FIG 9 - uploaded by John Dupuy
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Evolution in a quasi-periodically beating universe. The holonomy solution (solid) and connection solution (dotted) are shown for q = 4.0 with V0 = 10 6 , ˙ φ0 = 0.0141, and φ0 = 0.5 (in Planck units).
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Differences in pressure during expansion and contraction stages in cosmic evolution can result in a hysteresis-like phenomena in non-singular cyclic models sourced with scalar fields. We discuss this phenomena for spatially closed isotropic spacetime in loop quantum cosmology (LQC) for a quadratic and a cosh-like potential, with and without a negat...
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... occurs. It is to be noted that for the simulation shown in Fig. 8, different models result in solutions which are radically different after only a short amount of time. For these simulations, given the relatively small value of steepness parameter, there are no quasi-periodic beats. These arise for larger values of q which is discussed below. Fig. 9 shows the emergence of quasi-periodic beats which occur because of variations in the hysteresis loop. In the previous study based on cyclic brane-world model, quasi-periodic beats were found to be absent in this case, and instead a stochastic behavior was found [1]. Phenomena of beats appear and disappear as steepness parameter is ...
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... Beats appear as the steepness parameter, q, is increased. They emerge around q = 3.5 and subsequently become less regular as q is increased to values larger than q = 7.0. We find that though quasi-periodic beats appear in both of the LQC models, there are some major deviations between the models. An example is shown for the case of q = 4.0 in Fig. 9, where we see that the structure of expansion and contraction cycles does not exactly repeats itself and is quasi-periodic. Another example is shown for the case of q = 5.5 in Fig. 10. The quasi-periodic structure is evident in both the holonomy as well as connection quantization solutions, with a period of around T ≈ 300. Fig. 11 ...
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... of around T ≈ 300. Fig. 11 shows the case of q = 7.0 where the quasiperiodic structure in the effective dynamics of holonomy and connection quantizations is disappearing. For q > 7.0, the periodic structure seems to give way to more stochastic behavior in both of the models. Evolution for a universe subject to the same initial conditions as Fig. 9, except that q = 5.5. The solution from holonomy quantization is shown by solid curve, while from connection quantization is shown by dotted curve. case when only spatial curvature is present. Earlier investigation for this case for the brane-world cyclic model showed that as the steepness parameter is increased the behavior of the ...
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... occurs. It is to be noted that for the simulation shown in Fig. 8, different models result in solutions which are radically different after only a short amount of time. For these simulations, given the relatively small value of steepness parameter, there are no quasi-periodic beats. These arise for larger values of q which is discussed below. Fig. 9 shows the emergence of quasi-periodic beats which occur because of variations in the hysteresis loop. In the previous study based on cyclic brane-world model, quasi-periodic beats were found to be absent in this case, and instead a stochastic behavior was found [1]. Phenomena of beats appear and disappear as steepness parameter is ...
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... Beats appear as the steepness parameter, q, is increased. They emerge around q = 3.5 and subsequently become less regular as q is increased to values larger than q = 7.0. We find that though quasi-periodic beats appear in both of the LQC models, there are some major deviations between the models. An example is shown for the case of q = 4.0 in Fig. 9, where we see that the structure of expansion and contraction cycles does not exactly repeats itself and is quasi-periodic. Another example is shown for the case of q = 5.5 in Fig. 10. The quasi-periodic structure is evident in both the holonomy as well as connection quantization solutions, with a period of around T ≈ 300. Fig. 11 ...
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... of around T ≈ 300. Fig. 11 shows the case of q = 7.0 where the quasiperiodic structure in the effective dynamics of holonomy and connection quantizations is disappearing. For q > 7.0, the periodic structure seems to give way to more stochastic behavior in both of the models. Evolution for a universe subject to the same initial conditions as Fig. 9, except that q = 5.5. The solution from holonomy quantization is shown by solid curve, while from connection quantization is shown by dotted curve. case when only spatial curvature is present. Earlier investigation for this case for the brane-world cyclic model showed that as the steepness parameter is increased the behavior of the ...
