Late-time Attractor Research Articles

Transient and late time attractor tachyon dark energy: Can we distinguish it from quintessence?

The string inspired tachyon field can serve as a candidate of dark energy. Its equation of state parameter $w$ varies from 0 to $\ensuremath{-}1$. In the case of tachyon field potential $V(\ensuremath{\phi})\ensuremath{\rightarrow}0$ slower (faster) than $1/{\ensuremath{\phi}}^{2}$ at infinity, dark energy (dark matter) is a late time attractor. We investigate the tachyon dark energy models under the assumption that $w$ is close to $\ensuremath{-}1$. We find that all the models exhibit unique behavior around the present epoch which is exactly the same as that of the thawing quintessence.

A Two-Field Dilaton Model of Dark Energy

We investigate the cosmological evolution of a two-field model of dark energy, where one is a dilaton field with canonical kinetic energy and the other is a phantom field with a negative kinetic energy term. Phase-plane analysis shows that the “phantom"-dominated scaling solution is the stable late-time attractor of this type of model. We find that during the evolution of the universe, the equation of state w changes from w > −1 to w < −1, which is consistent with recent observations.

Dynamics of a scalar field in Robertson-Walker spacetimes

We analyze the dynamics of a single scalar field in Friedmann-Robertson-Walker universes with spatial curvature. We obtain the fixed point solutions which are shown to be late time attractors. In particular, we determine the corresponding scalar field potentials which correspond to these stable solutions. The analysis is quite general and incorporates expanding and contracting universes with both positive and negative scalar potentials. We demonstrate that the known power law, exponential, and de Sitter solutions are certain limits of our general set of solutions.

STATEFINDER DIAGNOSTIC FOR QUINTESSENCE WITH OR WITHOUT THERMAL INTERACTION

The cosmological dynamics of a minimally coupled scalar field that couples to the background matter with thermal interactions is investigated using statefinder diagnostics. The time evolution of the statefinder pairs {r, s} and {r, q} are obtained under the circumstance that different values of model parameters are chosen. We show that the thermal coupling term does not affect the location of the late-time attractor, but exerts an influence on the evolution of the statefinder parameters. The most notable feature of the r–s plane for the thermal coupling model, which is distinguished from the other dark energy models, is that some part of the curve with thermal coupling can form a closed loop in the second quadrant (r &gt; 1, s &lt; 0).

What is the fate of a black hole embedded in an expanding universe?

Within a large class of exact solutions of the Einstein equations describing a black hole embedded in a Friedmann universe it is shown that, under certain assumptions, only those with comoving Hawking–Hayward quasi-local mass are generic, in the sense that they are late-time attractors.

The quintom model with O(N) symmetry

We investigate the quintom model of dark energy in the generalizedcase where the corresponding canonical and phantom fields possessO(N) symmetries. Assuming exponential potentials we find that thisO(N) quintom paradigm exhibits novel properties comparing to the simple canonical and phantomscenarios. In particular, we find that the universe cannot result in a quintessence-type solution withw>−1, even in the cases where the phantom field seems to be irrelevant. On the contrary, thereare always late-time attractors which correspond to accelerating universes withw<−1 and with a recent crossing of the phantom divide, and for a very large area of theparameter space they are the only ones. This is in contrast with the previous simplequintom results, where an accelerating universe is a possible late-time stable solution but itis not guaranteed.

Scaling attractors for quintessence in a flat universe with a cosmological term

For evolution of a flat universe, we classify late time and future attractors with the scalingbehaviour of scalar field quintessence in the case of a potential which at definite values ofits parameters and initial data corresponds to exact scaling in the presence of acosmological constant.

Curvature perturbations from ekpyrotic collapse with multiple fields

A scale-invariant spectrum of isocurvature perturbations is generated during collapse in the ekpyrotic scaling solution in models where multiple fields have steep negative exponential potentials. The scale invariance of the spectrum is realized by a tachyonic instability in the isocurvature field. This instability drives the scaling solution to the late-time attractor that is the old ekpyrotic collapse dominated by a single field. We show that the transition from the scaling solution to the single-field-dominated ekpyrotic collapse automatically converts the initial isocurvature perturbations about the scaling solution to comoving curvature perturbations about the late-time attractor. The final amplitude of the comoving curvature perturbation is determined by the Hubble scale at the transition.

Late-time behaviour of the tilted Bianchi type VIh models

We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VIh using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VIh state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a ‘loophole’ is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VIh case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.

Inflation over a local maximum of a potential

We calculate the power spectrum of curvature perturbations when the inflaton field is rolling over the top of a local maximum of a potential. We show that the evolution of the field can be decomposed into a late-time attractor, which is identified as the slow roll solution, plus a rapidly decaying non-slow roll solution, corresponding to the field rolling ''up the hill'' to the maximum of the potential. The exponentially decaying transient solution can map to an observationally relevant range of scales because the Universe is also expanding exponentially. We consider the two branches separately and we find that they are related through a simple transformation of the slow roll parameter {eta} and they predict identical power spectra. We generalize this approach to the case where the inflaton field is described by both branches simultaneously and find that the mode equation can be solved exactly at all times. Even though the slow roll parameter {eta} is evolving rapidly during the transition from the transient solution to the late-time attractor solution, the resultant power spectrum is an exact power-law spectrum. Such solutions may be useful for model building on the string landscape.

Ekpyrotic collapse with multiple fields

A scale-invariant spectrum of isocurvature perturbations is generated during collapse in thescaling solution in models where two or more fields have steep negative exponentialpotentials. The scale invariance of the spectrum is realized by a tachyonic instability in theisocurvature field. We show that this instability is due to the fact that the scaling solutionis a saddle point in the phase space. The late-time attractor is identified with asingle-field-dominated ekpyrotic collapse in which a steep blue spectrum for isocurvatureperturbations is found. Although quantum fluctuations do not necessarily to disrupt theclassical solution, an additional preceding stage is required to establish classicalhomogeneity.

A quintessentially geometric model

We consider string inspired cosmology on a solitaryD3 brane moving in the background of a ring of branes located on a circle of radiusR. The motionof the D3 brane transverse to the plane of the ring gives rise to a radion field whichcan be mapped to a massive non-BPS Born–Infeld type field with acosh potential. For certain bounds of the brane tension we find an inflationary phase ispossible, with the string scale relatively close to the Planck scale. The relevantperturbations and spectral indices are all well within the expected observational bounds.The evolution of the universe eventually comes to be dominated by dark energy,which we show is a late time attractor of the model. However we also find thatthe equation of state is time dependent, and will lead to late time quintessence.

Dynamics of quintessential inflation

In this paper, we study a realistic model of quintessential inflation with radiation and matter. By the analysis of the dynamical system and numerical work about the evolution of the equation of state and cosmic density parameter, we show that this model is a good match for the current astronomical observation. The conclusion we obtain is in favor of the model where the modular part of complex field plays the role of the inflaton whereas the argument part is the quintessence field. The numerical calculation shows that a heteroclinic orbit (solution of dynamical system) which interpolates between early-time de Sitter phase (an unstable critical point) and a late-time de Sitter attractor.

Scalar field dark matter: Nonspherical collapse and late-time behavior

We show the evolution of nonspherically symmetric balls of a self-gravitating scalar field in the Newtonian regime or equivalently an ideal self-gravitating condensed Bose gas. In order to do so, we use a finite differencing approximation of the Schr\"odinger-Poisson (SP) system of equations with axial symmetry in cylindrical coordinates. Our results indicate: (i) that spherically symmetric ground state equilibrium configurations are stable against nonspherical perturbations and (ii) that such configurations of the SP system are late-time attractors for nonspherically symmetric initial profiles of the scalar field, which is a generalization of such behavior for spherically symmetric initial profiles. Our system and the boundary conditions used, work as a model of scalar field dark matter collapse after the turnaround point. In such case, we have found that the scalar field overdensities tolerate nonspherical contributions to the profile of the initial fluctuation.

COSMOLOGICAL DYNAMICS OF DILATONIC (PHANTOM) DARK ENERGY MODEL

In this paper, we study the cosmological dynamics of dilatonic dark energy model and its phantom model — with negative kinetic energy. When the potential is taken as the form [Formula: see text], we investigate the existence of a late time attractor solution, and find out the sufficient condition. One interesting feature found by us is that the evolutions of components of comic density are locally fluctuating on the way to the late time attractor. But this local fluctuation cannot hold the trend that the equation of state ω evolves to -1 and the cosmic density parameter Ωσ evolves to 1, which are important features for a dark energy model that can meet the current observations.

Ghosts, instabilities, and superluminal propagation in modified gravity models

We consider modified gravity models involving inverse powers of fourth order curvatureinvariants. Using these models’ equivalence to the theory of a scalar field coupled to alinear combination of the invariants, we investigate the properties of the propagatingmodes. Even in the case for which the fourth derivative terms in the field equations vanish,we find that the second derivative terms can give rise to ghosts, instabilities, andsuperluminal propagation speeds. We establish the conditions which the theories mustsatisfy in order to avoid these problems in Friedmann backgrounds, and show that the latetime attractor solutions generically exhibit superluminally propagating tensor or scalarmodes.

Gravitational Cooling of Self‐gravitating Bose Condensates

Equilibrium configurations for a self-gravitating scalar field with self-interaction are constructed. The corresponding Schr\"odinger-Poisson (SP) system is solved using finite differences assuming spherical symmetry. It is shown that equilibrium configurations of the SP system are late-time attractor solutions for initially quite arbitrary density profiles, which relax and virialize through the emission of scalar field bursts; a process dubbed gravitational cooling. Among other potential applications, these results indicate that scalar field dark matter models (in its different flavors) tolerate the introduction of a self-interaction term in the SP equations. This study can be useful in exploring models in which dark matter in galaxies is not point-like.

Inflation model constraints from the Wilkinson Microwave Anisotropy Probe three-year data

We extract parameters relevant for distinguishing among single-field inflation models from the Wilkinson Microwave Anisotropy Probe (WMAP) three-year data set, and also from WMAP in combination with the Sloan Digital Sky Survey (SDSS) galaxy power spectrum. Our analysis leads to the following conclusions: (1) the Harrison---Zel'dovich model is consistent with both data sets at a 95% confidence level; (2) there is no strong evidence for running of the spectral index of scalar perturbations; (3) potentials of the form $V\ensuremath{\propto}{\ensuremath{\phi}}^{p}$ are consistent with the data for $p=2$, and are marginally consistent with the WMAP data considered alone for $p=4$, but ruled out by WMAP combined with SDSS. We perform a ``Monte Carlo reconstruction'' of the inflationary potential, and find that: (1) there is no evidence to support an observational lower bound on the amplitude of gravitational waves produced during inflation; (2) models such as simple hybrid potentials which evolve toward an inflationary late-time attractor in the space of flow parameters are strongly disfavored by the data, (3) models selected with even a weak slow-roll prior strongly cluster in the region favoring a red power spectrum and no running of the spectral index, consistent with simple single-field inflation models.

Quintom models with an equation of state crossing−1

In this paper, we investigate a kind of special quintom model, which is made of a quintessence field $\phi_1$ and a phantom field $\phi_2$, and the potential function has the form of $V(\phi_1^2-\phi_2^2)$. This kind of quintom fields can be separated into two kinds: the hessence model, which has the state of $\phi_1^2>\phi_2^2$, and the hantom model with the state $\phi_1^2<\phi_2^2$. We discuss the evolution of these models in the $\omega$-$\omega'$plane ($\omega$ is the state equation of the dark energy, and $\omega'$ is its time derivative in unites of Hubble time), and find that according to $\omega>-1$ or $<-1$, and the potential of the quintom being climbed up or rolled down, the $\omega$-$\omega'$ plane can be divided into four parts. The late time attractor solution, if existing, is always quintessence-like or $\Lambda$-like for hessence field, so the Big Rip doesn't exist. But for hantom field, its late time attractor solution can be phantom-like or $\Lambda$-like, and sometimes, the Big Rip is unavoidable. Then we consider two special cases: one is the hessence field with an exponential potential, and the other is with a power law potential. We investigate their evolution in the $\omega$-$\omega'$ plane. We also develop a theoretical method of constructing the hessence potential function directly from the effective equation of state function $\omega(z)$. We apply our method to five kinds of parametrizations of equation of state parameter, where $\omega$ crossing -1 can exist, and find they all can be realized. At last, we discuss the evolution of the perturbations of the quintom field, and find the perturbations of the quintom $\delta_Q$ and the metric $\Phi$ are all finite even if at the state of $\omega=-1$ and $\omega'\neq0$.

Attractor solutions for general hessence dark energy

As a candidate for the dark energy, the hessence model has been recently introduced. We discuss the critical points of this model in an almost general case, that is for arbitrary hessence potential and almost arbitrary hessence-background matter interaction. It is shown that, in all models, there always exist some stable late-time attractors. It is shown that our general results coincide with those solutions obtained earlier for special cases, but some of them are new. These new solutions have two unique characteristics. First, the hessence field has finite value in these solutions and, second, their stabilities depend on the second derivative of the hessence potential.