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Effective time variation of G in a model universe with variable space dimension

Time variation of Newtonian gravitational constant, $G$, is studied in the model universe with variable space dimension proposed recently. Using the Lagrangian formulation of these models, we find the effective gravitational constant as a function of time. To compare it with observational data, a test theory for the time variation of $G$ is formulated. We have assumed a power law behavior of the time variation of $G$ where the exponent $β$ is itself time dependent. Within this test theory we are able to restrict the free parameter of the theories under consideration and give upper bounds for the space dimension at the Planck era. The time variation of $G$ at earlier times, such as the time of nucleosynthesis is also predicted which express the needs to look for related observational data.