The IKKT matrix model is viewed as a gauge theory of space-time and matter, which arises through an analog of the Higgs effect on suitable vacua, describing 3+1 dimensional space-time branes in the weak coupling regime. In particular, we consider vacua where the SO(9,1) invariance is spontaneously broken to SO(3,1). These vacua describe a cosmological FLRW space-time, on which (an extended version of) gravity arises through quantum effects. Some progress towards understanding the resulting physics is discussed.