and radiation ${\Omega }_u/{\Omega }_r$ when the parameter $a_t$ is varied. The dotted red, green dotted-dashed, blue dashed, and solid black lines are for $a_t=0.5$, 0.6, 0.7, and 0.8, respectively; the horizontal orange thick line responds to the case of ${\Omega }_u={\Omega }_r$, and the other relevant parameters are fixed with the mean values as shown in Table . In the early epoch, ${\Omega }_u={\Omega }_{dm}$.

Figure 7

The effects on CMB temperature power spectra of the model parameter $c_{s,\mathrm{eff}}^2$. The dotted red, green dotted-dashed, blue dashed, and solid black lines are for $c_{s,\mathrm{eff}}^2=0$, 0.1, 0.5, and 1, respectively; the other relevant parameters are fixed with the mean values as shown in Table .

Figure 8

The 1D marginalized distributions on individual parameters and 2D contours with 68% C.L., 95% C.L., and 99.7% C.L. between each other using the combination of the observational data points from the full CMB information, BAO, and SNIa for the UDF model.

Figure 9

The evolutional curves of the EoS for the UDF model and one for $\Lambda \mathrm{CDM}$ model, where $w_u={\rho }_{\Lambda }/({\rho }_{\Lambda }+{\rho }_{\mathrm{CDM}})$ for $\Lambda \mathrm{CDM}$. In this figure, the red dashed line is for the UDF model with mean values as shown in Table , and the blue solid line is for $\Lambda \mathrm{CDM}$ model with mean values taken from Ref. 35 with $\mathrm{WMAP}+\mathrm{BAO}+H_0$ constraint results.

Figure 10

The CMB $C_l^{TT}$ temperature power spectra vs multipole moment $l$, where the black dots with error bars denote the observational data points with their corresponding uncertainties from WMAP 7 yr results, the red dashed line is for the UDF model with mean values as shown in Table , and the blue solid line is for the $\Lambda \mathrm{CDM}$ model with mean values taken from Ref. 35 with $\mathrm{WMAP}+\mathrm{BAO}+H_0$ constraint results.

Figure 11

The 1D marginalized distributions on individual parameters and 2D contours with 68% C.L., 95% C.L., and 99.7% C.L. between each other using the combination of the observational data points from the full CMB information, BAO, and SNIa when the effective sound speed $c_{s,\mathrm{eff}}^2$ is variable.

Figure 12

The 1D marginalized distributions on individual parameters and 2D contours with 68% C.L., 95% C.L., and 99.7% C.L. between each other using the combination of the observational data points from CMBR, BAO, and SNIa when the effective sound speed $c_{s,\mathrm{eff}}^2$ is a constant.