Redshift Drift fluctuations from N-body simulations

TL;DR

This work investigates redshift-drift fluctuations within ΛCDM by employing Gadget4 N-body simulations to compute the drift’s angular power spectrum across redshifts z = 0.5, 1, 2. Building a perturbative theory for drift fluctuations and mapping Newtonian fields to relativistic quantities, it derives and tests the drift power spectra against linear theory via CLASS and Halofit. The results show drift fluctuations of order 10^-2, increasing with redshift and displaying nonlinear features that diverge from linear predictions at large and intermediate scales. While providing a valuable baseline methodology for future analyses with surveys like SKA and ELT/ANDES, the study also emphasizes limitations due to light-cone integration, lack of baryonic physics, and finite-box effects, calling for more sophisticated simulations and relativistic treatments. Overall, the paper establishes a framework for connecting N-body simulations to real-time cosmological observables and sets the stage for forthcoming refinements as observational precision improves.

Abstract

Measurements of the redshift drift -- the real time variation of the redshift of distance sources -- are expected in the next couple of decades using next generation facilities such as the ANDES spectrograph at the ELT and the SKAO survey. The unprecedented precision of such observations will demand precise theoretical and numerical modeling of the effect in the standard $Λ$CDM cosmology. In this work, we use the \texttt{Gadget4} $N$-body code to simulate the redshift drift and its fluctuations in $Λ$CDM cosmologies, deriving the corresponding power spectra from a simulation with $1024^3$ particles in a $1\textrm{Gpc}\,h^{-1}$ box. Our results represent an initial step toward deriving the redshift drift fluctuation power spectra from $N$-body simulations and establishing a methodology for the statistical analysis of the redshift drift effect using data from future large-scale surveys. However, further work is required to refine the approach and achieve an accurate modeling of the redshift drift fluctuation power spectra.

Figures (6)

• Figure 1: Matter power spectra for redshifts $z=0.5\,,1,\,2$. In the figures we compare two routines against the power spectra obtained from the Gadget4 simulations: the halofit routine and the linear matter power spectrum from CLASS. The vertical red lines mark $2k_\text{fund}$ and $k_\text{Nyq}/2$.
• Figure 2: Angular power spectrum of matter for redshifts $z=0.5\,,1,\,2$. The power spectra are calculated in three different ways: using the CLASSgal code, using the FFTlog routine to obtain the angular spectra from the matter power spectrum of the simulation, and using the Limber approximation for the angular spectra from the simulation. The vertical red lines mark $2 \ell_\text{fund}$ and $\ell_\text{Nyq}/2$.
• Figure 3: Velocity gradient power spectra $P_{\theta\theta}(k)$ obtained from the class code (red), from the Pylians3 routine (blue) and from the continuity equation \ref{['eq:continuity']} (orange).
• Figure 4: Histogram for the redshift drift fluctuations in the simulation box for redshifts $z=0.5,\,1,\,2$. We plot a normal distribution with the same standard deviation for comparison (dashed blue), highlighting a strong kurtosis.
• Figure 5: Adimensional redshift drift power spectra at redshifts $z=0.5,\,1,\,2$ with and without shot noise. The solid lines give the estimated spectra minus the shot noise and the dashed lines give the full estimated spectra. The vertical red lines mark $2k_\text{fund}$ and $k_\text{Nyq}/2$.