Nonlinear evolution of initially biased tracers in modified gravity

Abstract

In this work we extend the perturbation theory for modified gravity (MG) in two main aspects. First, the construction of matter overdensities from Lagrangian displacement fields is shown to hold in a general framework, allowing us to find Standard Perturbation Theory (SPT) kernels from known Lagrangian Perturbation Theory (LPT) kernels. We then develop a theory of biased tracers for generalized cosmologies, extending already existing formalisms for ΛCDM. We present the correlation function in Convolution-LPT and the power spectrum in SPT for ΛCDM, f (R) Hu-Sawicky, and DGP braneworld models. Our formalism can be applied to many generalized cosmologies and to facilitate it, we are making public a code to compute these statistics. We further study the relaxation of bias with the use of a simple model and of excursion set theory, showing that in general the bias parameters have smaller values in MG than in General Relativity.

Marked correlation functions in perturbation theory

“…However, we do not obtain larger differences in the bias of MG and GR for more massive halos as predicted in the peak-background split formalism. This may be an indication of a breakdown of bias models that assume conservation of tracers [33,35,64]: for example, it is known that in F4 fewer small mass halos survive because of a faster merging rate than in GR [26]. We also note that the number of available halos in the interval log 10 M > 13.5 is quite limited due to the limited size of the simulations so the scatter in the correlation function is large.…”

“…, (A.6) and the second order growth functions, D (2) , are the solutions to equations [31][32][33] (T − A(k))D…”

“…section 8.3 of [43] and ref. [33]. Hence, we will introduce curvature bias, as well as tidal bias, later in appendix D. In order for some quantities to be well defined, we also smooth matter overdensities with a scale R Λ that we take to be ideally R Λ R, hence we simply denote δ = δ Λ ; at the end, in numerical calculations we set R Λ = 0.…”

“…Schematically, these two quantities appear in the combination ν c = δ c (M )/σ 2 (M ), hence one expects to obtain b MG < b GR . In figure 4 we show the linear and second order local biases for halos obtained with the Sheth-Tormen like prescription of [33] and averaged over mass bins as in refs. [35,45].…”

“…These are constructed by 2-and 3-point correlations of Lagrangian displacements, and are well known in the literature; we refer the reader to the above references for their expressions in ΛCDM, and to refs. [31,33] for MG. In this section we display those functions that are not presented in the above references but are necessary for the marked correlation functions.…”