We derive slow-roll conditions for thawing quintessence. We solve the equation of motion of $ϕ$ for a Taylor expanded potential (up to the quadratic order) in the limit where the equation of state $w$ is close to -1 to derive the equation of state as a function of the scale factor. We find that the evolution of $ϕ$ and hence $w$ are described by only two parameters. The expression for $w(a)$, which can be applied to general thawing models, coincides precisely with that derived recently by Dutta and Scherrer for hilltop quintessence. The consistency conditions of $|w+1|\ll 1$ are derived. The slow-roll conditions for freezing quintessence are also derived.
Thawing and freezing quintessence models are compared thermodynamically. Both of them are found to disobey the Generalized Second Law of Thermodynamics. However, for freezing models, there is still a scope as this breakdown occurs in the past, deep inside the radiation dominated era, when a standard scalar field model with a pressureless matter is not a correct description of the matter content. The thawing model has a pathological breakdown in terms of thermodynamics in a finite future.
We look at observational constraints on the thawing class of scalar field models proposed to explain the late time acceleration of the universe. Using the recently introduced `Statefinder Hierarchy', we compare these thawing class of models with other widely studied dark energy (and modified gravity) models to check the underlying parameter degeneracies. We put constraints on the deviations of these thawing models from the canonical ΛCDM model using a large class of observational data, e.g, the Supernova Type Ia data, the BAO data, the CMB data and data from the measurements of the Hubble para…
We derive the slow-roll conditions for a non-minimally coupled scalar field (extended quintessence) during the radiation/matter dominated era extending our previous results for thawing quintessence. We find that the ratio $\ddotϕ/3H\dotϕ$ becomes constant but negative, in sharp contrast to the ratio for the minimally coupled scalar field. We also find that the functional form of the equation of state of the scalar field asymptotically approaches that of the minimally coupled thawing quintessence.
We examine the Swampland conjectures in the context of generic slow-roll thawing quintessence models. Defining $λ\equiv |V^{\prime}(ϕ_i)/V(ϕ_i)|$ and $K \equiv \sqrt{1 - 4V^{\prime \prime}(ϕ_i)/3V(ϕ_i)}$, where $ϕ_i$ is the initial value of $ϕ$, we find regions of parameter space consistent with both observational data and with the refined de Sitter conjecture, and we show that all such models satisfy the distance conjecture. We quantify the degree of fine-tuning on $λ$ needed to achieve these results.
Using the latest observational data we obtain a lower bound on the initial value of the quintessence field in thawing quintessence models of dark energy. For potentials of the form V(ϕ) ϕ^{\pm2} we find that the initial value |ϕ_i|>7x10^{18}\gev. We then relate ϕ_i to the duration of inflation by assuming that the initial value of the quintessence field is determined by quantum fluctuations of the quintessence field during inflation. From the lower bound on $ϕ_i$ we obtain a lower bound on the number of e-foldings of inflation, namely, N>2x10^{11}. We obtain similar bounds for other power law …
For two types of quintessence models having thawing and tracking properties, there exist analytic solutions for the dark energy equation of state w expressed in terms of several free parameters. We put observational bounds on the parameters in such scenarios by using the recent data of Supernovae type Ia, Cosmic Microwave Background, and Baryon Acoustic Oscillations. The observational constraints are quite different depending on whether or not the recent BAO data from BOSS are taken into account. With the BOSS data the upper bounds of today's values of w (=w_0) in thawing models is very close …
The late time acceleration of the Universe can be characterized in terms of an extra, time dependent, component of the universe -- dark energy. The simplest proposal for dark energy is a scalar-tensor theory -- quintessence -- which consists of a scalar field, $ϕ$, whose dynamics is solely dictated by its potential, $V(ϕ)$. Such a theory can be uniquely characterized by the equation of state of the scalar field energy momentum-tensor. We find the time dependence of the equation of state for a broad family of potentials and, using this information, we propose an analytic prior distribution for …
Quintessence is a canonical scalar field introduced to explain the late-time cosmic acceleration. The cosmological dynamics of quintessence is reviewed, paying particular attention to the evolution of the dark energy equation of state w. For the field potentials having tracking and thawing properties, the evolution of w can be known analytically in terms of a few model parameters. Using the analytic expression of w, we constrain quintessence models from the observations of supernovae type Ia, cosmic microwave background, and baryon acoustic oscillations. The tracking freezing models are hardly…
Quintessence, a scalar field model, has been proposed to account for the acceleration of the Universe at present. We discuss how accurately quintessence models are discriminated by future cosmological surveys, which include experiments of CMB, galaxy clustering, weak lensing, and the type Ia SNe surveys, by making use of the conventional parameterized dark energy models. We can see clear differences between the thawing and the freezing quintessence models at more than $1σ$ ($2σ$) confidence level as long as the present equation of state for quintessence is away from $-1$ as $w_X \gtrsim -0.95 …
Current cosmological data puts increasing pressure on models of dark energy in the freezing class, e.g. early dark energy or those with equation of state $w$ substantially different from $-1$. We investigate to what extent data will distinguish the thawing class of quintessence from a cosmological constant. Since thawing dark energy deviates from $w=-1$ only at late times, we find that deviations $1+w\lesssim0.1$ are difficult to see even with next generation measurements; however, modest redshift drift data can improve the sensitivity by a factor of two. Furthermore, technical naturalness pre…
We discuss the general dynamical behaviors of quintessence field, in particular, the general conditions for tracking and thawing solutions are discussed. We explain what the tracking solutions mean and in what sense the results depend on the initial conditions. Based on the definition of tracking solution, we give a simple explanation on the existence of a general relation between $w_ϕ$ and $Ω_ϕ$ which is independent of the initial conditions for the tracking solution. A more general tracker theorem which requires large initial values of the roll parameter is then proposed. To get thawing solu…
In this work we model the quintessence potential in a Taylor series expansion, up to second order, around the present-day value of the scalar field. The field is evolved in a thawing regime assuming zero initial velocity. We use the latest data from the Planck satellite, baryonic acoustic oscillations observations from the Sloan Digital Sky Survey, and Supernovae luminosity distance information from Union2.1 to constrain our models parameters, and also include perturbation growth data from the WiggleZ, BOSS and the 6dF surveys. The supernova data provide the strongest individual constraint on …
Constraining Quintessence Models with ISW-tSZ Cross-Correlations: A Comparative Analysis of Thawing, Tracker, and Scaling-Freezing Dynamics
Guangdong Technion - Israel Institute of Technology（广东以色列理工学院）；North-West University（西北大学）；Adekunle Ajasin University（阿德昆莱·阿贾辛大学）；Indian Institute of Technology Indore（印度学院印多尔分校）；Jamia Millia Islamia（贾米亚米利亚伊斯兰大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（国家理论与计算科学研究所）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；University of Malta（马耳他大学）；Southwest Jiaotong Univer（西南交通大学）
The recent GW170817 measurement favors the simplest dark energy models, such as a single scalar field. Quintessence models can be classified in two classes, freezing and thawing, depending on whether the equation of state decreases towards $-1$ or departs from it. In this paper we put observational constraints on the parameters governing the equations of state of tracking freezing, scaling freezing and thawing models using updated data, from the Planck 2015 release, joint light-curve analysis and baryonic acoustic oscillations. Because of the current tensions on the value of the Hubble paramet…
We examine the evolution of quintessence models with potentials satisfying (V'/V)^2<<1 and V"/V<<1, in the case where the initial field velocity is nonzero. We derive an analytic approximation for the evolution of the equation of state parameter, w, for the quintessence field. We show that such models are characterized by an initial rapid freezing phase, in which the equation of state parameter w decreases with time, followed by slow thawing evolution, for which w increases with time. These models resemble constant-V models at early times but diverge at late times. Our analytic approximation g…
Reconstructing the slope of a nearly flat quintessence potential from cosmography
Institute of Research and Development, Duy Tan University（发展研究院）；Faculty of Natural Sciences, Duy Tan University（自然科学学院）；Centre for Space Research, North-West University（空间研究中心）；Department of Mathematics and Applied Mathematics, University of Cape Town（数学与应用数学系）；South African Astronomical Observatory（南非天文台）；Department of Physics and Astronomy, Vanderbilt University（物理与天文学系）
Higher-Order Analytical Expansion of Thawing Dark Energy with an Exponential Potential
The Graduate University for Advanced Studies (SOKENDAI)（高等研究院）；National Astronomical Observatory of Japan（日本国立天文台）；The University of Tokyo（东京大学）；KEK（高能加速器研究机构）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学汤川理论物理国际研究所）
The Pseudo-Nambu-Goldstone Boson (PNGB) potential, defined through the amplitude $M^4$ and width $f$ of its characteristic potential $V(ϕ) = M^4[1 + \cos(ϕ/f)]$, is one of the best-suited models for the study of thawing quintessence. We analyze its present observational constraints by direct numerical solution of the scalar field equation of motion. Observational bounds are obtained using Supernovae data, cosmic microwave background temperature, polarization and lensing data from {\it Planck}, direct Hubble constant constraints, and baryon acoustic oscillations data. We find the parameter rang…
The Most Probable Behaviour of the Dark Energy Equation of State Indicates a Thawing Quintessence Field: Tomographic Alcock-Paczyński Test with Redshift-Space Correlation Function II
We derive slow-roll conditions for thawing k-essence with a separable Lagrangian $p(X,ϕ)=F(X)V(ϕ)$. We examine the evolution of the equation of state parameter, $w$, as a function of the scale factor $a$, for the case where $w$ is close to -1. We find two distinct cases, corresponding to $X \approx 0$ and $F_X \approx 0$, respectively. For the case where $X\approx0$ the evolution of $ϕ$ and hence $w$ is described by only two parameters, and $w(a)$ is model-independent and coincides with similar behavior seen in thawing quintessence models. This result also extends to non-separable Lagrangians …
In this work we investigate the possibility of constraining a thawing Quintessence scalar field model for dark energy. We propose using the imprint of baryon acoustic oscillation (BAO) on the cross-correlation of post-reionization 21-cm signal and galaxy weak lensing convergence field to tomographically measure the angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$. The projected errors in these quantities are then used to constrain the Quintessence model parameters. We find that independent $600$hrs radio interferometric observation at four observing frequencies $916 $MHz, $65…
In this paper, with the presence of swampland conjecture, we use the complex form of a scalar field and investigate the anisotropic constant-roll of an inflationary scenario. Recently, the complex quintessence field has been used to describe the accelerating expansion of the universe which has had interesting results connecting with various conditions. Therefore, the Lagrangian density of the quintessence field leads to obtaining the equations of the complex scalar field. Also, we use the anisotropic constant-roll conditions and the field equation and calculate the exact solutions for some cos…
In this paper we show that a pseudo-Nambu-Goldstone boson (PNGB) quintessence of spontaneous symmetry breaking (SSB) is responsible for an epoch of the late time cosmic acceleration. We suggest that an N=2 PNGB quintessence with SSB can give rise to the fast-roll cosmic acceleration in evolution of the Universe. In the N=2 PNGB quintessence model, the standard slow-roll condition in which the absolute value of the tachyonic mass squared $|m_q^2|$ of this model is much less than the square of the Hubble constant $H^2$, is broken down to the fast-roll condition, $|m_q^2|=O(H^2)$. However, it is …
We present a new parameterization of quintessence potentials for dark energy based directly upon the dynamical properties of the equations of motion. Such parameterization arises naturally once the equations of motion are written as a dynamical system in terms of properly defined polar variables. We have identified two different classes of parameters, and we dubbed them as dynamical and passive parameters. The dynamical parameters appear explicitly in the equations of motion, but the passive parameters play just a secondary role in their solutions. The new approach is applied to the so-called …
We derive general conditions for the existence of stable scaling solutions for the evolution of noncanonical quintessence, with a Lagrangian of the form $\mathcal{L}(X,ϕ)=X^α-V(ϕ)$, for power-law and exponential potentials when the expansion is dominated by a background barotropic fluid. Our results suggest that in most cases, noncanonical quintessence with such potentials does not yield interesting models for the observed dark energy. When the scaling solution is not an attractor, there is a wide range of model parameters for which the evolution asymptotically resembles a zero-potential solut…
We provide evidence that slow roll is not possible in any parametrically controlled regime of the moduli space of string theory. This is proven in full generality in the asymptotic limit of the moduli space of type II and heterotic Calabi-Yau compactifications for the dilaton and any number of Kähler moduli. Our results suggest that in order to build quintessence into string theory one must work in the interior of moduli space where numerical, even if not parametric, control could still be achieved.
We consider Brans-Dicke type nonminimally coupled scalar field as a candidate for dark energy. In the conformally transformed Einstein's frame, our model is similar to {\it coupled quintessence} model. In such models, we consider potentials for the scalar field which satisfy the slow-roll conditions: $[(1/V)(dV/dϕ)]^2 << 1$ and $(1/V)(d^2V/dϕ^2) << 1$. For such potentials, we show that the equation of state for the scalar field can be described by a universal behaviour, provided the scalar field rolls only in the flat part of the potentials where the slow-roll conditions are satisfied. Our wor…
Many cosmological models invoke rolling scalar fields to account for the observed acceleration of the expansion of the universe. These theories generally include a potential V(phi) which is a function of the scalar field phi. Although V(phi) can be represented by a very diverse set of functions, recent work has shown the under some conditions, such as the slow roll conditions, the equation of state parameter w is either independent of the form of V(phi) or is part of family of solutions with only a few parameters. In realistic models of this type the scalar field couples to other sectors of th…
Falsifiable anthropic model from the string landscape
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理与天文学院）；CSST Science Center for the Guangdong-Hong Kong-Macau Greater Bay Area（粤港澳大湾区子午线工程科学中心）
In this work we generalize the constant-roll condition for minimally coupled canonical scalar field inflation. Particularly, we shall assume that the scalar field satisfies the condition $\ddotϕ=α(ϕ) V'(ϕ)$, and we derive the field equations under this assumption. We call the framework extended constant-roll framework. Accordingly we calculate the inflationary indices and the corresponding observational indices of inflation. In order to demonstrate the inflationary viability, we choose three potentials that are problematic in the context of slow-roll dynamics, namely chaotic, linear power-law …
Cosmological models in 1+1 dimensions are an ideal setting for investigating the quantum structure of inflationary dynamics -- gravity is renormalizable, while there is room for spatial structure not present in the minisuperspace approximation. We use this fortuitous convergence to investigate the mechanism of slow-roll eternal inflation. A variant of 1+1 Liouville gravity coupled to matter is shown to model precisely the scalar sector of cosmological perturbations in 3+1 dimensions. A particular example of quintessence in 1+1d is argued on the one hand to exhibit slow-roll eternal inflation a…
