Characterising galaxy cluster scaling relations as cosmic isotropy tracers using FLAMINGO simulations

The standard cosmological model, $\Lambda$CDM, assumes isotropy on large cosmic scales. However, recent studies using galaxy cluster scaling relations have reported an apparent $H_0$ anisotropy at $5.4\sigma$ that could be attributed to large bulk flows extending beyond ${500}\,\mathrm{Mpc}$, which is in disagreement with $\Lambda$CDM. To quantify the statistical tension of the observational galaxy cluster data used in past studies with $\Lambda$CDM, we utilised the isotropic (${2.8}\,\mathrm{Gpc})^3$ run of the FLAMINGO ($\Lambda$CDM) simulations, the largest hydrodynamical cosmological simulation available to date. We created 1728 simulated lightcones and studied the apparent level of anisotropy traced by X-ray and thermal Sunyaev-Zeldovich scaling relations in the same cluster sample selection and methodology as in the past study. We find the probability of such apparent anisotropies randomly emerging in cluster scaling relations within a $\Lambda$CDM universe to be $0.12\%\, (3.2\sigma)$. The discrepancy goes up to $\sim 3.6\sigma$ when modelled as a bulk flow at $z < 0.1$. We also find that statistical noise accounts for over $80\%$ of the anisotropy amplitude in each lightcone, with large peculiar velocities contributing less than $20\%$. We also show that anisotropy amplitudes are highly sensitive to the intrinsic scatter in the scaling relations, with tighter relations providing stronger constraints. Nevertheless, the tension between the past results and $\Lambda$CDM persists, albeit at a lower significance than previously reported.