Figure 1:
Examples of bouncing solutions with positive curvature (left) or a negative potential (right, negative cosmological constant). The solid lines show solutions of equations with a bounce as a consequence of quantum corrections, while the dashed lines show classical solutions running into the singularity at where diverges. 

Figure 2:
Example of a solution of and showing early loop inflation and later slowroll inflation driven by a scalar that has pushed up its potential by loop effects. The lefthand side is stretched in time so as to show all details. An idea of the duration of different phases can be obtained from Figure 3. 

Figure 3:
Movie The initial push of a scalar up its potential and the ensuing slowroll phase together with the corresponding inflationary phase of . 

Figure 4:
Movie An illustration of the Bianchi IX potential (40) and the movement of its walls, rising toward zero and and along the diagonal direction, toward the classical singularity with decreasing volume . The contours are plotted for the function . 

Figure 5:
Movie An illustration of the Bianchi IX potential in the anisotropy plane and its exponentially rising walls. Positive values of the potential are drawn logarithmically with solid contour lines and negative values with dashed contour lines. 

Figure 6:
Approximate effective wall of finite height [80] as a function of , compared to the classical exponential wall (upper dashed curve). Also shown is the exact wall (lower dashed curve), which for smaller than the peak value coincides well with the approximation up to a small, nearly constant shift. 

Figure 7:
Movie An illustration of the effective Bianchi IX potential and the movement and breakdown of its walls. The contours are plotted as in Figure 4. 

Figure 8:
Movie An illustration of the effective Bianchi IX potential in the anisotropy plane and its walls of finite height, which disappear at finite volume. Positive values of the potential are drawn logarithmically with solid contour lines and negative values with dashed contour lines. 

Figure 9:
Discrete subset of eigenvalues of (left) for two choices of (and ), together with the approximation from Equation (26) and small power laws. The classical divergence at small , where the behavior differs strongly from eigenvalues, is cut off. The right panel shows the dependence of the initial increase on . 

Figure 10:
Internal time evolution for expectation values and spread of two bouncing states, one, which is unsqueezed (solid lines), and one, which is being squeezed (dashed). 

Figure 11:
Ratio of fluctuations before () and after () the bounce in the form as a function of a state parameter in relation to the Hamiltonian for in Planck units. For larger , the curve becomes even steeper, showing how precisely one has to tune the state parameter in order to have a near symmetric state with . See [74] for further details. 

Figure 12:
Movie The coordinate time evolution [103] of a wave packet starting at the bottom and moving toward the classical singularity (vertical dotted line) for different values of an ambiguity parameter. Some part of the wave packet bounces back (and deforms) according to the effective classical solution (dashed), but other parts penetrate to negative . The farther away from the effective bounce happens, depending on the ambiguity parameter, the smaller the part penetrating to negative is. The coordinate time evolution represents a physical state obtained after integrating over [103]. 
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