The present thesis is devoted to the reconstruction of the dark energy models using diverse observational data sets. The parametric approach has been adopted for the reconstruction of cosmological models. The reconstruction of kinematical quantities and the possibility of interaction between dark energy and dark matter has also been emphasised. In first chapter, a brief introduction to cosmology has been presented. In the second chapter, a reconstruction of the dark energy equation of state parameter for a quintessence scalar field model has been discussed. In the third chapter, a parametric reconstruction of the effective or total equation of state has been discussed. In the fourth chapter, a kinematic approach in the reconstruction of dark energy model through the parametrization of the cosmological jerk parameter has been discussed. The fifth chapter is also about a kinematic approach to the reconstruction of dark energy. The reconstruction has been done with an assumption that the jerk parameter is a very slowly varying function. The sixth chapter is devoted to the reconstruction of the interaction rate in holographic dark energy model. Finally, chapter seven contains the concluding remarks and relevant discussions regarding the overall work presented in the thesis.
In the present paper, we investigate the dark energy equation of state using the Gaussian processes analysis method, without confining a particular parametrization. The reconstruction is carried out by adopting the background data including supernova and Hubble parameter, and perturbation data from the growth rate. It suggests that the background and perturbation data both present a hint of dynamical dark energy. However, the perturbation data have a more promising potential to distinguish non-evolution dark energy including the cosmological constant model. We also test the influence of some p…
We develop an efficient, non-parametric Bayesian method for reconstructing the time evolution of the dark energy equation of state w(z) from observational data. Of particular importance is the choice of prior, which must be chosen carefully to minimise variance and bias in the reconstruction. Using a principal component analysis, we show how a correlated prior can be used to create a smooth reconstruction and also avoid bias in the mean behaviour of w(z). We test our method using Wiener reconstructions based on Fisher matrix projections, and also against more realistic MCMC analyses of simulat…
In this paper we perform a reconstruction of the scalar field potential responsible for cosmic acceleration using SNe Ia data. After describing the method, we test it with real SNe Ia data-Union2.1 and JLA SNe datasets. We demonstrate that with the current data precision level, the full reconstruction is not possible. We discuss the problems which arise during the reconstruction process and the ways to overcome them.
Motivated by earlier works on reconstruction of modified gravity models with dark energy components, we extend them by considering a newly proposed model of (m, n)- type of holographic dark energy for two models of modified gravity, f(R) and f(T) theories, where R and T represent Ricci scalar and torsion scalar respectively. Specifically we reconstruct the two later gravity models and discuss their viability and cosmography. The obtained gravity models are ghost free, compatible with local solar system tests and describe effective positive gravitational constant.
We study the power of current and future observational Hubble parameter data (OHD) on non-parametric estimations of the dark energy equation of state, $w(z)$. We propose a new method by conjunction of principal component analysis (PCA) and the criterion of goodness of fit (GoF) criterion to reconstruct $w(z)$, ensuring the sensitivity and reliability of the extraction of features in the EoS. We also give an new error model to simulate future OHD data, to forecast the power of future OHD on the EoS reconstruction. The result shows that current OHD, despite in less quantity, give not only a simi…
The evolution of dark energy density is a crucial quantity in understanding the nature of dark energy. Often, the quantity is described by the so-called equation of state, that is the ratio of dark energy pressure to its density. In this scenario, the dark energy density is always positive throughout cosmic history and a negative value is not allowed. Assuming a homogeneous and isotropic universe, we reconstruct the dark energy density directly from observational data and investigate its evolution through cosmic history. We consider the latest SNIa, BAO and cosmic chronometer data and reconstr…
Scalar Fields (SF) have emerged as natural candidates for dark energy as quintessential or phantom fields, as they are the main ingredient of inflation theories. Instead of assuming some form for the scalar field potential, however, this work reconstructs the SF potential directly from observational data, namely, \textbf{Hubble and SNe Ia data}. We show that two popular forms for the SF potentials, namely, the power-law and the quadratic free-field, are compatible with the reconstructions thus obtained, at least for some choices of the priors of the matter density and curvature parameters and …
We quantify the effects of the voids known to exist in the Universe upon the reconstruction of the dark energy equation of state $w$. We show that the effect can start to be comparable with some of the other errors taken into account when analysing supernova data, depending strongly upon the low redshift cut-off used in the sample. For the supernova data alone, the error induced in the reconstruction of $w$ is much larger than the percent level. When the Baryonic Acoustic Oscillations and the CMB data are included in the fit, the effect of the voids upon the determination of $w$ is much lessen…
An interaction between the vacuum energy and dark matter is an intriguing possibility which may offer a way of solving the cosmological constant problem. Adopting a general prescription for momentum exchange between the two dark components, we reconstruct $α(a)$, the temporal evolution of the coupling strength between dark matter and vacuum energy, in a nonparametric Bayesian approach using combined observational data sets from the cosmic microwave background, supernovae and large scale structure. An evolving interaction between the vacuum energy and dark matter removes some of the tensions be…
Dynamical models for dark energy are an alternative to the cosmological constant. It is important to investigate properties of perturbations in these models and go beyond the smooth FRLW cosmology. This allows us to distinguish different dark energy models with the same expansion history. For this, one often needs the potential for a particular expansion history. We study how such potentials can be reconstructed obtaining closed formulae for potential or reducing the problem to quadrature. We consider three classes of models here: tachyons, quintessence, and, interacting dark energy. We presen…
Directional detection is a promising Dark Matter search strategy. Indeed, WIMP-induced recoils present a direction dependence toward the Cygnus constellation, while background-induced recoils exhibit an isotropic distribution in the galactic rest frame. Taking advantage on these characteristic features and even in the presence of a sizeable background, we show for the first time the possibility to constrain the WIMP properties, both from particle and galactic halo physics, leading to an identification of non-baryonic Dark Matter. However, such results need highly accurate track reconstruction …
Impact of a negative cosmological constant on the reconstruction of dark energy in light of DESI BAO data
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院，UCAS）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；International Center for Theoretical Physics Asia-Pacific（亚太理论物理中心）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
An important issue in cosmology is reconstructing the effective dark energy equation of state directly from observations. With so few physically motivated models, future dark energy studies cannot only be based on constraining a dark energy parameter space. We present a new non-parametric method which can accurately reconstruct a wide variety of dark energy behaviour with no prior assumptions about it. It is simple, quick and relatively accurate, and involves no expensive explorations of parameter space. The technique uses principal component analysis and a combination of information criteria …
A basic aim of ongoing and upcoming cosmological surveys is to unravel the mystery of dark energy. In the absence of a compelling theory to test, a natural approach is to better characterize the properties of dark energy in search of clues that can lead to a more fundamental understanding. One way to view this characterization is the improved determination of the redshift-dependence of the dark energy equation of state parameter, w(z). To do this requires a robust and bias-free method for reconstructing w(z) from data that does not rely on restrictive expansion schemes or assumed functional fo…
We reconstruct the Equation of State of Dark Energy (EoS) from current data using a non-parametric approach where, rather than assuming a specific time evolution of this function, we bin it in time. We treat the transition between the bins with two different methods, i.e. a smoothed step function and a Gaussian Process reconstruction, investigating whether or not the two approaches lead to compatible results. Additionally, we include in the reconstruction procedure a correlation between the values of the EoS at different times in the form of a theoretical prior that takes into account a set of…
Gaussian processes are a fully Bayesian smoothing technique that allows for the reconstruction of a function and its derivatives directly from observational data, without assuming a specific model or choosing a parameterization. This is ideal for constraining dark energy because physical models are generally phenomenological and poorly motivated. Model-independent constraints on dark energy are an especially important alternative to parameterized models, as the priors involved have an entirely different source so can be used to check constraints formulated from models or parameterizations. A c…
The present work is based on the holographic dark energy model with Hubble horizon as the infrared cut-off. The interaction rate between dark energy and dark matter has been reconstructed for three different parameterizations of the deceleration parameter. Observational constraints on the model parameters have been obtained by maximum likelihood analysis using the observational Hubble parameter data (OHD), type Ia supernovab data (SNe), baryon acoustic oscillation data (BAO) and the distance prior of cosmic microwave background (CMB) namely the CMB shift parameter data (CMBShift). The interact…
Understanding the origin of the accelerated expansion of the Universe poses one of the greatest challenges in physics today. Lacking a compelling fundamental theory to test, observational efforts are targeted at a better characterization of the underlying cause. If a new form of mass-energy, dark energy, is driving the acceleration, the redshift evolution of the equation of state parameter w(z) will hold essential clues as to its origin. To best exploit data from observations it is necessary to develop a robust and accurate reconstruction approach, with controlled errors, for w(z). We introduc…
Non-parametric reconstruction of the dark energy equation of state (EoS) aims to determine the EoS as a function of redshift without invoking any particular dark energy model, so that the resulting EoS can be free of model-induced biases or artifacts. Without proper regularization, however, such reconstruction is often overwhelmed by the noise of poorly constrained modes. An intuitive regularization scheme is to assume a priori the dark energy EoS to evolve at most slowly with time, which may be enforced by a correlation between the EoS at different epochs. Indeed, studies that impose the corr…
Model-independent reconstruction of the Interacting Dark Energy Kernel: Binned and Gaussian process
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学研究所）；Department of Physics, Istanbul Technical University（伊斯坦布尔理工大学物理系）；School of Mathematics and Statistics, University of Sheffield（谢菲尔德大学数学与统计学院）
The main aim of this paper is to perform a model comparison for some reconstructions of the key properties that describe the dark energy of the Universe i.e. energy density and the equation of state (EoS). We carry out this process by using a binning and a linear interpolation methodologies, and on top of that, we incorporate a correlation function mechanism. An extension of the two of them was also introduced, where internal amplitudes are allowed to vary in height as well as in position. The reconstructions were made with data from the Hubble parameter, Supernovae Type Ia and Baryon Acoustic…
Discovering the mass of neutrinos is a principle goal in high energy physics and cosmology. In addition to cosmological measurements based on two-point statistics, the neutrino mass can also be estimated by observations of neutrino wakes resulting from the relative motion between dark matter and neutrinos. Such a detection relies on an accurate reconstruction of the dark matter-neutrino relative velocity which is affected by non-linear structure growth and galaxy bias. We investigate our ability to reconstruct this relative velocity using large N-body simulations where we evolve neutrinos as d…
Interacting dark matter (DM) - dark energy (DE) models have been intensively investigated in the literature for their ability to fit various data sets as well as to explain some observational tensions persisting within the $Λ$CDM cosmology. In this work, we employ the Gaussian processes (GP) algorithm to perform a joint analysis by using the geometrical cosmological probes such as Cosmic chronometers, Supernova Type Ia, Baryon Acoustic Oscillations, and the H0LiCOW lenses sample to infer a reconstruction of the coupling function between the dark components in a general framework, where the DE …
With a parametric form of the equation of state parameter of dark energy, a quintessence potential has been reconstructed. The potential is found to be a generalization of a double exponential potential. The constraints on the parameters are obtained by maximum likelihood analysis using observational Hubble data, type Ia supernova data, baryon acoustic oscillation data and the CMB shift parameter data. Th emodel shows preference towards the phantom behaviour of dark energy.
We represent a nonparametric method to reconstruct the equation of state for dark energy directly from observational Hubble parameter data. We use principal component analysis (PCA) to extract the signal from data with noise. Moreover, we modify Akaike information criterion (AIC) to guarantee the quality of reconstruction and avoid over-fitting simultaneously. The results show that our method is robust in reconstruction of dark energy equation of state. Although current observational Hubble parameter data alone can not give a strong constraint yet, our results indicate that future observations…
We provide a model-independent reconstruction of dark energy from $z=0$ to $ \gtrsim 10^5$. We parameterise the model by a perfect fluid with a series of physically well-motivated bins in energy-density, such that the equation of state is always $-1 \le w \le 1$. Our method is capable of describing a range of theoretical models with smooth modifications to the expansion history. Combining the latest CMB, BAO, SN and local $H_0$ measurements, we obtain a large improvement of $Δχ^2=41.3$ over LCDM, at the expense of 33 additional parameters in the fit, with dark energy contributing significantly…
We present a forward-modelled velocity field reconstruction algorithm that performs the reconstruction of the mass density field using only peculiar velocity data. Our method consistently accounts for the inhomogeneous Malmquist bias using analytic integration along the line-of-sight. By testing our method on a simulation, we show that our method gives an unbiased reconstruction of the velocity field. We show that not accounting for the inhomogeneous Malmquist bias can lead to significant biases in the forward-modelled reconstructions. We applied our method to a peculiar velocity data set cons…
The cause of the accelerated expansion of the Universe poses one of the most fundamental questions in physics today. In the absence of a compelling theory to explain the observations, a first task is to develop a robust phenomenology. If the acceleration is driven by some form of dark energy, then, the phenomenology is determined by the dark energy equation of state w. A major aim of ongoing and upcoming cosmological surveys is to measure w and its time dependence at high accuracy. Since w(z) is not directly accessible to measurement, powerful reconstruction methods are needed to extract it re…
An important issue in cosmology is reconstructing the effective dark energy equation of state directly from observations. With few physically motivated models, future dark energy studies cannot only be based on constraining a dark energy parameter space, as the errors found depend strongly on the parameterisation considered. We present a new non-parametric approach to reconstructing the history of the expansion rate and dark energy using Gaussian Processes, which is a fully Bayesian approach for smoothing data. We present a pedagogical introduction to Gaussian Processes, and discuss how it can…
We develop the reconstruction of a model of $f(T)$ gravity according to the holographic dark energy. $T$ is the torsion scalar and its initial value from the Teleparallel gravity is imposed for fitting the initial value of the function $f(T)$. The result shows a polynomial function for $f(T)$, and we also observe that, when $Ω_V\rightarrow 1$ at the future time, $ω_V$ may cross -1 for some values of the input parameter $b$. Another interesting aspect of the obtained model is that it provides the unification of the dark matter with the dark energy.
Model independent reconstructions of dark energy have received some attention. The approach that addresses the reconstruction of the dimensionless coordinate distance and its two first derivatives using a polynomial fit in different redshift windows is well developed \cite{DalyDjorgovski1,DalyDjorgovski2,DalyDjorgovski3}. In this work we offer new insights into the problem by focusing on two types of observational probes: SNeIa and GRBs. Our results allow to highlight some of the intrinsic weaknesses of the method. One of the directions we follow is to consider updated observational samples. O…
We study the dynamical properties of dark energy based on a large family of PADE parameterizations for which the dark energy density evolves as a ratio between two polynomials in the scale factor of the universe. Using the latest cosmological data we perform a standard likelihood analysis in order to place constraints on the main cosmological parameters of different PADE models. We find that the basic cosmological parameters, namely $(Ω_{m0},h,σ_{8})$ are practically the same for all PADE parametrizations explored here. Concerning the free parameters which are related to dark energy we show th…
We apply a parametric reconstruction method to a homogeneous, isotropic and spatially flat Friedmann-Robertson-Walker (FRW) cosmological model filled of a fluid of dark energy (DE) with constant equation of state (EOS) parameter interacting with dark matter (DM). The reconstruction method is based on expansions of the general interaction term and the relevant cosmological variables in terms of Chebyshev polynomials which form a complete set orthonormal functions. This interaction term describes an exchange of energy flow between the DE and DM within dark sector. To show how the method works we…
Merging galaxy clusters present a unique opportunity to study the properties of dark matter in an astrophysical context. These are rare and extreme cosmic events in which the bulk of the baryonic matter becomes displaced from the dark matter halos of the colliding subclusters. Since all mass bends light, weak gravitational lensing is a primary tool to study the total mass distribution in such systems. Combined with X-ray and optical analyses, mass maps of cluster mergers reconstructed from weak-lensing observations have been used to constrain the self-interaction cross-section of dark matter. …
Reconstructing the evolution history of the dark energy equation of state parameter $w(z)$ directly from observational data is highly valuable in cosmology, since it contains substantial clues in understanding the nature of the accelerated expansion of the Universe. Many works have focused on reconstructing $w(z)$ using Type Ia supernova data, however, only a few studies pay attention to Hubble parameter data. In the present work, we explore the merit of Hubble parameter data and make an attempt to reconstruct $w(z)$ from them through the principle component analysis approach. We find that cur…
Relaxing the conventional assumption of a minimal coupling between the dark matter (DM) and dark energy (DE) fields introduces significant changes in the predicted evolution of the Universe. Therefore, testing such a possibility constitutes an essential task not only for cosmology but also for fundamental physics. In a previous communication [Phys. Rev. D99, 043521, 2019], we proposed a new null test for the $Λ$CDM model based on the time dependence of the ratio between the DM and DE energy densities which is also able to detect potential signatures of interaction between the dark components. …
In this paper we study the impact of the fractional matter density uncertainty in the reconstruction of the equation of state of dark energy. We consider both standard reconstruction methods, based on the dynamical effect that dark energy has on the expansion of the Universe, as well as non-standard methods, in which the evolution of the dark energy equation of state with redshift is inferred through the variation of fundamental couplings such as the fine structure constant, $α$, or the proton-to-electron mass ratio, $μ$. We show that the negative impact of the matter density uncertainty in th…
The possibility of a non-gravitational interaction between the dark matter and the dark energy has been reconstructed using some recent datasets. The crucial aspect is that the interaction is not parametrized at the outset, but rather reconstructed directly from the data in a non-parametric way. The Cosmic Chronometer Hubble data, the Pantheon Supernova compilation of CANDELS and CLASH Multy-Cycle Treasury programs obtained by the HST, and the Baryon Acoustic Oscillation Hubble data have been considered in this work. The widely accepted Gaussian Process is used for the reconstruction. The resu…
Merging clusters of galaxies are unique in their power to directly probe and place limits on the self-interaction cross-section of dark matter. Detailed observations of several merging clusters have shown the intracluster gas to be displaced from the centroids of dark matter and galaxy density by ram pressure, while the latter components are spatially coincident, consistent with collisionless dark matter. This has been used to place upper limits on the dark matter particle self-inteaction cross-section of order 1 cm^2/g. The cluster Abell 520 has been seen as a possible exception. We revisit A…
Recently, in [1] we developed a parametric reconstruction method to a homogeneous, isotropic and spatially flat Friedmann-Robertson-Walker (FRW) cosmological model filled of a fluid of dark energy (DE) with constant equation of state (EOS) parameter interacting with dark matter (DM). The reconstruction method is based on expansions of the general interaction term and the relevant cosmological variables in terms of Chebyshev polynomials which form a complete set orthonormal functions. In this article, we reconstruct the interaction function expanding it in terms of only the first four Chebyshev…
We present a detailed and pedagogical analysis of recent cosmological data, including CMB, BAO, SnIa and the recent local measurement of $H_0$. We thus obtain constraints on the parameters of standard dark energy parameterizations, including $ΛCDM$, and $H(z)$ deformation models such as $wCDM$ (constant equation of state $w$ of dark energy), and the CPL model (corresponding to the evolving dark energy equation-of-state parameter $w(z) = w_0 + w_a \frac{z}{1+z}$). The fitted parameters include the dark matter density $Ω_{0m}$, the SnIa absolute magnitude $M$, the Hubble constant $H_0$ and the d…
We present the first reconstruction of dark matter maps from weak lensing observational data using deep learning. We train a convolution neural network (CNN) with a Unet based architecture on over $3.6\times10^5$ simulated data realizations with non-Gaussian shape noise and with cosmological parameters varying over a broad prior distribution. We interpret our newly created DES SV map as an approximation of the posterior mean $P(κ| γ)$ of the convergence given observed shear. Our DeepMass method is substantially more accurate than existing mass-mapping methods. With a validation set of 8000 sim…
In light of the statistical performance of cosmological observations, in this work we present an improvement on the Gaussian reconstruction of the Hubble parameter data $H(z)$ from Cosmic Chronometers, Supernovae Type Ia and Clustering Galaxies in a model-independent way in order to use them to study new constraints in the Horndeski theory of gravity. First, we have found that the prior used to calibrate the Pantheon supernovae data significantly affects the reconstructions, leading to a 13$σ$ tension on the $H_0$ value. Second, according to the $χ^{2}$-statistics, the reconstruction carried o…
This work is the reconstruction of the interaction rate of holographic dark energy whose infrared cut-off scale is set by the Hubble length. We have reconstructed the interaction rate between dark matter and the holographic dark energy for a specific parameterization of the effective equation of state parameter. We have obtained observational constraints on the model parameters using the latest Type Ia Supernova (SNIa), Baryon Acoustic Oscillations (BAO) and Cosmic Microwave Background (CMB) radiation datasets. We have found that for the present model, the interaction rate increases with expan…
We perform a comprehensive study of the dark energy equation of state (EoS) utilizing the model-independent Gaussian processes (GP). Using a combination of the Union 2.1 data set, the 30 newly added H(z) cosmic chronometer data points and Planck's shift parameter, we modify the usual GaPP code and provide a tighter constraint on the dark energy EoS than the previous literature about GP reconstructions. Subsequently, we take the "controlling variable method" to investigate directly the effects of variable matter density parameter $Ω_{m0}$, variable cosmic curvature $Ω_{k0}$ and variable Hubble …
In this paper we consider quintessence reconstruction of interacting holographic dark energy in a non-flat background. As system's IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as $L=ar(t)$. To this end we construct a quintessence model by a real, single scalar field. Evolution of the potential, $V(ϕ)$, as well as the dynamics of the scalar field, $ϕ$, are obtained according to the respective holographic dark energy. The reconstructed potentials show a cosmological constant behavior for the present time. We constrain the model parameters in …
On the Stability of Dark Energy Scalar Field Reconstruction from SNe Ia Data
A. I. Alikhanian National Science Laboratory (Yerevan Physics Institute)（阿·伊·阿里哈尼扬国家科学实验室（埃里温物理研究所））；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We combine cosmic chronometer and growth of structure data to derive the redshift evolution of the dark energy equation of state $w$, using a novel agnostic approach. The background and perturbation equations lead to two expressions for $w$, one purely background-based and the other relying also on the growth rate of large-scale structure. We compare the features and performance of the growth-based $w$ to the background $w$, using Gaussian Processes for the reconstructions. We find that current data is not precise enough for robust reconstruction of the two forms of $w$. By using mock data exp…
We baseline with current cosmological observations to forecast the power of the Dark Energy Spectroscopic Instrument (DESI) in two ways: 1. the gain in constraining power of parameter combinations in the standard $Λ$CDM model, and 2. the reconstruction of quintessence models of dark energy. For the former task we use a recently developed formalism to extract the leading parameter combinations constrained by different combinations of cosmological survey data. For the latter, we perform a non-parametric reconstruction of quintessence using the Effective Field Theory of Dark Energy. Using mock DE…
Wide area Large-Scale Structure (LSS) surveys are planning to map a substantial fraction of the visible universe to quantify dark energy through Baryon Acoustic Oscillations (BAO). At increasing redshift, for example that probed by proposed 21-cm intensity mapping surveys, gravitational lensing potentially limits the fidelity (Hui et al., 2007) because it distorts the apparent matter distribution. In this paper we show that these distortions can be reconstructed, and actually used to map the distribution of intervening dark matter. The lensing information for sources at z=1-3 allows accurate r…
