The second law of thermodynamics, in the presence of gravity, is known to hold at small scales, as in the case of black holes and self-gravitating radiation spheres. Using the Friedmann–Lemaître–Robertson–Walker metric and the history of the Hubble factor, we argue that this law also holds at cosmological scales. Based on this, we study the connection between the deceleration parameter and the spatial curvature of the metric,
, and set limits on the latter, valid for any homogeneous and isotropic cosmological model. Likewise, we devise strategies to determine the sign of the spatial curvature index k
. Finally, assuming the lambda cold dark matter model is correct, we find that the acceleration of the cosmic expansion is increasing today.
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