ABSTRACT The scalar field dark matter (SFDM) model, also called Fuzzy, Wave, Bose–Einstein, and Ultra-light Dark Matter, has received a lot of attention because it has been able to provide simpler and more natural explanations for various features of galaxies, such as the number of satellite galaxies and the cusp-core problem. We recently showed that this model is able to explain the vast polar orbits of satellite galaxies around their host, the so-called VPO, and to explain the X-ray and gamma-ray emissions in the vacuum regions of our galaxy, that is, the Fermi Bubbles. In all these phenomena, the quantum character of SFDM has been crucial. In this work, we study the quantum effects of SFDM at the cosmological level, to see these effects not only at the galactic scale, but also at the cosmological scale. Using a convenient ansatz, we were able to integrate the perturbed equations to show that the shape of the SFDM haloes resembling atoms is a generic result. The main conclusion of this work is that quantum mechanics, the successful microworld theory, could also explain the dark side of the Cosmos.