Venue: G. O. Jones 516
In this talk I will first give an overview of the pervasive role of black holes in cosmology, astrophysics and particle physics. In particular, I will emphasize their crucial role in llinkng macrophysics and microphysics. I will then focus on the ‘separate universe’ problem, a topic which I addressed both in my first published paper 40 years ago and in my last published paper before retirement. The claim that an overdense (positive curvature) region in the early universe cannot extend beyond some maximum scale and remain part of our universe, ﬁrst made by myself and Hawking, has recently been questioned by Kopp et al., who argue that one cannot constrain the form of primordial density perturbations using this argument. However, the notion of a separate-universe scale still applies and it places an important upper limit on the mass of primordial black holes forming at any epoch. Harada and myself have calculated this scale for equations of state of the form p = kρ, reﬁning earlier calculations on account of the Kopp et al. criticisms. For −1/3 < k < ∞, the scale is always of order the cosmological particle horizon size, with a numerical factor depending on k, and this conﬁrms the earlier claim that a primordial black hole cannot be much larger than the particle horizon at formation. For −1 < k < −1/3, as expected for some periods in the history of the universe, the situation changes radically, in that a suﬃciently large positive-curvature region produces a baby universe rather than a black hole. There is still a separate-universe scale but the interpretation of these solutions requires care.