This investigation explores using the beta function formalism to calculate analytic
solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar $ϕ$ with respect to the natural log of the scale factor $a$, $β(ϕ)=\frac{d ϕ}{d \ln(a)}$. Once the beta function is specified, modulo a boundary condition, the evolution of the scalar $ϕ$ as a function of the scale factor is completely determined. A rolling scalar field cosmology is defined by its action which can contain a range of physically motivated dark energy potentials. The beta function is chosen so that the associated "beta potential" is an accurate, but not exact, representation of the appropriate dark energy model potential. The basic concept is that the action with the beta potential is so similar to the action with the model potential that solutions using the beta action are accurate representations of solutions using the model action. The beta function provides an extra equation to calculate analytic functions of the cosmologies parameters as a function of the scale factor that are that are not calculable using only the model action. As an example this investigation uses a quintessence cosmology to demonstrate the method for power and inverse power law dark energy potentials. An interesting result of the investigation is that the Hubble parameter H is almost completely insensitive to the power of the potentials and that $Λ$CDM is part of the family of quintessence cosmology power law potentials with a power of zero.
This paper uses the beta function formalism to extend the analysis of quintessence cosmological parameters to the logarithmic and exponential dark energy potentials. The previous paper (Thompson 2018) demonstrated the formalism using power and inverse power potentials. The essentially identical evolution of the Hubble parameter for all of the quintessence cases and LambdaCDM is attributed to the flatness of the quintessence dark energy potentials in the dark energy dominated era. The Hubble parameter is therefore incapable of discriminating between static and dynamic dark energy. Unlike the ot…
We use linear perturbation theory to study perturbations in dynamical dark energy models. We compare quintessence and tachyonic dark energy models with identical background evolution. We write the corresponding equations for different models in a form that makes it easier to see that the two models are very hard to distinguish in the linear regime, especially for models with $(1 + w) \ll 1$. We use Cosmic Microwave Background data and parametric representations for the two models to illustrate that they cannot be distinguished for the same background evolution with existing observations. Furth…
We investigate cosmological models in which dynamical dark energy consists of a scalar field whose present-day value is controlled by a coupling to the neutrino sector. The behaviour of the scalar field depends on three functions: a kinetic function, the scalar field potential, and the scalar field-neutrino coupling function. We present an analytic treatment of the background evolution during radiation- and matter-domination for exponential and inverse power law potentials, and find a relaxation of constraints compared to previous work on the amount of early dark energy in the exponential case…
In a recent work, a particular class of $f(T)$ gravity, where $T$ is the teleparallel torsion scalar, has been derived. This class has been identified by flat-like universe (FLU) assumptions \cite{HN15}. The model is consistent with the early cosmic inflation epoch. A quintessence potential has been constructed from the FLU $f(T)$-gravity. We show that the first order potential of the induced quintessence is a quasi inverse power law inflation with an additional constant providing an end of the inflation with no need to an extra mechanism. At $e$-folds $N_{*}= 55$ before the end of the inflati…
We study the generation of a kination-dominated phase in the context of a quintessential model with an inverse-power-law potential and a Hubble-induced mass term for the quintessence field. The presence of kination is associated with an oscillating evolution of the quintessence field and the barotropic index. We find that, in sizeable regions of the parameter space, a tracker scaling solution can be reached sufficiently early to alleviate the coincidence problem. Other observational constraints originating from nucleosynthesis, the inflationary scale, the present acceleration of the universe a…
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…
The mass-varying neutrino scenario is analyzed for three trial quintessence potentials (Ferreira-Joyce, inverse exponential, and thawing oscillating). The neutrino mass is generated via Yukawa coupling to the scalar field which represents dark energy. The inverse exponential and oscillating potentials are shown to successfully generate the neutrino masses in the range $m \sim 10^{-2}-10^{-3}~$eV and to yield the current dark energy density in the regime of the late-time acceleration of the Universe. Depending on the choice of potentials, the acceleration could occur in two different regimes: (…
Brans-Dicke cosmology with an (inverse) power-law potential is revisited in the light of modern quintessence and inflation models. A simple ansatz relating scale factor and scalar field recovers most of the known solutions and generates new ones. A phase space interpretation of the ansatz is provided and these universes are mapped into solutions of f(R) cosmology.
Recently we proposed a new approach to the testing of dark energy models based on the observational data. In that work we focused particularly on quintessence models for demonstration and invoked a widely used parametrization of the dark energy equation of state. In this paper we take the more recent SN Ia, CMB and BAO data, invoke the same parametrization, and apply this method of consistency test to five categories of dark energy models, including the LCDM model, the generalized Chaplygin gas, and three quintessence models: exponential, power-law and inverse-exponential potentials. We find t…
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）
We introduce the N-body simulation technique to follow structure formation in linear and nonlinear regimes for the extended quintessence models (scalar-tensor theories in which the scalar field has a self-interaction potential and behaves as dark energy), and apply it to a class of models specified by an inverse power-law potential and a non-minimal coupling. Our full solution of the scalar field perturbation confirms that, when the potential is not too nonlinear, the effects of the scalar field could be accurately approximated as a modification of background expansion rate plus a rescaling of…
Recently, the Planck collaboration has released the first cosmological papers providing the high resolution, full sky, maps of the cosmic microwave background (CMB) temperature anisotropies. It is crucial to understand that whether the accelerating expansion of our universe at present is driven by an unknown energy component (Dark Energy) or a modification to general relativity (Modified Gravity). In this paper we study the coupled dark energy models, in which the quintessence scalar field nontrivially couples to the cold dark matter, with the strength parameter of interaction $beta$. Using th…
The time variation of the equation of state $w$ for quintessence scenario with a scalar field as dark energy is studied up to the third derivative ($d^3w/da^3$) with respect to the scale factor $a$, in order to predict the future observations and specify the scalar potential parameters with the observables. The third derivative of $w$ for general potential $V$ is derived and applied to several types of potentials. They are the inverse power-law ($V=M^{4+α}/Q^α$), the exponential ($V=M^4\exp{(βM/Q)}$), the cosine ($V=M^4(\cos (Q/f)+1)$) and the Gaussian types ($V=M^4\exp(-Q^2/σ^2)$), which are …
The time evolution of the equation of state $w$ for quintessence models with a scalar field as dark energy is studied up to the third derivative ($d^3w/da^3$) with respect to the scale factor $a$, in order to predict the future observations and specify the scalar potential parameters with the observables. The third derivative of $w$ for general potential $V$ is derived and applied to several types of potentials. They are the inverse power-law ($V=M^{4+α}/Q^α$), the exponential ($V=M^4\exp{(βM/Q)}$), the mixed ( $V=M^{4+γ}\exp{(βM/Q)}/Q^γ$), the cosine ($V=M^4(\cos (Q/f)+1)$) and the Gaussian t…
We present the constraints on the Quintessence scalar field model from the observational data of the variation of the fine structure constant obtained from Keck and VLT telescopes. Within the theoretical frame proposed by Bekenstein, the constraints on the parameters of the Quintessence scalar field model are obtained. By the consideration of the prior of $Ω_{m0}$ as WMAP 7 suggests, we obtain various results of the different samples. Based on these results, we also calculate the probability density function of the coupling constant $ζ$. The best-fit values show a consistent relationship betwe…
This study forges new tools to discriminate between dynamical and static dark energy. It provides accurate evolutionary templates of dynamical cosmological parameters and fundamental constants as analytic functions of the scale factor. They are designed to replace the commonly used parameterizations in likelihood calculations with evolutionary templates based on the physics of specific dynamical cosmologies and dark energy potentials. Thus they are termed Cosmology and Potential Specific, CPS, templates. A suite of CPS templates are calculated for a flat quintessence cosmology with a dark ener…
Neutrino capture on beta-decaying nuclei is currently the only known potentially viable method of detection of cosmic background neutrinos. It is based on the idea of separation of the spectra of electrons or positrons produced in captures of relic neutrinos on unstable nuclei from those from the usual $β$-decay and requires very high energy resolution of the detector, comparable to the neutrino mass. In this paper we suggest an alternative method of discrimination between neutrino capture and $β$-decay, based on periodic variations of angular correlations in inverse beta decay transitions ind…
