Showing papers on "Big Rip published in 2018"

Dynamical Systems Perspective of Cosmological Finite-time Singularities in $f(R)$ Gravity and Interacting Multifluid Cosmology

Abstract: In this work we shall investigate the occurrence of future cosmological finite-time singularities in the dynamical system corresponding to two cosmological theories, namely that of vacuum $f(R)$ gravity and that of three fluids. As we shall make clear, a finite-time cosmological singularity may be entirely different from a finite-time singularity of a dynamical system, since the latter mainly depends on the behavior of the dynamical system variables. The vacuum $f(R)$ gravity is an example for which the variables we will choose to quantify the phase space dynamics, do not necessarily blow up near a cosmological singularity. After appropriately choosing the variables, we shall investigate the behavior of the corresponding dynamical system near some types of cosmological finite-time singularities, for some limiting cases in which we can produce analytic solutions for the dynamical variables. The most interesting case from both a mathematical and physical point of view, is the big rip case, and particularly in the limiting case of a very strong singularity. The physically appealing outcome is that the resulting nonautonomous dynamical system is attracted asymptotically to an accelerating attractor solution, with equation-of-state parameter ${w}_{\mathrm{eff}}=\ensuremath{-}1$. Our analytic results, show that an extremely strong big rip singularity in vacuum $f(R)$ gravity theories is always related to an accelerating solution, or tends to acceleration. The converse statement though may not be true. We also perform the same analysis for the Type IV finite-time singularity, and we investigate the behavior of the dynamical system near the Type IV singularity, in the case that the singularity is extremely soft, in which case we are able to produce analytic expressions for the dynamical solutions. Also we briefly discuss how the removal of the finite-time singularity may be achieved by the addition of an ${R}^{2}$ term in the $f(R)$ gravity action. The second cosmology we shall study is a multifluid cosmology, consisting of three fluids: the interacting dark matter and dark energy fluids, and the baryonic fluid. By appropriately choosing the variables, we will show that the dynamical system can become an autonomous polynomial dynamical system, in which case, by using a dominant balance analysis, we shall investigate the occurrence of finite-time singularities in this system. We also study numerically and analytically, in some detail, the phase space of the dynamical system for some specific forms of the dark energy--dark matter interaction term.

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

Abstract: In this work we study the occurrence of finite-time cosmological singularities in a cosmological system comprising three fluids. Particularly, the system contains two dark fluids, namely, that of dark energy and dark matter, which are interacting, and of a noninteracting baryonic fluid. For the study we adopt the phase space approach by constructing the cosmological dynamical system in such a way that it is rendered as 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 loop quantum cosmology 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 governs the dark energy fluid.

Bulk viscous quintessential inflation

Abstract: In a spatially-flat Friedmann–Lemaitre–Robertson–Walker universe, the incorporation of bulk viscous process in general relativity leads to an appearance of a nonsingular background of the universe that both at early and late times depicts an accelerated universe. These early and late scenarios of the universe can be analytically calculated and mimicked, in the context of general relativity, by a single scalar field whose potential could also be obtained analytically where the early inflationary phase is described by a one-dimensional Higgs potential and the current acceleration is realized by an exponential potential. We show that the early inflationary universe leads to a power spectrum of the cosmological perturbations which match with current observational data, and after leaving the inflationary phase, the universe suffers a phase transition needed to explain the reheating of the universe via gravitational particle production. Furthermore, we find that at late times, the universe enters into the de Si...

Chaotic universe model.

Abstract: In this study, we consider nonlinear interactions between components such as dark energy, dark matter, matter and radiation in the framework of the Friedman-Robertson-Walker space-time and propose a simple interaction model based on the time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra type equations. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for 0 > w de >−1, w dm ≥ 0, w m ≥ 0 and w r ≥ 0 values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in the time evolution of the densities. These results provide that the time evolution of the universe is chaotic. The present model may have potential to solve some of the cosmological problems such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, the emergence of the galaxies, matter distribution and large-scale organization of the universe. The model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe and offers a new perspective and a new different scenario for the universe evolution.

f(R) quantum cosmology: avoiding the Big Rip

Abstract: Extended theories of gravity have gathered a lot of attention over the past years, for they not only provide an excellent framework to describe the inflationary era but also yield an alternative to the elusive and mysterious dark energy Among the different extended theories of gravity, in this work we focus on metric $f(R)$ theories In addition, it is well known that if the late-time acceleration of the Universe is stronger than the one induced by a cosmological constant, then some future cosmic singularities might arise, the big rip being the most virulent one Following this reasoning, in this work, we analyze the big rip singularity in the framework of $f(R)$ quantum geometrodynamics Invoking the DeWitt criterion, ie, that the wave function vanishes at the classical singularity, we prove that a class of solutions to the Wheeler-DeWitt equation fulfilling this condition can be found Therefore, this result hints toward the avoidance of the big rip in metric $f(R)$ theories of gravity

Linking little rip cosmologies with regular early universes

Abstract: Cosmological fluids with a generalized equation of state (GEoS) are here considered, whose corresponding EoS parameter $\ensuremath{\omega}$ describes a fluid with phantom behavior, namely, $\ensuremath{\omega}l\ensuremath{-}1$, but leading to universes free of singularities at any past or future, finite time, thus avoiding, in particular, the big bang and the big rip singularities, the last one considered to be typical in phantom fluid models. More specifically, such GEoS fluid cosmologies lead to regular little rip universes. A remarkable new property of these solutions is proven here, namely, that they avoid the initial singularity at early times; therefore, they are able to describe emergent universes. Solutions of this kind had been studied previously, but only either as late-time or as early-time solutions, never as solutions covering both epochs simultaneously. Appropriate conditions are proposed here that relate the little rip cosmologies with the initial regular universe, for the future and past regimes, respectively. This is done by taking as a starting point the conditions under which a given scale factor corresponds to a little rip universe.

Finite-time Singularities in Swampland-related Dark Energy Models

Abstract: In this work we shall investigate the singularity structure of the phase space corresponding to an exponential quintessence dark energy model recently related to swampland models. The dynamical system corresponding to the cosmological system is an autonomous polynomial dynamical system, and by using a mathematical theorem we shall investigate whether finite-time singularities can occur in the dynamical system variables. As we demonstrate, the solutions of the dynamical system are non-singular for all cosmic times and this result is general, meaning that the initial conditions corresponding to the regular solutions, belong to a general set of initial conditions and not to a limited set of initial conditions. As we explain, a dynamical system singularity is not directly related to a physical finite-time singularity. Then, by assuming that the Hubble rate with functional form $H(t)=f_1(t)+f_2(t)(t-t_s)^{\alpha}$, is a solution of the dynamical system, we investigate the implications of the absence of finite-time singularities in the dynamical system variables. As we demonstrate, Big Rip and a Type IV singularities can always occur if $\alpha 2$ respectively. However, Type II and Type III singularities cannot occur in the cosmological system, if the Hubble rate we quoted is considered a solution of the cosmological system.

On the consistency of the Wheeler-deWitt equation in the quantized Eddington-inspired Born-Infeld gravity

Abstract: We re-examine the quantum geometrodynamical approach within the Eddington-inspired-Born-Infeld theory of gravity, which was first proposed in our previous work [1]. A thorough analysis of the classical Hamiltonian with constraints is carried and the correctness and self-consistency of the modified Wheeler deWitt equation (WDW) is studied. We find that based on the newly obtained WDW equation derived with the use of the Dirac brackets, the conclusion reached in ref. [2] can be corroborated. The big rip singularity present in the classical theory, and induced by a phantom perfect fluid, is expected to be avoided when quantum effects encoded on the modified WDW equation are taken into account.

Cosmological perturbations in the entangled inflationary universe

Abstract: In this paper, the model of a multiverse made up of universes that are created in entangled pairs that conserve the total momentum conjugated to the scale factor is presented. For the background spacetime, assumed is a Friedmann-Robertson-Walker metric with a scalar field with mass $m$ minimally coupled to gravity. For the fields that propagate in the entangled spacetimes, the perturbations of the spacetime and the scalar field, whose quantum states become entangled too, are considered. They turn out to be in a quasithermal state, and the corresponding thermodynamical magnitudes are computed. Three observables are expected to be caused by the creation of the universes in entangled pairs: a modification of the Friedmann equation because of the entanglement of the spacetimes, a modification of the effective value of the potential of the scalar field by the backreaction of the perturbation modes, and a modification of the spectrum of fluctuations because the thermal distribution is induced by the entanglement of the partner universes. The later would be a distinctive feature of the creation of universes in entangled pairs.

Quantum behavior of the "Little Sibling" of the Big Rip induced by a three-form field

Abstract: A canonical quantization \`a la Wheeler-DeWitt is performed for a model of three-form fields in a homogeneous and isotropic universe. We start by carrying out the Hamiltonian formalism of this cosmological model. We then apply this formalism to a Little Sibling of the Big Rip (LSBR), an abrupt event milder than a Big Rip and that is known to be generic to several minimally coupled three-form fields for a variety of potentials. We obtain a set of analytical solutions of the Wheeler-DeWitt equation using different analytical approximations and explore the physical consequences of them. It turns out that there are quantum states where the wave function of the universe vanishes, i.e. the DeWitt condition is fulfilled for them. Given that this happens only for some subset of solutions of the Wheeler-DeWitt equation, this points out that the matter inducing the LSBR is equally important in the process as, it has been previously shown, a minimally coupled phantom scalar field feeding classically a LSBR is smoothed at the quantum level, i.e. all the quantum states lead to a vanishing wave function.

Black Holes in the Turbulent Phase of Viscous Rip Cosmology

Abstract: We study the phantom fluid in the late universe, thus assuming the equation of state parameter $w$ to be less than $-1$. The fluid is assumed to consist of two components, one laminar component $\rho$ and one turbulent component $\rho_T$, the latter set proportional to $\rho$ as well as to the Hubble parameter, $\rho_T =3\tau H\rho$ with $\tau$ a positive constant associated with the turbulence. The effective energy density is taken to be $\rho_e= \rho + \rho_T$, and the corresponding effective pressure is $p_e=w \rho_e$, with $w$ constant. These basic assumptions lead to a Big Rip universe; the physical quantities diverging during a finite rip time $t_s$. We then consider the mass accretion of a black hole in such a universe. The most natural assumption of setting the rate $dM/dt$ proportional to $M^2$ times the sum $\rho_e+p_e$, leads to a negative mass accretion, where $M(t)$ goes to zero linearly in $(t_s-t)$ near the singularity. The Hubble parameter diverges as $(t_s-t)^{-1}$, whereas $\rho_e$ and $p_e$ diverge as $(t_s-t)^{-2}$. We also discuss other options and include, for the sake of comparison, some essential properties of mass accretion in the early (inflationary) universe.

Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem

Abstract: We study a new exactly solvable model of coupling of the Dark Energy and Dark Matter, in the framework of which the kernel of non-gravitational interaction is presented by the integral Volterra-type operator well-known in the classical theory of fading memory. Exact solutions of this isotropic homogeneous cosmological model were classified with respect to the sign of the discriminant of the cubic characteristic polynomial associated with the key equation of the model. Energy-density scalars of the Dark Energy and Dark Matter, the Hubble function and acceleration parameter are presented explicitly; the scale factor is found in quadratures. Asymptotic analysis of the exact solutions has shown that the Big Rip, Little Rip, Pseudo Rip regimes can be realized with the specific choice of guiding parameters of the model. We show that the Coincidence problem can be solved if we consider the memory effect associated with the interactions in the Dark Sector of the universe.

Generic absence of strong singularities and geodesic completeness in modified loop quantum cosmologies.

Abstract: Different regularizations of the Hamiltonian constraint in loop quantum cosmology yield modified loop quantum cosmologies, namely mLQC-I and mLQC-II, which lead to qualitatively different Planck scale physics. We perform a comprehensive analysis of resolution of various singularities in these modified loop cosmologies using effective spacetime description and compare with earlier results in standard loop quantum cosmology. We show that the volume remains non-zero and finite in finite time evolution for all considered loop cosmological models. Interestingly, even though expansion scalar and energy density are bounded due to quantum geometry, curvature invariants can still potentially diverge due to pressure singularities at a finite volume. These divergences are shown to be harmless since geodesic evolution does not break down and no strong singularities are present in the effective spacetimes of loop cosmologies. Using a phenomenological matter model, various types of exotic strong and weak singularities, including big rip, sudden, big freeze and type-IV singularities, are studied. We show that as in standard loop quantum cosmology, big rip and big freeze singularities are resolved in mLQC-I and mLQC-II, but quantum geometric effects do not resolve sudden and type-IV singularities.

The Avoidance of the Little Sibling of the Big Rip Abrupt Event by a Quantum Approach

Abstract: We address the quantisation of a model that induces the Little Sibling of the Big Rip (LSBR) abrupt event, where the dark energy content is described by means of a phantom-like fluid or a phantom scalar field. The quantisation is done in the framework of the Wheeler–DeWitt (WDW) equation and imposing the DeWitt boundary condition; i.e., the wave function vanishes close to the abrupt event. We analyse the WDW equation within two descriptions: First, when the dark energy content is described with a perfect fluid. This leaves the problem with the scale factor as the single degree of freedom. Second, when the dark energy content is described with a phantom scalar field in such a way that an additional degree of freedom is incorporated. Here, we have applied the Born–Oppenheimer (BO) approximation in order to simplify the WDW equation. In all cases, the obtained wave function vanishes when the LSBR takes place, thus fulfilling the DeWitt boundary condition.

More on the holographic Ricci dark energy model: smoothing Rips through interaction effects?

Abstract: The background cosmological dynamics of the late Universe is analysed on the framework of a dark energy model described by an holographic Ricci dark energy component. Several kind of interactions between the dark energy and the dark matter components are considered herein. We solve the background cosmological dynamics for the different choices of interactions with the aim to analyse not only the current evolution of the universe but also its asymptotic behaviour and, in particular, possible future singularities removal. We show that in most of the cases, the Big Rip singularity, a finger print of this model in absence of an interaction between the dark sectors, is substituted by a de Sitter or a Minkowski state. Most importantly, we found two new future bouncing solutions leading to two possible asymptotic behaviours, we named Little Bang and Little Sibling of the Big Bang. At a Little Bang, as the size of the universe shrinks to zero in an infinite cosmic time, the Hubble rate and its cosmic time derivative blow up. In addition, at a Little sibling of the Big Bang, as the size of the universe shrinks to zero in an infinite cosmic time, the Hubble rate blows up but its cosmic time derivative is finite. These two abrupt events can happen as well in the past.

The anisotropic distribution of the dark energy within the scope of LRS Bianchi type I model

Abstract: We investigate the anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with dark matter and anisotropic dark energy. We assume that the shear scalar $(\sigma )$ is proportional to expansion scalar $(\theta )$ . A special law is introduced for two skewness parameters that describe the deviation of pressure from isotropy. This law can lead to models: the hybrid expansion, the big rip and the little rip. The behavior of the Universe is discussed depending on the numerical parameters of the models.

An outline of cellular automaton universe via cosmological KdV equation

Abstract: It has been long known that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. We submit that Robert Kurucz’s hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion . Our model is preliminary but close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new model can be verified with observation data.

Spacetime Singularities in Generalized Brans-Dicke Theories

Abstract: We study the formation of classical singularities in Generalized Brans-Dicke theories that are natural extensions to Brans-Dicke where the kinetic term is modified by a new coupling function $\omega(\varphi)$. We discuss the asymptotic limit $\omega(\varphi)\rightarrow\infty$ and show that the system generically does not approach General Relativity. Given the arbitrariness of $\omega(\varphi)$, one can search for coupling functions chosen specifically to avoid classical singularities. However, we prove that this is not the case. Homogeneous and spherically symmetric collapsing objects form singularities for arbitrary coupling functions. On the other hand, expanding cosmological scenarios are completely free of Big Rip type singularities. In an expanding universe, the scalar field behaves at most as stiff matter, which makes these cosmological solutions asymptotically approach General Relativity.

Ghost Dark Energy in a Cyclic Universe

Abstract: In this paper, we investigate the Ghost Dark Energy (GDE) and the Generalized Ghost Dark Energy (GGDE) in a cyclic universe in which the high-energy regime is modified by the effects of quantum gravity, causing a turnaround (and a bounce) of the universe. First, we study the non-interacting cases for both of these models. We find that, in the absence of interaction in a cyclic universe, the deceleration parameter becomes a constant; as a result, the universe cannot move from an accelerated expansion phase to a deceleration phase and so cannot reach turnaround point and starts to contract. Then, we extend our study to the interacting GDE and GGDE models. We obtain the evolution of the dark energy density, the deceleration and the equation of state parameters for these models in a cyclic universe. In this case, the transition from an accelerated expansion phase to the deceleration phase in the future (near the turnaround point) can be achieved in a cyclic universe.

Self-acceleration and matter content in bicosmology from Noether symmetries

Abstract: In bigravity, when taking into account the potential existence of matter fields minimally coupled to the second gravitation sector, the dynamics of our Universe depends on some matter that cannot be observed in a direct way In this paper, we assume the existence of a Noether symmetry in bigravity cosmologies in order to constrain the dynamics of that matter By imposing this assumption we obtain cosmological models with interesting phenomenology In fact, considering that our universe is filled with standard matter and radiation, we show that the existence of a Noether symmetry implies that either the dynamics of the second sector decouples, being the model equivalent to general relativity (GR), or the cosmological evolution of our universe tends to a de Sitter state with the vacuum energy in it given by the conserved quantity associated with the symmetry The physical consequences of the genuine bigravity models obtained are briefly discussed We also point out that the first model, which is equivalent to GR, may be favored due to the potential appearance of instabilities in the second model

The Routledge Companion to the New Cosmology

Abstract: Just what is Einstein's Theory of Relativity? The Big Bang Theory? Curvature of Spacetime? What do astronomers mean when they talk of a 'flat universe'? This approachable and authoritative guide to the cosmos answers these questions, and more. Taking advantage of the distinctive Companion format, readers can use the extensive, cross-referenced background chapters as a fascinating and accessible introduction to the current state of cosmological knowledge - or, they can use the convenient A-Z body of entries as a quick reference to a wide range of terms and concepts. Entries include topics such as: Black Hole; Doppler Effect; Fermi, Enrico; Heat Death of the Universe; Life in the Universe; Olber's Paradox; Quantum Field Theory; Supernova; and much more.

Quantum behavior of the "Little Sibling" of the Big Rip induced by a three-form field.

Abstract: A canonical quantization \`a la Wheeler-DeWitt is performed for a model of three-form fields in a homogeneous and isotropic universe. We start by carrying out the Hamiltonian formalism of this cosmological model. We then apply this formalism to a Little Sibling of the Big Rip (LSBR), an abrupt event milder than a Big Rip and that is known to be generic to several minimally coupled three-form fields for a variety of potentials. We obtain a set of analytical solutions of the Wheeler-DeWitt equation using different analytical approximations and explore the physical consequences of them. It turns out that there are quantum states where the wave function of the universe vanishes, i.e. the DeWitt condition is fulfilled for them. Given that this happens only for some subset of solutions of the Wheeler-DeWitt equation, this points out that the matter inducing the LSBR is equally important in the process as, it has been previously shown, a minimally coupled phantom scalar field feeding classically a LSBR is smoothed at the quantum level, i.e. all the quantum states lead to a vanishing wave function.

Compactified cosmological simulations of the infinite universe

Abstract: We present a novel $N$-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach eliminates the need for periodic boundary conditions, a mere numerical convenience which is not supported by observation and which modifies the law of force on large scales in an unrealistic fashion. We demonstrate that our method outclasses standard simulations executed on workstation-scale hardware in dynamic range, it is balanced in following a comparable number of high and low $k$ modes and, its fundamental geometry and topology match observations. Our approach is also capable of simulating an expanding, infinite universe in static coordinates with Newtonian dynamics. The price of these achievements is that most of the simulated volume has smoothly varying mass and spatial resolution, an approximation that carries different systematics than periodic simulations. Our initial implementation of the method is called StePS which stands for Stereographically Projected Cosmological Simulations. It uses stereographic projection for space compactification and naive $\mathcal{O}(N^2)$ force calculation which is nevertheless faster to arrive at a correlation function of the same quality than any standard (tree or P$^3$M) algorithm with similar spatial and mass resolution. The $N^2$ force calculation is easy to adapt to modern graphics cards, hence our code can function as a high-speed prediction tool for modern large-scale surveys. To learn about the limits of the respective methods, we compare StePS with GADGET-2 \citep{Gadget2_2005MNRAS.364.1105S} running matching initial conditions.

Wave asymptotics at a cosmological time-singularity

Abstract: We investigate the propagation of the scalar waves in the FLRW universes beginning with a Big Bang and ending with a Big Crunch, a Big Rip, a Big Brake or a Sudden Singularity. We obtain the sharp description of the asymptotics for the solutions of the linear Klein-Gordon equation, and similar results for the semilinear equation with a subcritical exponent. We prove that the number of cosmological particle creations is finite under general assumptions on the initial Big Bang and the final Big Crunch or Big Brake.

Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem

Abstract: We study a new exactly solvable model of coupling of the Dark Energy and Dark Matter, in the framework of which the kernel of non-gravitational interaction is presented by the integral Volterra-type operator well-known in the classical theory of fading memory. Exact solutions of this isotropic homogeneous cosmological model were classified with respect to the sign of the discriminant of the cubic characteristic polynomial associated with the key equation of the model. Energy-density scalars of the Dark Energy and Dark Matter, the Hubble function and acceleration parameter are presented explicitly; the scale factor is found in quadratures. Asymptotic analysis of the exact solutions has shown that the Big Rip, Little Rip, Pseudo Rip regimes can be realized with the specific choice of guiding parameters of the model. We show that the Coincidence problem can be solved if we consider the memory effect associated with the interactions in the Dark Sector of the Universe.

Wave asymptotics at a cosmological time-singularity: classical and quantum scalar fields

Abstract: We investigate the propagation of the scalar waves in the FLRW universes beginning with a Big Bang and ending with a Big Crunch, a Big Rip, a Big Brake or a Sudden Singularity. We obtain the sharp description of the asymptotics for the solutions of the linear Klein-Gordon equation, and similar results for the semilinear equation with a subcritical exponent. We prove that the number of cosmological particle creation is finite under general assumptions on the initial Big Bang and the final Big Crunch or Big Brake.