2171 words - 9 pages

Cosmology in general predates the physics that we rely upon in the twenty-first century. Its history is intertwined with religion as an attempt to understand or explain the workings of the world. Science on the grandest scale has felt great impedence from religious dogma and pontificators, specificly, the relationship between Gallileo and the Catholic church. The entire history of cosmology is a subject too broad for a small project to contend with, so I want to explore the workings of just the Big Bang theory; its creation, evolution and adaptation to new data, and revision with inflationary theory.

The Beginning:

After Isaac Newton revolutionized mechanics, the term 'cosmology' (or ...view middle of the document...

Obviously the universe has not collapsed, which puzzled Newton.

Einstein was also puzzled by the appropriate boundary conditions to apply to an aparently infinite volume universe, that has not collapsed. In the model of 1917 he tried to describe a universe that exists in a steady state, that is, not collapsing and not expanding. The creation of the big bang model was an inadvertant by-product of his classic 'cylindrical universe,' because such a steady universe must have a mysterious cosmological constant holding it up, and keeping it from collapsing.

A Short History of Big Bang Theory

Steady State and Cylindrical Universe:

The formulation of boundary conditions for an apparently infinite universe nearly confounded Einstein, who wrote that at some points he felt he should be confined to a madhouse. What emerged from his application of general relativity theory, however, was a surprisingly simple and almost naiive model of gravitational behavior of matter at large over time. His universe essentially had a boundary which remained fixed in time, and a center.

From Cosmological Considerations on the General Theory of Relativity, he first considers Possion's equation:

Where phi is the gravitational potential, K is a constant, and rho a particular density for a region of space. Applied to a Newtonian universe with a universal force of gravity, the universe will collapse after a time dependant upon the density. To force the universe to be in a steady state, an extra term can be added. Einstein does this with no small consternation, commenting that it is simply 'a foil for what is to follow.'

This is a differential equation, where lambda denotes a universal constant, rho the density, modeled to decrease to zero as distance approaches infinity, so that the universe may have finite space according to Newton, but infinite mass.

A solution to the differential equation, if rho-naught is actually equal to the mean density of matter in the universe, is:

The resulting universe, with the gravitational potential balanced by the cosmological constant, is a bounded universe with no center with respect to the mean gravitational potential or the mean density. If two of the spatial dimensions are supressed (so that the boundary appears to be finite in space and the 3-d + time sphere is projected on a 3-d surface), the model can be imagined like so:

The tensor form of the gravitational field equations is this:

With the cosmological constant added:

where the sub-scripts are tensors, where m,n = 0,1,2,3, therefore ten second order differential equations exist. Rmn is the Ricci curve tensor, and R is a curvature invariant derived from Rmn. The constant k is related to the constant of gravity as k = 8piG/c^4. The field equations relate geometrical and physical entities - on the left side, the geometry of space; on the right, Tmn is the Energy-momentum tensor, describing the physical contents of space.

Einstein commented that lambda "is...

Tap into the world’s largest open writing community