Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 29
Table 3: The Scale Factor (equations 67–77) for different instants of time during
the evolution of the Universe: tp (Planck time), ti (beginning of inflation), te
(end of inflation), tEW− (beginning of the EW transition – Section 3.2), tEW+
(end of the EW transition – Section 3.2), t− (beginning of the QCD transition
– Section 2.4), t+ (end of the QCD transition – Section 2.4), teq (last scattering
surface), tSN (the instant when the Universe starts to accelerate) and t0 (present
time). Notice that we have indicated two values for t−. The first one corresponds
to the Bag Model results and the second one to the Lattice Fit results (cf.
Section 2.4).
t(s) R(t)
tp ∼ 10 −43 ∼ 10 −60
ti ∼ 10 −35 ∼ 10 −56
te ∼ 10 −33 ∼ 10 −27
tEW− 2.30 × 10 −10 2.9 × 10 −15
tEW+ 3.15 × 10 −10 3.5 × 10 −15
Log 10Rt
t− 6.25 × 10 −5 1.4 × 10 −12 (QCD Bag)
t− 9.35 × 10 −5 1.9 × 10 −12 (QCD Lattice)
t+ 1.08 × 10 −4 2.1 × 10 −12
teq 2.5 × 10 12 3.2 × 10 −4
tSN 2.8 × 10 17 0.73
t0 4.3 × 10 17 1
-11.6
-11.7
-11.8
-11.9
QCD
-4.4 -4.3 -4.2 -4.1 -4 -3.9 -3.8 -3.7
Log 10t1s
Figure 6: The scale factor during the QCD transition as a function of time.
The gray region corresponds to the dust–like epoch, according to the Bag Model
(Sections 2.3.1 and 2.4). The curves correspond, from top to bottom, to the:
crossover case (nqcd =1/2), Lattice Fit (nqcd =2/3 and t− =9.35 × 10 −5 s)
and Bag Model (nqcd =2/3 and t− =6.25 × 10 −5 s).