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Abstract
The persistent disagreement between locally measured and globally inferred values of the Hubble constant, commonly known as the Hubble tension, has become one of the most challenging problems in modern cosmology. While many proposed explanations involve modifications to early-Universe physics or dark energy, the possible role of local spacetime inhomogeneities and continuous matter creation remains relatively unexplored. In this work, we develop a spherically symmetric inhomogeneous cosmological model based on the Lemaître Tolman–Bondi (LTB) spacetime within the framework of the Hoyle–Narlikar C-field theory. The model introduces a curvature-dependent matter creation mechanism, in which the creation rate is governed by the local spatial curvature gradient inside a cosmic under-density. The modified Einstein field equations are solved analytically to obtain the localized Misner–Sharp mass, position-dependent expansion parameters, and other relevant kinematical quantities. Numerical illustrations show that the proposed mechanism naturally enhances the local expansion rate within the under-dense region while gradually approaching the standard homogeneous cosmological behaviour at large distances. As a result, the model provides a physically consistent framework in which local and global measurements of the Hubble parameter can differ without altering the large-scale evolution of the Universe. These findings suggest that curvature-coupled matter creation in an inhomogeneous spacetime offers a promising theoretical perspective for understanding the Hubble tension and encourages further observational and phenomenological investigations.
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