Structure formation in a $\mathrm{\Lambda }$ viscous CDM universe

The possibility of dark matter being a dissipative component represents an option for the standard view where cold dark matter (CDM) particles behave on large scales as an ideal fluid. By including a physical mechanism in the dark matter description like viscosity, we construct a more realistic model for the Universe. Also, the known small scale pathologies of the standard CDM model either disappear or become less severe. We study clustering properties of a $\mathrm{\Lambda }\mathrm{CDM}$-like model in which dark matter is described as a bulk viscous fluid. The linear power spectrum, the nonlinear spherical "top hat" collapse, and the mass functions are presented. We use the analysis with such structure formation tools in order to place an upper bound on the magnitude of the dark matter’s viscosity.

Figure 1

Top panel: Dark matter perturbation growth as a function of the redshift. We assume ${\mathrm{\Omega }}_{\mathrm{dm}0}={\mathrm{\Omega }}_v=0.27$ with, from top to bottom, $\tilde{\xi }=0.1$ and 0.05, fixing $\nu =0$. Bottom panel: Relative growth with respect to the $\mathrm{\Lambda }\mathrm{CDM}$ case, i.e., $\frac{{\delta }_{\mathrm{dm}}}{{\delta }_v}-1$.

Figure 2

Top panel: Baryonic perturbation growth as a function of the redshift. ${\mathrm{\Omega }}_{\mathrm{dm}0}={\mathrm{\Omega }}_v=0.27$ with, from top to bottom, $\tilde{\xi }=0.1$ and 0.05, fixing $\nu =0$. Bottom panel: Relative growth with respect to the $\mathrm{\Lambda }\mathrm{CDM}$ case, i.e., $\frac{{\delta }_b^{\mathrm{\Lambda }\mathrm{CDM}}}{{\delta }_b^{\mathrm{\Lambda }\mathrm{vCDm}}}-1$.

Figure 3

Expansion of the collapsed region. ${\mathrm{\Omega }}_{\mathrm{dm}0}={\mathrm{\Omega }}_v=0.27$ with, from top to bottom, $\tilde{\xi }=0.1$ and 0.05, fixing $\nu =0$.

Figure 4

Value of ${\delta }_c$. ${\mathrm{\Omega }}_{\mathrm{dm}0}={\mathrm{\Omega }}_v=0.27$ with, from top to bottom, $\tilde{\xi }=0.1$ and 0.05 fixing $\nu =0$.

Figure 5

Linear matter power spectrum at $z=0$, for viscosity parameter in the range $10^{-5}>\tilde{\xi }>10^{-7}$. The relative computed values of ${\sigma }_8$ are also shown. The red solid line represents the $\mathrm{\Lambda }\mathrm{CDM}$ reference.

Figure 6

Sheth and Thormen’s predictions [18] at $z=0$, for a viscosity parameter in the range $10^{-5}>\tilde{\xi }>10^{-7}$, assuming linear density contrast ${\delta }_c=1.69$. The red solid line shows the $\mathrm{\Lambda }\mathrm{CDM}$ reference.