Quantum supersymmetric FRW cosmology with a scalar field

We analyze the quantum supersymmetric cosmological Friedmann-Robertson-Walker model with a scalar field, with a conditional probability density and the scalar field identified as time. The Hilbert space has a spinorial structure and there is only one consistent solution, with a conserved probability density. The dynamics of the scale factor is obtained from its mean value. The uncertainty relations are fulfilled and the corresponding fluctuations are consistent with a semiclassical Universe. We give two examples which turn out to have negative potential.

Figure 1

Stable potential generated by the superpotential (59), $m=1$ and $c=0.24$.

Figure 2

Dependence profile of $|\psi (a,\varphi ){|}^2$ for the superpotential (59), $m=1$ and $c=0.24$.

Figure 3

Profile of $a$ for the superpotential (59), $m=1$ and $c=0.24$.

Figure 4

Profile of $\ddot{a}$ for the superpotential (59), $m=1$ and $c=0.24$.

Figure 5

Profile of $\dot{a}$, including its quantum fluctuations, for the superpotential (59), $m=1$ and $c=0.24$.

Figure 6

Central region of the unstable potential generated by the superpotential (61), $m=3$ for the solid line and $m=6.6$ for the dashed line.

Figure 7

Unstable potential generated by the superpotential (61), $m=3$ for the solid line and $m=6.6$ for the dashed line. The details of its central region are shown in Fig. 6.

Figure 8

Dependence profile of $|\psi (a,\varphi ){|}^2$ for the superpotential (61), $m=6.6$.

Figure 9

Profile of $a$ for the superpotential (61), $m=3$ for the solid line and $m=6.6$ for the dashed line.

Figure 10

Profile of $\ddot{a}$ for the superpotential (61), $m=3$ for the solid line and $m=6.6$ for the dashed line.

Figure 11

Profile of $\dot{a}$, including its quantum fluctuations, for the superpotential (61), $m=6.6$.