In this study, we consider constructing a cosmological model for the Maxwell
    gravity. Inspired by the Einstein-Yang-Mills theory, we describe the Maxwell
    gauge field in terms of two time-dependent scalar fields. For a cosmological
    scenario, we use a homogeneous and isotropic
    Friedmann-Lemaitre-Robertson-Walker universe and derive the Friedmann equations
    together with new contributions. Then we show that the minimal model of the
    Maxwell gravity describes an expanding universe without acceleration together
    with a constant equation of state parameter in a special condition.

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