Extended General Relativity for a Curved Universe

The recent Planck Legacy release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background, which endorses the early universe positive curvature with a confidence level exceeding 99%. Although general relativity performs accurately in the present universe where spacetime is almost flat, the necessity of dark matter/energy and the lost boundary term might be signs of its incompleteness. Utilising Einstein–Hilbert action, I present extended field equations considering the pre-existing universal curvatures. The new extended field equations are inclusive of Einstein field equations in addition to the boundary term and the conformal curvature term contributions.