Study of the anisotropy of cosmic expansion on ZTF type Iasupernovae simulations

TL;DR

The paper probes the isotropy of cosmic expansion by targeting a possible dipole in the Hubble constant $H_0$ using ZTF Type Ia supernova simulations. It introduces and compares three dipole-injection schemes in simulated data, then develops a multi-step fitting procedure to recover the dipole amplitude $\Delta H_0$ and its direction $(\alpha_0,\delta_0)$, while simultaneously standardizing SN Ia light curves. The authors find that injecting the dipole via the magnitude method ($m_B$-method) yields unbiased amplitude recovery, e.g., $\Delta H_0 = 3.01 \pm 0.19$ km s$^{-1}$ Mpc$^{-1}$, with directional uncertainties of a few degrees; including large-scale structure maintains robustness with $\Delta H_0 = 3.05 \pm 0.33$ km s$^{-1}$ Mpc$^{-1}$. They also demonstrate that peculiar velocities can mimic a spurious dipole in the absence of an injected signal, necessitating an explicit error model combining statistical and systematic components. The study establishes a viable framework for applying the method to ZTF DR2.5/DR3 data and future surveys (e.g., LSST) to test the cosmological principle with greater precision.

Abstract

The cosmological principle assumes the isotropy of the Universe at large scales. It is a foundational assumption in the $Λ$CDM model, which is the current standard model of cosmology. Recent tensions give legitimacy to investigating the possibility of anisotropies in the Universe. The large sky coverage achieved by the Zwicky Transient Facility survey (ZTF) allows us to test the veracity of the cosmological principle using observations of Type Ia supernovae (SNe Ia). In this article, we develop a methodology to measure potential anisotropies in the Hubble constant $H_0$. We test our method on realistic simulations of the second data release (DR2) of ZTF SNe Ia in which we introduce a dipole. We develop an unbiased method both to introduce a dipole in the simulations and to recover it. We test a potential $H_0$ dependency of our method while varying the dipole amplitude. We analyse the impact of introducing large-scale structures in the simulations and the efficiency of using a volume-limited sample, which is an unbiased subsample of the ZTF SNe Ia sample. Finally, we build an error model applied to the recovered dipole amplitude ($ΔH_0$) and its direction ($α_0$, $δ_0$). Our analysis allows us to recover a dipole with an error on the amplitude of $0.33\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, and uncertainties of $3.4^\circ$ and $6.1^\circ$ on the right ascension and declination, respectively, for an initial dipole amplitude of $ΔH_0 = 3\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The resulting dipole is independent of the chosen $H_0$ value and sky coverage. This paper paves the way for a future precise ZTF dipole investigation.

Figures (16)

• Figure 1: Skymap colored following the amplitude of the dipole, with the black stars representing the initial dipole direction of an amplitude of $3~\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The orange triangles are the fit directions for the 20 simulations when the $m_B$-method is used. The fitted amplitude in the legend corresponds to the median value over the 20 simulations.
• Figure 2: Fit for the $z$-method on the top panel, the $m_B$-method on the middle, and the $d_l$-method on the bottom. Left to right, the result for the 20 simulations for the dipole amplitude, $\Delta H_0$, the right ascension, $\alpha_0$, and the declination, $\delta_0$. In each panel, the initial value is represented with the black dashed line, and the median of the twenty simulation fits is in the gray line with the $1\sigma$ error represented by the gray band. For those fits, the SNe Ia colors and stretches are the ones input in the simulations.
• Figure 3: Skymap with the number of the initial dipole introduced. We used the center of each different patches here to obtained the 48 different dipole location. The color of each patches allow to differentiated the 48 different location of dipole.
• Figure 4: Difference between the output of the fit and the true value. From left to right for the dipole amplitude, the $\alpha_0$, and the $\delta_0$ directions of the dipole. The green line is for the $z$-method introduced in Sec. \ref{['sec:methodo_dip_z']}, in blue for the $m_B$-method introduced in Sec. \ref{['sec:methodo_dip_mb']}, and in pink for the $d_l$-method. The pink band corresponds to the typical error for the three methods. The medians are done in the label for the three different methods. As for Fig. \ref{['fig:Compa_fit_3methode']}, the SNe Ia colors and stretches are the ones input in the simulations.
• Figure 5: Skymap of the 48 different dipole fits, with the $m_B$-method, for 20 independent simulations, and using the SALT color and stretch parameters. Each cross corresponds to the input location of the 48 dipoles, and is colored according to the median of the 20 simulations sensitivity, as shown with the colorbar on the left. Each cross is associated with a patch which is colored according to the median to the difference between the input (here $3~\mathrm{km\,s^{-1}\,Mpc^{-1}}$) and output amplitude of the dipole. All the gray ellipses are centered on the median of the different simulation fits, the ellipses represent the $1\sigma$ deviations of the fitted direction ($\sigma_{\alpha_0},\sigma_{\delta_0}$).