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

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.