Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 85
Log 10t1s
-3.7
-3.8
-3.9
-4
-4.1
t2
t1
0 0.02 0.04 0.06 0.08 0.1
TTc
Figure 33: The width of the QCD Crossover in terms of time as a function
of the parameter ∆T (cf. equation 152) when tc =1.08 × 10 −4 s (dashed line)
corresponding to Tc ≈ 170 MeV. Here, t1 represents the instant when the sound
speed gets less than 95% of its ‘background’ value (1/3) and t2 represents the
instant when the sound speed reaches, once again, 95% of its ‘background’ value.
Thus, the width of the QCD Crossover, for a given ∆T , is given by t2 − t1.
Table 20: The width of the QCD phase transition according to the Bag Model,
Lattice Fit and Crossover when Tc = 170 MeV. The sound speed vanishes in
the interval t− < t < t+ and is below 95% of its ‘background’ value c 2 s,0 =1/3
in the interval t1 < t < t2. Here ∆t represents the interval during which the
sound speed value is less than 95% of 1/3.
Model t1(×10 −5 s) t−(×10 −5 s) t+(×10 −5 s) t2(×10 −5 s) ∆t(×10 −5 s) ∆t
∆tBAG
Bag – 6.25 10.8 – 4.6 1
Lattice 0.051 9.37 10.8 – 10.7 2.33
Crossover (∆T =0.01Tc) 10.1 – – 11.7 1.6 0.35
Crossover (∆T =0.05Tc) 8.5 – – 15.0 6.5 1.41
Crossover (∆T =0.1Tc) 7.1 – – 19.6 12.5 2.72