2. Basic theory
where the symbols are defined as follows (with the corresponding units):
where dots denote derivatives with respect to t, G is the gravitational constant, the matter density (this paper assumes negligible pressure), the cosmological constant and the sign of k determines the curvature of the 3-dimensional space.
this is the radius of curvature of the 3-dimensional space at time t. For it is convenient to define the scale factor R to be . In the following the index 0 will be used to denote the present value of a given quantity, fixed, as usual, at the time of observation. 2 The explicit dependence on t will be dropped for brevity. Taking matter conservation into account and using the present-day values, we have
Note: Throughout this paper, the sign should be taken to signify the positivesolution, except that always.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998