A theoretical prediction for the dipole in nearby distances using cosmography

TL;DR

The paper addresses how to interpret a dipole in luminosity distances from nearby inhomogeneities without committing to a fixed background cosmology. It develops a covariant, general-relativistic cosmography framework and introduces a quiet-universe smoothing to predict the dipole, then validates this prediction against fully relativistic ray-traced distances from NR simulations. The smoothed cosmography reproduces the ray-traced dipole to within about 10% for redshifts up to ~0.07 in quasi-linear regimes and shows up to an order of magnitude improvement over unsmoothed local cosmography; nonlinear structure reduces the accuracy to ~0.02 in redshift, highlighting the importance of scale-aware averaging. The results provide a model-independent interpretation of nearby dipoles, with practical implications for analyzing low-redshift observations and guiding future surveys in the context of possible deviations from standard ΛCDM.

Abstract

Cosmography is a widely applied method to infer kinematics of the Universe at small cosmological scales while remaining agnostic about the theory of gravity at play. Usually cosmologists invoke the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric in cosmographic analyses, however generalised approaches allow for analyses outside of any assumed geometrical model. These methods have great promise to be able to model-independently map the cosmic neighborhood where the Universe has not yet converged to isotropy. In this regime, anisotropies can bias parameter inferences if they are not accounted for, and thus must be included for precision cosmology analyses, even when the principle aim is to infer the background cosmology. In this paper, we develop a method to predict the dipole in luminosity distances that arises due to nearby inhomogeneities. This is the leading-order correction to the standard isotropic distance-redshift law. Within a very broad class of general-relativistic universe models, we provide an interpretation of the dipole in terms of the gradients in expansion rate and density which is free from any underlying background cosmology. We use numerical relativity simulations, with improved initial data methods, alongside fully relativistic ray tracing to test the power of our prediction. We find our prediction accurately captures the dipole signature in our simulations to within ~10% for redshifts $z\lesssim 0.07$ in reasonably smooth simulations. In the presence of more non-linear density fields, we find this reduces to $z\lesssim 0.02$. This represents up to an order of magnitude improvement with respect to what is achieved by naive, local cosmography-based predictions. Our paper thus addresses important issues regarding convergence properties of anisotropic cosmographic series expansions that would otherwise limit their applicability to very narrow redshift ranges.

Figures (11)

• Figure 1: All-sky maps (Mollweide projection) of the ray-traced luminosity distance, $D_L$ (left panels), the dipole extracted from $D_L$ (i.e., $D_{L,{\rm dip}}$; middle panels), and the predicted dipole from the smoothed cosmography, $d_{L,{\rm dip}}$ (right panels). We show maps for one observer in the simulation with $L=2.56\,h^{-1}$ Mpc and $N=256$ on two constant-redshift slices: top row is $z\approx 0.0033$ and bottom row is $z\approx 0.0717$. For the dipoles, the fitted direction is shown with a white cross.
• Figure 2: Relative difference between the predicted dipole $d_{L,{\rm dip}}$ and the ray traced dipole $D_{L,{\rm dip}}$ as a function of redshift (smoothing scale) for a set of 20 observers in the $N=256$, $L=2.56\,h^{-1}$ Gpc simulation. The left panel shows the absolute value of the difference in amplitude for individual observers (dashed, coloured curves) and the average over all observers (solid, black curves). The right panel shows the alignment of the dipole unit direction vectors for the predicted signal ${\bf d}$ and for the ray-traced signal ${\bf D}$, for individual observers (dashed, coloured curves) and the mean over all observers (dashed, black curve). Both panels show $1\%$ and 10% differences as horizontal lines for reference and a shaded band representing the approximate numerical error floor for the calculations.
• Figure 3: Relative difference between the predicted dipole $d_{L,{\rm dip}}$ and the ray traced dipole $D_{L,{\rm dip}}$ as a function of redshift. We show the difference with only the second-order contribution to the dipole prediction (i.e. only \ref{['eq:dL2dip_av']}; dashed curves) and with both second- and third-order contributions (i.e., both \ref{['eq:dL2dip_av']} and \ref{['eq:dL3dip_av']}; solid curves). Individual observers are shown as grey curves and the mean over all observers in black. The horizontal grey dotted lines indicate a $\pm10\%$ difference.
• Figure 4: Dipole amplitude (normalised by the ray-traced monopole distance) as a function of redshift (smoothing scale) for the ray-traced dipole (solid curve), the predicted dipole from smoothing (dashed curve), and the dipole extracted from the local third-order cosmography (dotted curve). Each curve shows the average dipole amplitude across 20 observers.
• Figure 5: Left: absolute value of the relative difference in the dipole amplitude (with respect to the ray traced distance) as a function of redshift for the smoothed prediction (dashed) and the local third order comsography (dotted). Coloured curves show the difference for individual observers and the black thick curves are the average over 20 observers. Right: difference of the dot product between the predicted and ray-traced dipole direction vectors from one as a function of redshift. Solid curves show the case where ${\bf d}$ is obtained from the smoothed prediction and dotted curves are when ${\bf d}$ is from the local third order cosmography. Black curves show the mean over 20 observers for both cases. Both panels are for observers in the $N=256$, $L=2.56\,h^{-1}$ Gpc simulation.