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We investigate the impact of cosmic rays (CR) and different modes of CRtransport on the properties of Milky Way-mass galaxies in cosmologicalmagneto-hydrodynamical simulations in the context of the AURIGA project. Wesystematically study how advection, anisotropic diffusion and additionalAlfv\'en-wave cooling affect the galactic disc and the circum-galactic medium(CGM). Global properties such as stellar mass and star formation rate varylittle between simulations with and without various CR transport physics,whereas structural properties such as disc sizes, CGM densities or temperaturescan be strongly affected. In our simulations, CRs affect the accretion of gasonto galaxies by modifying the CGM flow structure. This alters the angularmomentum distribution which manifests itself as a difference in stellar andgaseous disc size. The strength of this effect depends on the CR transportmodel: CR advection results in the most compact discs while the Alfv\'en-wavemodel resembles more the AURIGA model. The advection and diffusion modelsexhibit large ($r\sim50$ kpc) CR pressure-dominated gas haloes causing asmoother and partly cooler CGM. The additional CR pressure smoothes small-scaledensity peaks and compensates for the missing thermal pressure support at lowerCGM temperatures. In contrast, the Alfv\'en-wave model is only CR pressuredominated at the disc-halo interface and only in this model the gamma-rayemission from hadronic interactions agrees with observations. In contrast toprevious findings, we conclude that details of CR transport are critical foraccurately predicting the impact of CR feedback on galaxy formation.

The effects of cosmic rays on the formation of Milky Way-mass galaxies in a cosmological context