Testing the imprint of nonstandard cosmologies on void profiles using Monte Carlo random walks

Using Monte Carlo random walks of a log-normal distribution, we show how to qualitatively study void properties for nonstandard cosmologies. We apply this method to an $f(R)$ modified gravity model and recover the $N$-body simulation results of [I. Achitouv, M. Baldi, E. Puchwein, and J. Weller, Phys. Rev. D 93, 103522 (2016).] for the void profiles and their deviation from GR. This method can potentially be extended to study other properties of the large scale structures such as the abundance of voids or overdense environments. We also introduce a new way to identify voids in the cosmic web, using only a few measurements of the density fluctuations around random positions. This algorithm allows us to select voids with specific profiles and radii. As a consequence, we can target classes of voids with higher differences between $f(R)$ and standard gravity void profiles. Finally, we apply our void criteria to galaxy mock catalogues and discuss how the flexibility of our void finder can be used to reduce systematic errors when probing the growth rate in the galaxy-void correlation function.

Figure 1

PDF of the Gaussian $\mathrm{\Delta }(R)$ (blue histogram) and log-normal ${\mathrm{\Delta }}_{\mathrm{LN}}(R)$ (black histogram) Monte Carlo random walks at three different smoothing scales. The solid curve shows the associated Eqs. (6) and (9).

Figure 2

Averaged void profiles from Monte Carlo random walks for the nonlinear integrated density fluctuations ${\mathrm{\Delta }}_{\mathrm{LN}}(R)$ (red curve). The light red bands show the standard deviation around this averaged profile. The corresponding linear density fluctuation is shown by the blue curve, and the black curve shows the density fluctuation ${\delta }_{\mathrm{LN}}$ computed from the integrated density fluctuations.

Figure 3

Averaged void profiles from Monte Carlo random walks for the nonlinear integrated density fluctuations ${\mathrm{\Delta }}_{\mathrm{LN}}(R)$ (red curve). The corresponding linear density fluctuation is shown by the blue curve, and the black curve show the density fluctuation ${\delta }_{\mathrm{LN}}(R)$. The dotted curves show the same for $f_{R0}=-10^{-4}$.

Figure 4

Averaged void profiles from Monte Carlo random walks for the nonlinear density fluctuations ${\delta }_{\mathrm{LN}}(R)$ for GR (black curves) and $f_{R0}=-10^{-4}$ (violet curves) in the case of different density criteria to identify voids. The void profiles with a ridge are shown by the solid curves, while the dashed curves show the ones without a ridge. The bottom panel shows the ratio between the $f(R)$ density profiles with respect to the GR ones.

Figure 5

Sample of the voids with the $3+1$ criteria (blue circles) for a slice of a mock $dz=20\mathrm{Mpc}.{\mathrm{h}}^{-1}$. Galaxies are shown by the black squares.

Figure 6

Mean density profile for the voids identified with the $3+1$ criteria using 10 mocks.

Figure 7

Mean density profile for the voids identified with the $3+1$ criteria using 10 mocks. The solid curve corresponds to the $+1$ condition $\delta (R=R_v)>0$ (same as Fig. 6) and the long-dashed curve corresponds to $\delta (R=R_v)>-0.5$, while the short-dashed curve corresponds to $\delta (R=R_v)>0.2$.

Figure 8

Mean density profile for the voids identified with the $3+1$ criteria defined in Sec. 4a and for different void sizes.

Figure 9

Mean density profile for the spurious voids identified with the $3+1$ criteria defined in Sec. 4a and for different void sizes.

Figure 10

Best fitting values for $f{\sigma }_8$ as a function of the ridge amplitude. The different colors correspond to voids with the same radius but a density fluctuation at the ridge ${\delta }_{\text{ridge}}=-0.1$, 0.1, 0.2, 0.4, 0.5, 0.6 for blue, dark green, green, orange, pink, and red squares, respectively.