A guided tour of conceptions of the universe, from the beginnings of modern science to the present.

After a brief look at the cosmological ideas of the ancients, Barrow (Mathematical Sciences/Cambridge Univ.; *100 Essential Things You Didn’t Know You Didn’t Know: Math Explains Your World*, 2009, etc.) moves on to the more rigorous formulations arising once Newton’s gravitational theory became part of the astronomer’s vocabulary. Both the time scale and the amount of space that theory needs to account for expanded radically over the course of the 19th century, until Edwin Hubble’s discovery of the expansion of the universe presented cosmology with a key data point. Even Einstein had to adapt his original idea of a static universe to Hubble’s observations by adding a fudge factor to General Relativity, the infamous cosmological constant. By that point, others were calculating what kinds of universe Einstein’s laws permitted. After Karl Schwarzschild pointed out that the universe need not conform to Euclidean geometry, alternative models proliferated: Willem de Sitter, Georges Lemaître and the Russian mathematician Alexander Friedmann found ways to tweak the known variables to find possible universes. But the expansion of the universe implied a beginning, a position developed in the 1940s by George Gamow and his associates, now known as the Big Bang. Observations reinforced the idea, and the insights of quantum mechanics began to illuminate the early moments following the initial explosion. A refinement was added in the 1980s by Alan Guth, who postulated a period of rapid inflation following the Big Bang as a solution to several problems, notably the shortage of magnetic monopoles. Barrow brings the discussion up to date by noting that observations in the 1990s forced cosmologists to propose dark matter and dark energy, two entities detectable only by their effects on normal matter. Most recently, some cosmologists propose that we inhabit a small corner of a multiverse, in which multiple universes with different laws coexist. The author covers the various possibilities clearly, with math kept to a minimum, occasionally offering his own speculations to enliven the account.

A solid overview of the evolution of cosmology, with illuminating coverage of the current state of the art. A useful complement to Roger Penrose’s *Cycles of Time* (2011).