Spatial Curvature and Thermodynamics

Reasonable parametrizations of the current Hubble data set of the expansion rate of our homogeneous and isotropic universe, after suitable smoothing of these data, strongly suggests that the area of the apparent horizon increases irrespective of whether the spatial curvature of the metric is open, flat or closed. Put in another way, any sign of the spatial curvature appears consistent with the second law of thermodynamics.