Splashback. In this main part of the chapter, we t the observed weak lensing signal using the spherical density prole presented in DK14. This prole is designed to reproduce the expected attening of the density prole at large radii due to the presence of infalling material, as seen in numerical simulations.
Splashback. Once the symmetron eld is found as a function of time, the present-day phase-space distribution of recently accreted material can be obtained by integrating numerically the equation of motion (3.4) with added fth force (3.23) for dierent collapse times. We nd that after imposing self-similarity the collapse equations can be written only as a function of three dimensionless symmetron parameters: the redshift of sym- metry breaking zssb, the dimensionless coupling β, and the ratio λ0/R(t0) between the vacuum Compton wavelength λ0 and the present-day turnaround radius R(t0). An important combination of these parameters is λ f = (1 + zssb)3β2 0 , (3.33) R2(t0) For 2 ~ ⌧ which explicitly sets the strength of the symmetron force according to Equation (3.15). From our testing, we found that values λ0/R(t0) [0.02, 0.1] oer nontrivial cases. λ R(t0) we always obtain thin-shell-like solutions, while for λ R(t0) the eld is heavy and simply relaxes onto the minimum of the potential V˜ (χ) in Equation (3.18). ~ ~ ~ In Figure 3.2 we illustrate our method and show how the symmetron force modies the phase-space conguration of the latest accreted orbits (left-side plot). We nd that the splashback position is signicantly aected for parameter values f 1, zssb 2 and λ0/R(t0) 0.1. These values imply M . 10—3Mp, which is in agreement with local tests of gravity (Hinterbichler and Khoury, 2010). ⌧ From the same gure (right-side plot), it is clear that the innermost regions of the overdensity are screened from the eects of the fth force at all times, and this becomes relevant in the outer regions only for z zssb. Past this point, the force prole slowly transitions from a thick-shell- to a thin-shell-like behavior, in which the force gets pro- gressively concentrated around the surface of the screened region (Taddei et al., 2014). Due to the sudden drop in density associated with splashback, this surface is delimited by the splashback radius. A systematic exploration of the symmetron eects on this feature as a function of all parameters is presented in Figure 3.3, which represents our main result. ' ⌧ A clear trend with zssb is visible. Notice that the fractional change on the splashback position has an optimal peak as a function of zssb that is independent of f . If we call zsp the accretion redshift of the shell currently sitting at the splashback position after its rst pericenter, i.e. the splashback shell, we see that the eect is maximized when zsp zssb. This is easily expla...
Splashback
