We present a summary of the findings in energy-momentum powered gravity (EMPG) model studied in O Akarsu, N. Katirci, S. Kumar, Phys. Rev. D 97 (2018) 024011. In contrast to theories of non-linear gravity, which are based on generalizing the Einstein-Hilbert curvature contribution to the Lagrangian, we consider non-linear contributions of the usual energy-momentum tensor to the matter Lagrangian. We consider a particular form of them as $f(T_{\mu\nu}T^{\mu\nu})$ as $f(T_{\mu\nu}T^{\mu\nu})=\alpha(T_{\mu\nu}T^{\mu\nu})^{\eta}$, where $\alpha$ and $\eta$ are real constants, dubbed as energy-momentum powered gravity (EMPG). We look for viable cosmologies arising from EMPG in the context of the late-time accelerated expansion of the Universe at the background level. We obtain late time acceleration in a dust-dominated Universe without invoking dark energy source like cosmological constant. With a recent compilation of 28 Hubble parameter measurements, we constrain the parameters of the EMPG model and we conclude that, although the underlying physics in the EMPG model is entirely different in the sense that the energy in the EMPG Universe is sourced by pressureless matter only, this model describes an evolution of the Universe similar to that in the $\Lambda$CDM model.