Qualitative study in loop quantum cosmology

Saló, Llibert Aresté; Amorós, Jaume; Haro, Jaume de

doi:10.1088/1361-6382/aa9311

Cited by 7 publications

(9 citation statements)

References 60 publications

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“…The essential features of LQC can be found in various articles, see for example Refs. [97][98][99][100][101][102][103][104][105][106][107], so we start of with the LQC Friedmann equation which for the flat FRW metric of Eq. (1) becomes,…”

Section: The Loop Quantum Cosmology Framework and Interacting Damentioning

confidence: 99%

“…The dynamical system approach for studying the dynamical evolution of various cosmological systems is quite popular in the modern cosmology literature and in this paper we shall appropriately form an autonomous dynamical system for the cosmological system at hand. We shall use two theoretical frameworks, namely the classical Einstein-Hilbert framework and the loop quantum cosmology (LQC) framework [97][98][99][100][101][102][103][104][105][106][107], and for each case we shall study the trajectories in the phase space, the existence of de Sitter fixed points and finally we shall examine the stability of the de Sitter fixed points. To our surprise, in both cases the effect of a generalized EoS in the dark energy fluid leads to stable exactly de Sitter fixed points.…”

Section: Introductionmentioning

confidence: 99%

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Generalized logarithmic equation of state in classical and loop quantum cosmology dark energy–dark matter coupled systems

Oikonomou

2019

Annals of Physics

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In this paper we shall study the phase space of a coupled dark energy-dark matter fluids system, in which the dark energy has a generalized logarithmic corrected equation of state. Particularly, the equation of state for the dark energy will contain a logarithmic function of the dark energy density ρ d and will also have quadratic and Chaplygin gas-like terms, expressed in terms of ρ d . We shall use the dynamical system approach in order to study the cosmological dynamics, and by appropriately choosing the dynamical system variables, we shall construct an autonomous dynamical system. The study will be performed in the context of classical and loop quantum cosmology, and the focus is on finding stable de Sitter attractors. As we demonstrate, in both the classical and loop quantum cosmology cases, there exist stable de Sitter attractors in the phase space, with the loop quantum cosmology case though having a wider range of the free parameter values for which the stable de Sitter attractors may occur. It is emphasized that the use of a generalized dark energy equation of state makes possible the existence of de Sitter attractors, which were absent in the case that a simple logarithmic term constitutes the dark energy equation of state.PACS numbers:

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Section: The Loop Quantum Cosmology Framework and Interacting Damentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized logarithmic equation of state in classical and loop quantum cosmology dark energy–dark matter coupled systems

Oikonomou

2019

Annals of Physics

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“…Before we start, we shall briefly review some essential information of LQC, and for details, the reader is referred to Refs. [92][93][94][95][96][97][98][99][100][101][102]. We focus on holonomy corrected LQC, in the context of which, the spacetime is discrete, and the Hamiltonian of the theory is written in terms of the holonomies h j = e − iλσ j 2 , where σ j denote the Pauli matrices, and it is equal to,…”

Section: The Loop Quantum Cosmology Framework and Interacting Damentioning

confidence: 99%

“…This result is intriguing, so a question naturally spring to mind, does these singular solutions exist even if Loop Quantum Cosmology (LQC) effects are taken into account? The LQC theoretical framework [92][93][94][95][96][97][98][99][100][101][102], is known to remove any classical singularities of cosmological models, see for example [103] for a characteristic example of this sort of behavior. Thus, we shall extend the analysis performed in the classical case, and study the dynamical system of the interacting dark energy and superfluid dark matter fluids.…”

Section: Introductionmentioning

confidence: 99%

Classical and loop quantum cosmology phase space of interacting dark energy and superfluid dark matter

Oikonomou¹

2019

Phys. Rev. D

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In this paper we study in detail the phase space of a cosmological system consisting of two coupled fluids, namely a dark energy fluid coupled with a superfluid dark matter fluid. The dark matter fluid is assumed to have a superfluid equation of state, hence it is not pressureless and our aim is to find the impact of this non-trivial equation of state on the phase space of the coupled system. We shall use two theoretical contexts, namely that of classical cosmology and that of loop quantum cosmology. In the classical case, we investigated the existence and stability of fixed points, and as we will show, no de Sitter fixed points occur, however matter and radiation domination fixed points occur, which are hyperbolic and unstable. We also show that there exist limited sets of initial conditions for which singular solutions occur in the phase space. With regard to the loop quantum cosmology case, we demonstrate that stable de Sitter fixed points exist, for some values of the free parameters of the theory, and interestingly enough, for the same values, singular solutions corresponding to general sets of initial conditions occur. To our knowledge this feature does not occur so frequently in loop quantum cosmological frameworks. We also demonstrate that non-singular solutions corresponding to a general set of initial conditions occur, however these occur when the dark matter superfluid has negative pressure, so it is a rather physically unappealing situation.PACS numbers:

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“…Singularities in cosmology occur in various theoretical contexts, like for example modified gravity [1][2][3][4][5][6] or even multifluid cosmology [7][8][9][10][11][12][13][14][15]. The definition of a singular point in cosmology was given some time ago from Hawking and Penrose [16], and most of the theorems proven by them make use of the null energy condition and also of the facts that at a singular point of the spacetime, geodesics incompleteness occurs and also the curvature scalars diverge.…”

Section: Introductionmentioning

confidence: 99%

Study of finite-time singularities of loop quantum cosmology interacting multifluids

Odintsov

Oikonomou

2018

Phys. Rev. D

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In this work we study the occurrence of finite-time cosmological singularities in a cosmological system comprising from three fluids. Particularly, the system contains two dark fluids, namely that of dark energy and dark matter, which are interacting, and of a non-interacting baryonic fluid. For the study we adopt the phase space approach by constructing the cosmological dynamical system in such a way so that it rendered to be an autonomous polynomial dynamical system, and in order to achieve this, we appropriately choose the variables of the dynamical system. By employing a rigid mathematical framework, that of dominant balances analysis, we demonstrate that there exist nonsingular solutions of the dynamical system, which correspond to a general set of initial conditions, which proves that no Big Rip or Type III finite-time singularities occur in this LQC multifluid dynamical system. Thus the new feature of this work is that we are able to do this using an analytic technique instead of adopting a numerical approach. In addition, we perform a fixed point analysis of the cosmological dynamical system, and we examine the behavior of the total effective equation of state parameter, at the fixed points, as a function of the free parameters of the system. Finally, we investigate the phenomenological implications of the dark energy equation of state which we assumed that it governs the dark energy fluid.

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Qualitative study in loop quantum cosmology

Cited by 7 publications

References 60 publications

Generalized logarithmic equation of state in classical and loop quantum cosmology dark energy–dark matter coupled systems

Generalized logarithmic equation of state in classical and loop quantum cosmology dark energy–dark matter coupled systems

Classical and loop quantum cosmology phase space of interacting dark energy and superfluid dark matter

Study of finite-time singularities of loop quantum cosmology interacting multifluids

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