Cosmic Degeneracies I: Joint N-body Simulations of Modified Gravity and Massive Neutrinos

TL;DR

The paper tackles the problem of observational degeneracies between $f(R)$ Modified Gravity and a massive neutrino background in the nonlinear regime of structure formation. It introduces the first joint N-body simulations that evolve both extensions simultaneously, using MG-GADGET and a neutrino-particle module within GADGET3, across GR and $f(R)$ with $n=1$, $\bar{f}_{R0}=-1\times 10^{-4}$ and $\Sigma_i m_{\nu_i} \in \{0,0.2,0.4,0.6\}$ eV in a 1$\,\text{Gpc}/h$ volume, analyzing the nonlinear matter power spectrum, halo mass function, and halo bias. The key finding is that MG and neutrinos individually produce large deviations from $Λ$CDM, but their combination yields predictions that closely resemble $Λ$CDM (e.g., deviations at $z=0$ within $\sim10\%$ for $P_{mm}$, $\sim20\%$ for the HMF, and $\sim5\%$ for the bias), indicating a significant degeneracy and a theoretical limit to discriminating power without independent neutrino mass measurements. This work highlights the necessity of joint modeling of multiple extensions in cosmological analyses and suggests that high-redshift evolution or bias measurements could partially help break the degeneracy in future studies.

Abstract

We present the first suite of cosmological N-body simulations that simultaneously include the effects of two different and theoretically independent extensions of the standard $Λ$CDM cosmological scenario - namely an $f(R)$ theory of Modified Gravity (MG) and a cosmological background of massive neutrinos - with the aim to investigate their possible observational degeneracies. We focus on three basic statistics of the large-scale matter distribution, more specifically the nonlinear matter power spectrum, the halo mass function, and the halo bias, for which we determine the deviation with respect to the fiducial $Λ$CDM cosmology in the context of both separate and combined simulations of $f(R)$ MG and massive neutrinos scenarios. Our results show that while these two extended models separately determine very prominent and potentially detectable features in all the three statistics, when we allow them to be simultaneously at work these features are strongly suppressed, resulting in much weaker deviations from the standard model's predictions. In particular, when an $f(R)$ gravity model with $f_{R0}=-1\times 10^{-4}$ is combined with a total neutrino mass of $Σ_{i}m_{ν_{i}}=0.4$ eV, the resulting matter power spectrum, halo mass function, and bias at z=0 are found to be consistent with the standard model's predictions at the 10%, 20%, and 5% accuracy levels, respectively. Therefore, our results imply an intrinsic theoretical limit to the effective discriminating power of present and future observational data sets with respect to these widely considered extensions of the standard cosmological scenario in the absence of independent measurements of the neutrino masses from laboratory experiments, even though the high-redshift evolution might still allow to partially break the degeneracy [Abridged].

Figures (10)

• Figure 1: The linear matter power spectra adopted for the initial conditions of the simulations with different total neutrino mass.
• Figure 2: The nonlinear matter power spectrum ratio with respect to the fiducial model for different values of the total neutrino mass as labelled. The different panels refer to $z=0$ ( top), $z=0.6$ ( middle), and $z=1.3$ ( bottom). The grey shaded area represents the region obtained with CAMB and HALOFIT by setting all cosmological parameters to their fiducial Planck values except $\sigma _{8}$ which is allowed to vary within its 2-$\sigma$ confidence interval.
• Figure 3: As Fig. \ref{['fig:power_GR']} but for the combined simulations of $f(R)$ gravity and massive neutrinos.
• Figure 4: The matter power spectrum suppression due to the presence of massive neutrinos in both GR (solid lines) and $f(R)$ (dashed lines) models as compared to the massless neutrino case at different redshifts: $z=0$ ( left), $z=0.6$ ( middle), and $z=1.3$ ( right).
• Figure 5: The evolution of the matter density perturbations amplitude as a function of redshift normalised to the fiducial model at three different scales in the linear ($k=0.1\, h/$Mpc, left), mildly-nonlinear ($k=0.5\, h/$Mpc, middle), and nonlinear ($k=1\, h/$Mpc, right) regimes of structure formation.