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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 ![]() ![]() |
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Figure 2:
Example of a solution of ![]() ![]() |
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Figure 3:
Movie The initial push of a scalar ![]() ![]() |
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Figure 4:
Movie An illustration of the Bianchi IX potential (40 ![]() ![]() ![]() ![]() ![]() |
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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. |
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Figure 6:
Approximate effective wall of finite height [80] as a function of ![]() ![]() ![]() |
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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. |
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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. |
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Figure 9:
Discrete subset of eigenvalues of ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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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). |
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Figure 11:
Ratio of fluctuations before ( ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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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 ![]() ![]() ![]() ![]() |
http://www.livingreviews.org/lrr-2008-4 | ![]() This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 2.0 Germany License. Problems/comments to |