November 27, 2014
In the present paper we study the evolution of the modes of a scalar field in a cyclic cosmology. In order to keep the discussion clear, we study the features of a scalar field in a toy model, a Friedman-Robertson-Walker universe with a periodic scale factor, in which the universe expands, contracts and bounces infinite times, in the approximation in which the dynamic features of this universe are driven by some external factor, without the backreaction of the scalar field under study. In particular, we show that particle production exhibits features of the cyclic cosmology. Also, by studying the Berry phase of the scalar field, we show that contrarily to what is commonly believed, the scalar field carries information from one bounce to another in the form of a global phase which occurs to be generically non-zero. {The Berry phase is then evaluated numerically in the case of the effective Loop Quantum Cosmology closed Universe. We observe that Berry's phase is nonzero, but that in the quantum regime the particle content is non-negligible.
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We discuss how a cyclic model for the flat universe can be constructively derived from Loop Quantum Gravity. This model has a lower bounce, at small values of the scale factor, which shares many similarities with that of Loop Quantum Cosmology. We find that quantum gravity corrections can be also relevant at energy densities much smaller than the Planckian one and that they can induce an upper bounce at large values of the scale factor.
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A Universe filled with a homogeneous scalar field exhibits `Cosmological hysteresis'. Cosmological hysteresis is caused by the asymmetry in the equation of state during expansion and contraction. This asymmetry results in the formation of a hysteresis loop: $\oint pdV$, whose value can be non-vanishing during each oscillatory cycle. For flat potentials, a negative value of the hysteresis loop leads to the increase in amplitude of consecutive cycles and to a universe with olde...
In Loop Quantum Gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to massless scalar field. In our previous research we introduced a method to reduce the model to homogeneous-isotropic sector at the quantum level. In this paper we propose a method to restrict to the spatially flat sector. After this restriction th...
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We analyze the evolution of cosmological perturbations in the cyclic model, paying particular attention to their behavior and interplay over multiple cycles. Our key results are: (1) galaxies and large scale structure present in one cycle are generated by the quantum fluctuations in the preceding cycle without interference from perturbations or structure generated in earlier cycles and without interfering with structure generated in later cycles; (2) the ekpyrotic phase, an e...
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