- #1
Jimster41
- 783
- 82
This is an embarrassing clarification to request, but I keep getting confused, even when sort of following the hypersine model thread and others like it.
Is this correct?
[itex]a(t)[/itex] "Scale Factor" - length multiplicative factor, a function of time as experienced by an observer co-moving with the CMB
[itex]\dot { a } (t)\quad =\quad \frac { { d }^{ ' } }{ dt } a(t)[/itex] "rate of change of length" or "rate of expansion"
[itex]\ddot { a } (t)\quad =\quad \frac { { d }^{ '' } }{ dt } a(t)[/itex] Rate of change of "rate of expansion", aka [itex]\lambda [/itex], aka the "cosmological constant".
When someone says, in the context of cosmology that "space-time" looks flat they mean that [itex]\lambda [/itex] is very close to one, that the rate of expansion or the rate of change in length seems nearly constant.
When someone talks about positive cosmological curvature they mean [itex]\lambda [/itex] is positive and the rate of expansion is increasing. This is associated with [itex]\Omega [/itex].
too many rates of, then giving them new names... oof
Is this correct?
[itex]a(t)[/itex] "Scale Factor" - length multiplicative factor, a function of time as experienced by an observer co-moving with the CMB
[itex]\dot { a } (t)\quad =\quad \frac { { d }^{ ' } }{ dt } a(t)[/itex] "rate of change of length" or "rate of expansion"
[itex]\ddot { a } (t)\quad =\quad \frac { { d }^{ '' } }{ dt } a(t)[/itex] Rate of change of "rate of expansion", aka [itex]\lambda [/itex], aka the "cosmological constant".
When someone says, in the context of cosmology that "space-time" looks flat they mean that [itex]\lambda [/itex] is very close to one, that the rate of expansion or the rate of change in length seems nearly constant.
When someone talks about positive cosmological curvature they mean [itex]\lambda [/itex] is positive and the rate of expansion is increasing. This is associated with [itex]\Omega [/itex].
too many rates of, then giving them new names... oof