- #1
oldman
- 633
- 5
The Robertson-Walker (RW) metric is, in a spatially flat Standard Model universe, a simplemodification of the Minkowskian metric of Special Relativity (SR), thus:
The SR metric of space-time along any arbitrarily chosen line, where a coordinate r measures distance in metres from some arbitrary origin, is :
ds^2 = c^2 dt^2 - dr^2.
(Here t is time and s is the interval between events. ^2 means squared and d indicates differential coordinate separation)
For a flat Standard Model universe the RW metric may be obtained by inserting a scale factor a(t) as a multiplying metric coefficient for the (now re-gauged and assumed to be co-moving with matter) coordinate r, thus:
ds^2 = c^2 dt^2 - a^2(t) dr^2 .
The scale factor, which is a function of (universal) time, measures the homogeneous expansion of the highly symmetric SM universe, in which along any line proper distances in metres are a(t) r.
The effect of this modification on the propagation of light is to introduce a red-shift of light transmitted between any two points of space-time, when a(t) increases monotonically with time.
The essence of this modification is that it effects a change in the ratio between the metric coefficients of the time and space coordinates. The spatial metric coefficient is selected to be the one that is to be re-gauged and to differ from the SR value of unity. Because this is the choice that is made (rather than letting the time coefficient, or both coefficients, differ from unity via appropriate factors) we call the change "expansion".
My question is:
are such choices arbitrary, and is the use of the term "expansion" to describe change in cosmology therefore only a semantic convenience?
The SR metric of space-time along any arbitrarily chosen line, where a coordinate r measures distance in metres from some arbitrary origin, is :
ds^2 = c^2 dt^2 - dr^2.
(Here t is time and s is the interval between events. ^2 means squared and d indicates differential coordinate separation)
For a flat Standard Model universe the RW metric may be obtained by inserting a scale factor a(t) as a multiplying metric coefficient for the (now re-gauged and assumed to be co-moving with matter) coordinate r, thus:
ds^2 = c^2 dt^2 - a^2(t) dr^2 .
The scale factor, which is a function of (universal) time, measures the homogeneous expansion of the highly symmetric SM universe, in which along any line proper distances in metres are a(t) r.
The effect of this modification on the propagation of light is to introduce a red-shift of light transmitted between any two points of space-time, when a(t) increases monotonically with time.
The essence of this modification is that it effects a change in the ratio between the metric coefficients of the time and space coordinates. The spatial metric coefficient is selected to be the one that is to be re-gauged and to differ from the SR value of unity. Because this is the choice that is made (rather than letting the time coefficient, or both coefficients, differ from unity via appropriate factors) we call the change "expansion".
My question is:
are such choices arbitrary, and is the use of the term "expansion" to describe change in cosmology therefore only a semantic convenience?