Loitering Model: a(t)


Loitering model with m = 0.3 and v = 1.71
 
Evolution of scale factor for a Lemaitre model close to the "loitering" condition where matter's pull and the vacuum's push are nearly balanced. The condition is found by setting both da/dt and d2a/dt2 to zero. The condition is: k = 1 - (v + m) = -3/2 (2 v m2)1/3. Just one example is plotted from close to the loitering sequence. It has m = 0.3 and v = 1.71 and an age of 3.6 tH. To achieve significantly longer ages than tH requires fine tuning. Notice also that in these kinds of models we always live at a rather special time just before a rapid exponential runaway. This arises because of demanding a current Hubble constant which is significant.

Figure made for this website.

Include figure 7.7 in Longair (or the equivalents from Carroll et al)