If the Universe was birthed from a singularity which became a black hole, then our universe black hole would be spewing Hawking Radiation. The mass of the black hole would be decreasing. Thus time dilation from mass would be decreasing. This would give the appearance of expanding space/time in the radial direction. The rate of hawking radiation would be increasing due to inverse relationship of blackhole size and radiation. Thus the mass loss rate is increasing, and thus the time dilation rate change would be increasing, and thus the expansion rate would appear to be increasing.