Whereas the nature of dark components in the Universe remains unknown, alternative models of gravity have been developed to offer a geometric explanation to the origin of such components. In this work we use the Minimal Geometric Deformation approach to study extensions of the theory of General Relativity in a cosmological context. This is possible since such approach allows the decoupling of gravitational sources, and the Einstein field equations can be analytically solved with the presence of a new gravitational sector once a known GR solution is considered. In particular, we implement such approach in Friedmann–Robertson–Walker and Kantowski–Sachs universes. We demonstrate that the gravitational decoupling leads to modifications of well known cosmological solutions. For instance, we show that an effective spatial curvature in the Friedmann–Robertson–Walker metric, as well as several kind of matter components in the Kantowski–Sachs case, are obtained. Thus, we found that it is possible to obtain spatial curvature and new matter terms from geometry, which in cosmology they could be useful in addressing problems such as the spatial flatness of the Universe, dark matter and dark energy.

尽管宇宙中暗成分的性质仍是未知的，但已经开发出了引力的替代模型来为此类成分的起源提供几何解释。在这项工作中，我们使用最小几何变形方法来研究宇宙论背景下广义相对论的扩展。这是可能的，因为这种方法允许重力源解耦，并且一旦考虑了已知的GR解，就可以在存在新的重力扇形的情况下解析爱因斯坦场方程。特别是，我们在Friedmann–Robertson–Walker和Kantowski–Sachs宇宙中实施了这种方法。我们证明了重力解耦导致了众所周知的宇宙学解决方案的修改。例如，我们证明了弗里德曼-罗伯逊-沃克度量中的有效空间曲率，以及坎图夫斯基-萨克斯案例中的几种物质成分。因此，我们发现有可能从几何学中获得空间曲率和新物质项，这在宇宙学中对解决诸如宇宙的空间平坦度，暗物质和暗能量等问题可能很有用。