Nonlinear matter spectra in coupled quintessence

We consider cosmologies in which a dark-energy scalar field interacts with cold dark matter. The growth of perturbations is followed beyond the linear level by means of the time-renormalization-group method, which is extended to describe a multicomponent matter sector. Even in the absence of the extra interaction, a scale-dependent bias is generated as a consequence of the different initial conditions for baryons and dark matter after decoupling. The effect is enhanced significantly by the extra coupling and can be at the 2%–3% level in the range of scales of baryonic acoustic oscillations. We compare our results with $N$-body simulations, finding very good agreement.

Figure 1

Comparison of results from $N$-body simulations and our calculation ($\beta =0.05$). We display the ratio of the nonlinear and linear spectra for $z=0$.

Figure 2

Comparison of results from $N$-body simulations and our calculation ($\beta =0.1$). We display the ratio of the nonlinear and linear spectra for $z=0$.

Figure 3

Dark matter density-density spectra for various $\beta$ at $z=0$, normalized with respect to the smooth function of 44. The spectra have been multiplied by an additional $\beta$-dependent factor in order to be equal to 1 for $k\to 0$. We indicate the maximum $k$ for which a certain level of accuracy is achieved by TRG and SPT.

Figure 4

Baryonic matter density-density spectra for various $\beta$ at $z=0$, normalized similarly to those in Fig. 3.

Figure 5

Dark matter velocity-velocity spectra for various $\beta$ at $z=0$, normalized similarly to those in Fig. 3.

Figure 6

The bias in the BAO region for $z=1.12$.