Einstein, Barcelona, Symmetry & Cosmology: The Birth of an Equation for the Universe

Abstract

Albert Einstein visited Spain only once, precisely one hundred years ago. The circumstances, of a very different kind, of this visit will be explained here. In special, some important events happened to Einstein during that period, which, eventually, were key for converting modern cosmology into a genuine physical theory. Among them is the famous Einstein-Friedmann controversy, first, on the mathematical validity of Friedmann’s equations and, later, their possible usefulness as a reliable tool to describe the real world. A summary of the deepest ideas underlying Einstein’s contributions to the theory of relativity, which he had already completed before his visit, will precede the discussion, also supplemented with a description, in very simple terms, of the three main relativistic theories, namely Galileo’s one, and Einstein’s special and general theory. They pave the way towards a definitive theory of total relativity, so far unattainable. It will be recalled that the most general relativity principle, faithfully reflecting Ernst Mach’s far-reaching ideas, might have much to do with the symmetry-breaking paradigm, a most crucial tool in quantum field theory and high energy physics.

How Much Cosmic Time Does It Take for a Star to Collapse Forming a Black Hole?

“…T 0 = 10 7 GeV correspond approximately to a cosmic time around t 0 = 10 −40 sec ∼ = 2 × 10 3 t pl , which can be taken as a minimal time where the classical evolution of the universe can be safely depicted by GR. Finally, it is important to stress that one can continue back in time, for t < t 0 , the evolution of the universe but using a new theory where General Relativity, as Einstein believed, is a limiting case (see Section 3.4 of [13]). There are some ideas to build up this extension of GR, for example, introducing quantum effects as in semi-classical gravity taking into account the vacuum energy density of massless conformally coupled fields (see, for instance, [14,15]) or loop quantum gravity [16], or modifying the Hilbert-Einstein action as in f (R) gravity [17,18].…”