M. R. Setare, E. N. Saridakis
We investigate the phase-space structure of the quintom paradigm in the framework of a spatially flat, open, or closed isotropic and homogeneous universe. We examine the dynamical evolution under the assumption of late-time dark energy domination, without specifying the explicit quintom potential form. The obtained cosmological behavior is qualitatively different than that acquired from the single phantom model.
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In this paper, we study the possibility of model building of cyclic universe with Quintom matter in the framework of Loop Quantum Cosmology. After a general demonstration, we provide two examples, one with double-fluid and another double-scalar field, to show how such a scenario is obtained. Analytical and numerical calculations are both presented in the paper.
In the present work, we investigate the universe dominated by quintom or hessence energies in Loop Quantum Cosmology (LQC). Interestingly enough, we find that there are some stable attractors in these two cases. In the case of quintom, all stable attractors have the feature of decelerated expansion. In the case of hessence, most of stable attractors have the feature of decelerated expansion while one stable attractor can have decelerated or accelerated expansion depend on the model parameter. In all cases, the equation-of-state parameter (EoS) of all stable attractors are larger than -1 and th…
A Focused Review of Quintom Cosmology: From Quintom Dark Energy to Quintom Bounce
本文回顾了 Quintom 宇宙学，重点讨论了 Quintom 跳跃和循环宇宙，探讨了动态黑暗能量理论及其在宇宙学中的应用。
We review the paradigm of quintom cosmology. This scenario is motivated by the observational indications that the equation of state of dark energy across the cosmological constant boundary is mildly favored, although the data are still far from being conclusive. As a theoretical setup we introduce a no-go theorem existing in quintom cosmology, and based on it we discuss the conditions for the equation of state of dark energy realizing the quintom scenario. The simplest quintom model can be achieved by introducing two scalar fields with one being quintessence and the other phantom. Based on the…
Equivalence of $f(Q)$ cosmology with quintom-like scenario: the phantom field as effective realization of the non-trivial connection
本研究证明带非平凡联络的$f(Q)$宇宙学与类quintom模型动力学等价，发现非线性$f(Q)$和联络对应的标量场组合出正则场与phantom场，为phantom场提供了非特设的新实现思路。
We investigate quintom cosmology in FRW universes using isomorphic models consisting of three coupled oscillators, one of which carries negative kinetic energy. In particular, we examine the cosmological paradigms of minimally-coupled massless quintom, of two conformally-coupled massive scalars and of conformally-coupled massive quintom, and we obtain their qualitative characteristics as well as their quantitative asymptotic behavior. For open or flat geometries, we find that, independently of the specific initial conditions, the universe is always led to an eternal expansion.
Quintom cosmology and modified gravity after DESI 2024
本文利用高斯过程和最新DESI数据重建宇宙学背景演化，发现暗能量状态方程呈现quintom-B行为，并从场论与修改引力角度探讨了实现该演化的条件。
Unified dark energy from Chiral-Quintom model with a mixed potential in Friedmann--Lema\^ıtre--Robertson--Walker cosmology
本研究在FLRW宇宙学框架下提出含混合势的Chiral-Quintom双标量场暗能量模型，可描述加速宇宙、大撕裂等多种渐近宇宙学场景，实现暗能量的统一描述。
Considering the quintom model with arbitrary potential, it is shown that there always exists a solution which evolves from w > -1 region to w < -1 region. The problem is restricted to the slowly varying potentials, i.e. the slow-roll approximation. It is seen that the rate of this phase transition only depends on the energy density of matter at transition time, which itself is equal to the kinetic part of quintom energy density at that time. The perturbative solutions of the fields are also obtained.
We examine quintom dark energy models, produced by the combined consideration of a canonical and a phantom field, with nearly flat potentials and dark energy equation-of-state parameter $w_{DE}$ close to -1. We find that all such models converge to a single expression for $w_{DE}(z)$, depending only on the initial field values and their derivatives. We show that this quintom paradigm allows for a description of the transition through -1 in the near cosmological past. In addition, we provide the necessary conditions for the determination of the direction of the -1-crossing.
Quintom fields from chiral anisotropic cosmology
本研究在手性各向异性毕安基I型宇宙背景下，从经典与量子两方面分析Quintom场的非标准相互作用，得到解析解，以大反弹解释大爆炸奇点，证明各向异性会随时间或量子效应消失并趋于各向同性。
In this paper we investigate quintom cosmologies with arbitrary potentials from the dynamical systems perspective. The dynamical systems analysis is complete in the sense that it includes the asymptotic regime where both scalar fields diverge, which proves to be particularly relevant in connection with the existence of tracking phases. The results of the present study indicate that the existence of phantom attractors is not generic: for quintom models there may exist either de Sitter attractors associated with the saddle points of the potential, or tracking attractors in the asymptotic regime …
A class of dynamical dark energy models, dubbed Spinor Quintom, can be constructed by a spinor field $ψ$ with a nontraditional potential. We find that, if choosing suitable potential, this model is able to allow the equation-of-state to cross the cosmological constant boundary without introducing any ghost fields. In a further investigation, we show that this model is able to mimic a perfect fluid of Chaplygin gas with $p=-c/ρ$ during the evolution, and also realizes the Quintom scenario with its equation-of-state across -1.
For the quintom models with arbitrary potential $V=V(ϕ,σ)$, the asymptotic value of equation of state parameter w is obtained by a new method. In this method, w of stable attractors are calculated by using the ratio (d ln V)/(d ln a) in asymptotic region. All the known results, have been obtained by other methods, are reproduced by this method as specific examples.
Assuming the Hubble parameter is a continuous and differentiable function of comoving time, we investigate necessary conditions for quintessence to phantom phase transition in quintom model. For power-law and exponential potential examples, we study the behavior of dynamical dark energy fields and Hubble parameter near the transition time, and show that the phantom-divide-line w=-1 is crossed in these models.
We investigate quintom evolution in power-law potentials. We extract the early-time, tracker solutions, under the assumption of matter domination. Additionally, we derive analytical solutions at intermediate times, that is at low redshifts, which is the period during the transition from matter to dark-energy domination. A comparison with exact evolution reveals that the tracker solutions are valid within 98% for z>1.5, while the intermediate ones are accurate within 98% up to z=0.5. Using these expressions we extract two new w-parametrizations, one in terms of the redshift and one in terms of …
In this work, first, we study a flat Friedmann-Robertson-Walker Universe with two scalar fields but only one potential term, which can be thought as a simple quintessence plus a K-essence model. Employing the Hamiltonian formalism we are able to obtain the classical and quantum solutions. The second model studied, is also a flat Friedmann-Robertson-Walker Universe with two scalar fields, with the difference that the two potentials are considered as well as the standard kinetic energy and the mixed term (chiral field approach). Regarding this second model, it is shown that setting to zero the c…
We present a unified treatment of the phase space of a spatially flat homogeneous and isotropic universe dominated by a phantom field. Results on the dynamics and the late time attractors (Big Rip, de Sitter, etc.) are derived without specifying the form of the phantom potential, using only general assumptions on its shape. Many results found in the literature are quickly recovered and predictions are made for new scenarios.
The cosmological evolution in Nonlinear Born-Infeld(hereafter NLBI) scalar field theory with negative potentials was investigated. The cosmological solutions in some important evolutive epoches were obtained. The different evolutional behaviors between NLBI and linear(canonical) scalar field theory have been presented. A notable characteristic is that NLBI scalar field behaves as ordinary matter nearly the singularity while the linear scalar field behaves as "stiff" matter. We find that in order to accommodate current observational accelerating expanding universe the value of potential paramet…
We analyse the PVLAS results using a chameleon field whose properties depend on the environment. We find that, assuming a runaway bare potential $V(ϕ)$ and a universal coupling to matter, the chameleon potential is such that the scalar field can act as dark energy. Moreover the chameleon field model is compatible with the CAST results, fifth force experiments and cosmology.
In the context of scalar-tensor models of dark energy and inflation, the dynamics of vacuum scalar-tensor cosmology are analysed without specifying the coupling function or the scalar field potential. A conformal transformation to the Einstein frame is used and the dynamics of general relativity with a minimally coupled scalar field are derived for a generic potential. It is shown that the dynamics are non-chaotic, thus settling an existing debate.
In this talk I will describe the role of supersymmetric flat directions in the early Universe cosmology. Particularly I will discuss how supergravity effects lift the flat direction potential and leads to interesting cosmological consequences.
Using the factorization approach of quantum mechanics, we obtain a family of iso-spectral scalar potentials for noncommutative quantum cosmology. The family we build is based on a scattering Wheeler-DeWitt solution for the potential $V(ϕ)=V_0e^{-λϕ}$. We analyze the effects of noncommutativity on the iso-potentials and the possible relationship between noncommutativity and dark energy.
In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate the conditions that subsequently lead to slow-roll inflation. The consequences for this mechanism of various quantization ambiguities arising within loop quantum cosmology are considered. For the case of a quadratic potential, it is found that some quantization procedures are more likely to generate a phase of slow--roll inflation. In general, however, loop quantum cosmology is robust to ambiguities…
We examine in the context of supersymmetric models whether the usual cosmological upper bound on the axion decay constant can be relaxed by assuming a period of stronger QCD in the early universe. By evaluating the axion potential in the early universe and also taking into account the dilaton potential energy, it is argued that a stronger QCD is not useful for raising up the bound.
We study in detail the general solution for a scalar field cosmology with an exponential potential, correcting some imprecisions, encountered previously in the literature. In addition, we generalize this solution for a piecewise exponential potential, which is continuous, but not smooth (with cusps).
We consider a cosmological solution which can explain anisotropic evolution of spatial dimensions and the stabilization of extra dimensions in brane gas formalism. We evaluate the effective potentials, induced by brane gas, bulk flux and supergravity particles, which govern the sizes of the observed three and the extra dimensions. It is possible that the wrapped internal volume can oscillate between two turning points or sit at the minimum of the potential while the unwrapped three dimensional volume can expand monotonically. Including the supergravity particles makes the effective potential s…
We discuss the classical aspects of dynamics of scalar models with non-positive Higgs potentials in the FRW cosmology. These models appear as effective local models in non-local models related with string field theories. After a suitable field redefinition these models have the form of local Higgs models with a negative extra cosmological term and the total Higgs potential is non-positively defined and has rather small coupling constant. The non-positivity of the potential leads to the fact that on some stage of evolution the expansion mode gives place to the mode of contraction, due to that t…
We investigate non-linear Schrödinger-type formulation of cosmology of which our cosmological system is a general relativistic FRLW universe containing canonical scalar field under arbitrary potential and a barotropic fluid with arbitrary spatial curvatures. We extend the formulation to include phantom field case and we have found that Schrödinger wave function in this formulation is generally non-normalizable. Assuming power-law expansion, $a \sim t^q$, we obtain scalar field potential as function of time. The corresponding quantities in Schrödinger-type formulation such as Schrödinger total …
We consider the anisotropic evolution of spatial dimensions and the stabilization of internal dimensions in the framework of brane gas cosmology. We observe that the bulk RR field can give an effective potential which prevents the internal subvolume from collapsing. For a combination of $(D-3)$-brane gas wrapping the extra dimensions and 4-form RR flux in the unwrapped dimensions, it is possible that the wrapped subvolume has an oscillating solution around the minimum of the effective potential while the unwrapped subvolume expands monotonically. The flux gives a logarithmic bounce to the effe…
Cosmological inflation is discussed in the realm of Einstein-Cartan-Brans-Dicke (ECBD) gravity by constructing an effective inflaton potential and computing the number of e-folds.It is shown that spin-torsion density contributes to a decrease on the number of e-folds of inflation when the ratio of spin-torsion density to matter density is aprecciable as happens in the Early Universe.Quantum fluctuations of spin and inflatons are also investigated.Our results seems to be in agreement with Palle's proposal that quantum fluctuations of spin may trigger the primordial era of the universe.The main …
In this paper we consider tachyonic matter in spatially at FRW universe, and obtain behavior of some important cosmological parameters for two special cases of potentials. First we assume the exponential potential and then consider hyperbolic cosine type potential. In both cases we obtain behavior of the Hubble, deceleration and EoS parameters. Comparison with observational data suggest the model with hyperbolic cosine type scalar-field potentials has good model to describe universe.
$SO(10)$ grand unified models have an intermediate symmetry group in between $SO(10)$ and $SU(3)_{C} \otimes SU(2)_{L} \otimes U(1)_{Y}$. Hence they lead to a prediction for proton lifetime in agreement with the experimental lower limit. This paper reviews the recent work on the tree-level potential and the one-loop effective potential for such models, with application to inflationary cosmology. The open problems are the use of the most general form of tree-level potential for $SO(10)$ models in the reheating stage of the early universe, and the analysis of non-local effects in the semiclassic…
We consider the statistical properties of vacua and inflationary trajectories associated with a random multifield potential. Our underlying motivation is the string landscape, but our calculations apply to general potentials. Using random matrix theory, we analyze the Hessian matrices associated with the extrema of this potential. These potentials generically have a vast number of extrema. If the cross-couplings (off-diagonal terms) are of the same order as the self-couplings (diagonal terms) we show that essentially all extrema are saddles, and the number of minima is effectively zero. Avoidi…
We present a class of exact solutions for homogeneous, anisotropic cosmologies in four dimensions derived from the low-energy string effective action including a homogeneous dilaton $ϕ$ and antisymmetric tensor potential $B_{μν}$. Making this potential time-dependent produces an anisotropic energy-momentum tensor, and leads us to consider a Bianchi I cosmology. The solution for the axion field must then only be a linear function of one spatial coordinate. This in turn places an upper bound on the product of the two scale factors evolving perpendicular to the gradient of the axion field. The on…
We develop a technique for the reconstruction of the potential for a scalar field in cosmological models based on induced gravity. The potentials reproducing cosmological evolutions driven by barotropic perfect fluids, a cosmological constant, a Chaplygin gas and a modified Chaplygin gas are constructed explicitly.
We show that the general solution of scalar field cosmology in $d$ dimensions with exponential potentials for flat Robertson-Walker metric can be found in a straightforward way by introducing new variables which completely decouple the system. The explicit solution shows the region of parameters where the expansion has eternal acceleration, transient periods of acceleration, or no period of acceleration at all. In the cases of transient acceleration, the energy density exhibits a plateau during the accelerated expansion, where $p\cong -ρ$, due to dominance of potential energy. We determine the…
In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in solving other problems. The purpose of this work is to give an introduction both to the Hamiltonian formalism and to the cosmology of bigravity. We sketch three roads to the Hamiltonian of bigravity with the dRGT potential: the metric, the tetrad and the minisuperspace approaches.
We examine in detail the cosmology based on quantal (Bohmian) trajectories as suggested in a recent study arXiv:1404.3093[gr-qc]. We disagree with the conclusions regarding predicting the value of the cosmological constant $Λ$ and evading the big bang singularity. Furthermore, we show that the approach of using a quantum corrected Raychaudhuri equation (QRE), as suggested in arXiv:1404.3093[gr-qc], is unsatisfactory, because, essentially, it uses the Raychaudhuri equation, which is a kinematical equation, in order to predict dynamics. In addition, even within this inconsistent framework, the a…
Leading all-loop quantum contribution to the effective potential in the inflationary cosmology
该研究在领头对数近似下推导广义RG方程，构建$T^2$与$T^4$慢滚暴胀模型的全圈量子有效势，发现高阶圈修正平滑势行为且保留自发对称破缺，所得$n_s$和$r$与观测相符。
We investigate cosmologies with an arbitrary number of scalars and the most general multi-exponential potential. By formulating the equations of motion in terms of autonomous systems we complete the classification of power-law and de Sitter solutions as critical points, e.g. attractor and repeller solutions, in terms of the scalar couplings. Many of these solutions have been overlooked in the literature. We provide specific examples for double and triple exponential potentials with one and two scalars, where we find numerical solutions, which interpolate between the critical points. Some of th…
In power-law cosmology, we determine potential function of a canonical scalar field in FLRW universe in presence of barotropic perfect fluid. The combined WMAP5+BAO+SN dataset and WMAP5 dataset are used here to determine the value of the potential. The datasets suggest slightly closed universe. If the universe is closed, the exponents of the power-law cosmology are $q = 1.01$ (WMAP5 dataset) and $q=0.985$ (combined dataset). The lower limits of $a_0$ (closed geometry) are $5.1\E{26}$ for WMAP5 dataset and $9.85\E{26}$ for the combined dataset. The domination of the power-law term over the curv…
We study the Newtonian cosmology taking into account the leading classical and quantum corrections of order $\mathcal{O}(G^{2})$ in the Newtonian potential. We first derive the modified Friedmann equations starting from the non-relativistic conservation of kinetic energy and potential energy for an infinitesimal mass. We then consider the leading classical correction term and the quantum correction term in the Newtonian potential for deriving the Friedmann equation, however, the quantum correction term is too small and hence does not contribute in the physical results. We then investigate the …
We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For quantization, we employ geometrodynamics. In the case of constant potential, we discuss both Wheeler-DeWitt quantization and reduced quantization. We are able to give various solutions and discuss their asymptotics. For the case of general potential, we transform the Wheeler-DeWitt equation to a form where it leads to a difference equation. Such a difference equa…
Starobinsky potential and power suppression in hybrid Loop Quantum Cosmology
该研究在含Starobinsky势的混合圈量子宇宙学框架下，采用NO-AHD真空选择，通过解析与数值方法计算原初张量功率谱，证实了近似的准确性，并发现功率谱存在由反弹背景动力学决定的特征截断。
A self-consistent pre-inflationary extension of the inflationary scenario with the Starobinsky potential, favored by Planck data, is studied using techniques from loop quantum cosmology (LQC). The results are compared with the quadratic potential previously studied. Planck scale completion of the inflationary paradigm and observable signatures of LQC are found to be robust under the change of the inflaton potential. The entire evolution, from the quantum bounce all the way to the end of inflation, is compatible with observations. Occurrence of desired slow-roll phase is almost inevitable and n…
We present a phase-plane analysis of cosmologies containing a scalar field $ϕ$ with an exponential potential $V \propto \exp(-λκϕ)$ where $κ^2 = 8πG$ and $V$ may be positive or negative. We show that power-law kinetic-potential scaling solutions only exist for sufficiently flat ($λ^2<6$) positive potentials or steep ($λ^2>6$) negative potentials. The latter correspond to a class of ever-expanding cosmologies with negative potential. However we show that these expanding solutions with a negative potential are to unstable in the presence of ordinary matter, spatial curvature or anisotropic shear…
In the frame of the scalar field model with non minimal kinetic coupling to gravity, we study the cosmological solutions of the Chaplygin gas model of dark energy. By appropriately restricting the potential, we found the scalar field, the potential and coupling giving rise to the Chaplygin gas solution. Extensions to the generalized and modified Chaplygin gas have been made.
We consider the Noether Symmetry Approach for a cosmological model derived from a tachyon scalar field $T$ with a Dirac-Born-Infeld Lagrangian and a potential $V(T)$. Furthermore, we assume a coupled canonical scalar field $ϕ$ with an arbitrary interaction potential $B(T,ϕ)$. Exact solutions are derived consistent with the accelerated behavior of cosmic fluid.
We construct the general analytical solution for the $\mathcal{N}$-field product-exponential potential in an expanding FLRW background. We demonstrate the relevance of this analytical solution in more general contexts for the derivation of estimates for the transitional time between an arbitrary initial state and the slow-roll solutions. In certain cases, these estimates can also be used to demonstrate the non-linear convergence towards the slow-roll solutions. In addition, we extend the solution to include stiff matter as well.
It was shown recently that replacing classical geodesics with quantal (Bohmian) trajectories gives rise to a quantum corrected Raychaudhuri equation (QRE). In this article we derive the second order Friedmann equations from the QRE, and show that this also contains a couple of quantum correction terms, the first of which can be interpreted as cosmological constant (and gives a correct estimate of its observed value), while the second as a radiation term in the early universe, which gets rid of the big-bang singularity and predicts an infinite age of our universe.
We study a tachyon cosmological model based on the dynamics of a 3-brane in the bulk of the second Randall-Sundrum model extended to more general warp functions. A well known prototype of such a generalization is the bulk with a selfinteracting scalar field. As a consequence of a generalized bulk geometry the cosmology on the observer brane is modified by the scale dependent four-dimensional gravitational constant. In particular we study a power law warp factor which generates an inverse power-law potential $V\propto φ^{-n}$ of the tachyon field $φ$. We find a critical power $n_{\rm cr}$ that …
We examine the phase space of Hořava-Lifshitz cosmology for a wide range of self-interacting potentials for the scalar field under the detailed-balance condition and without imposing it, by means of the powerful method of $f$-devisers. A compactification approach is performed for the exponential potential and for potentials beyond the exponential one, extending the previous findings in the literature. By using this approach it is possible to describe the finite region of the phase space and the region where the phase-space variables becomes infinity. Furthermore, we present several results con…
In this paper, we study the pre-inflationary dynamics for the power-law potential $(V(ϕ) \propto ϕ^n)$ with $n<2$ in the framework of loop quantum cosmology. In the case where the kinetic energy of the inflaton dominates at the initial, the evolution of the universe can always be divided into three different phases prior to preheating: {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution of the expansion factor is independent not only on the initial conditions but also the inflationary potentials, and is given explicitly by an analytical solution. In con…
Inflation in unimodular loop quantum cosmology
该研究在单模圈量子宇宙学框架下，引入单模时间替代传统时间，推导不同势的解析与数值解，构建兼容观测且带量子引力印记的暴胀反弹模型。
Dark energy models can be seen as dynamical systems. In this paper we show that multi-field models with a curved field space give rise to new critical points and we analyse their stability. These are new accelerating solutions in late-time cosmology which exist even for steep potentials. This opens up the possibility to realise quintessence models even when quantum corrections spoil the flatness of the underlying potential. These non-linear sigma models arise naturally in supergravity and string models where their multi-field dynamics can help to avoid swampland bounds.
In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we present a case study to illustrate the value of this promising tool. Concretely, we take a spatially flat FRW model in the presence of a single scalar field, minimally coupled to gravity. Then, we extract the associated Schrödinger-Wheeler-DeWitt equation, allowing for a particular scope of factor ordering. Subsequently, we compute the corresponding supersy…
We argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum phys…
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