Beginning with the famous Olber’s paradox, a number of cosmological paradoxes, such as the missing mass, dark energy, and the baryon-to-photon ratio, have been and are today the subject of many scientific controversies. The Big Bang model, anticipated by Lemaitre in 1927 and reformulated twenty years later by Gamow, Alpher and Herman, is one of the most spectacular successes in the entire history of physics. It remains today surrounded by considerable theoretical speculation without sufficient observational support.This book discusses such paradoxes in depth with physical and logical content and historical perspective, and has not too technical content in order to serve a wide audience.

Cosmic Paradoxes was an outcome of a Conference-Summer Course on “Astrophysical Cosmology: Frontier Questions” held at El Escorial, Madrid, on August 16–19, 1993. The Scientific Directors were John C Mather, Director of NASA’s COBE (Cosmic Background Radiation Explorer), and Jose M Torroja, Secretary of the Spanish Academy of Sciences. Julio A Gonzalo, UAM, was in charge of coordinating the event. The first speaker was Ralph A Alpher, one of the pioneers who predicted very early the CBR (Cosmic Background Radiation). The CBR was observed by A Penzias and R Wilson, Bell Telephone Labs, in 1965. Thereafter it was measured with unprecedented precision by the COBE in 1989, characterizing the Planck spectral distribution of the CBR (J C Mather) and detecting its minute anisotropies (G Smoot). In 2003 the WMAP, NASA’s satellite successor of the COBE, confirmed COBE’s results, and gave an excellent quantitative estimate of the “age” of the universe as 13.7 ± 0.2 Gyrs, in support of the Big Bang theory of cosmic origins.In the Third Edition of this book, almost coincident with the launch reports of NASA’s James Webb Space Telescope (JWST), includes recent work discussing evidence in favor of an open finite universe. A further discussion of the Heisenberg–Lemaitre time (Appendix D) takes into consideration that the cosmic expansion velocity at very early times is Ṙ(yHL)≫c and reviews in more detail the thermal history of the universe.