The probability for primordial black holes

We consider two quantum cosmological models with a massive scalar field: an ordinary Friedmann universe and a universe containing primordial black holes. For both models we discuss the complex solutions to the Euclidean Einstein equations. Using the probability measure obtained from the Hartle-Hawking no-boundary proposal, we find that the only unsuppressed black holes start at the Planck size but can grow with the horizon scale during the roll down of the scalar field to the minimum

Stability in Cosmology, from Einstein to Inflation

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: (1) Einstein’s static universe and Eddington’s demonstration of its instability, and (2) the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one

Living God Pandeism: Evidential Support

Pandeism is the belief that God chose to wholly become our Universe, imposing principles at this Becoming that have fostered the lawful evolution of multifarious structures, including life and consciousness. This article describes and defends a particular form of pandeism: living God pandeism (LGP). On LGP, our Universe inherits all of God's unsurpassable attributes—reality, unity, consciousness, knowledge, intelligence, and effectiveness—and includes as much reality, conscious and unconscious, as is possible consistent with retaining those attributes. God and the Universe, together “God-and-Universe,” is also eternal into the future and the past. The article derives testable hypotheses from these claims and shows that the evidence to date confirms some of these while falsifying none. Theism cannot be tested in the same way

Stability in Cosmology, from Einstein to Inflation

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: (1) Einstein’s static universe and Eddington’s demonstration of its instability, and (2) the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one

God created the integers: the mathematical breakthroughs that changed history

Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians