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1. Big Bang Cosmology

The principle features of Big Bang cosmology under discussion have been a) “t=0", which represents the beginning of time in this cosmology (and thus the age of the universe), and b) the Anthropic Principle (“AP”), which points to the remarkable conditions placed on the fundamental constants and the laws of nature if the evolution of life in the universe is to be possible.

Science minisummary: Big Bang cosmology.For a non-technical introduction, see James Trefil and Robert M. Hazen, The Sciences: An Integrated Approach, Second Edition / Updated Edition (New York: John Wiley & Sons, Inc., 2000), Ch. 15, Donald...During the decade following the publication of his special theory of relativity, Einstein worked on applying it to a dynamical theory of gravity. His basic insight was to reconceptualize gravity as the curvature of spacetime instead of as a (Newtonian) force in space. Rather than being deflecting from their otherwise linear motion in a Euclidean space with three dimensions, masses would move along geodesics describing the shortest possible path in curved spacetime. Their motion, in turn, would alter the curvature of spacetime, thus giving the field equations General Theory of Relativity (GR) their highly non-linear form aptly described as: ‘spacetime tells mass how to move; mass tells spacetime how to curve’.Misner, Kip S. Thorne and John Archibald Wheeler, Gravitation, 5.

Shortly after the discovery of GR, solutions to Einstein’s equations were developed for two distinct classes of problems: i) point masses, which when applied to the solar system led to several key tests of the theory and their eventual confirmation (including the deflection of starlight by the sun and the precession in the perihelion of the orbit of Mercury), and ii) dust, which when eventually applied to the distribution of galaxies and galactic clusters described the universe as expanding in time. During the 1920s, telescopic observations by Edwin Hubble showed that galaxies were indeed receding from us and at a velocity proportional to their distance.Hubble’s data actually showed a linear relation between the magnitude and red shift of light from distant galaxies; magnitude was then interpreted in terms of distance, and red shift in terms of recessional...In essence, the expansion of the universe had been discovered!

There are in fact three types of expansion possible.One might wonder why we can talk about the universe expanding in time given that GR is based on SR: given relativity’s challenge to the idea of ‘the present’, how can there be a unique ‘present’...i) Closed model: spherical. In one model the universe has the shape of a 3-dimensional sphere of finite size. It expands up to a maximum size, approximately 100 billion years from now, then recontracts, eventually recollapsing to a singularity that mirrors t=0 with infinite temperatures and densities. ii) Open model 1: ‘flat’ and iii) open model 2: ‘saddle-shaped’. Both the ‘flat’ and ‘saddle-shaped’ models are infinite in size and expanding in time. In both cases the universe will expand forever and cool indefinitely towards absolute zero.The ‘flat’ model is pseudo-Euclidean like the geometry of special relativity. The ‘saddle-shaped’ model has negative curvature and cannot therefore be embedded in Euclidean space, so...The future of these models is often used to characterize them as ‘freeze’ (open, both cases) or ‘fry’ (closed). All three came to be called “Big Bang” models because they describe the universe as having a finite past life of 10-20 billion years and beginning in an event of infinite temperature and density, and zero volume. Since the age of the universe, t, is calculated as starting here, it is convenient to label it “t=0"; technically this event is referred to as an “essential singularity.”The event at t=0 is called an "essential singularity". A singularity is an event in which physical parameters go infinite; an essential singularity is one which we believe actually describes...In the 1960s, Stephen Hawking, Roger Penrose, and Robert Geroch proved key theorems which showed that the existence of an essential singularity, t=0, given Einstein’s GR, was unavoidable.For a technical introduction see Misner, Kip S. Thorne and John Archibald Wheeler, Gravitation, Ch. 34, esp. 34.4, 34.6; see also R. Penrose, "Gravitational Collapse and Space-Time Singularities,"...

Contributed by: Dr. Robert Russell

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