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 reconstruct the dark energy density in both flat and non-flat universes up to redshift $z\sim 3$. The results are well in agreement with the $Λ$CDM up to redshift $z\sim 1.5$, whereas all data and methods, in our analysis, provide a negative dark energy density at high redshifts.
We introduce a novel implementation of orbit-based (or Schwarzschild) modeling that allows dark matter density profiles to be calculated non-parametrically in nearby galaxies. Our models require no assumptions to be made about velocity anisotropy or the dark matter profile. The technique can be applied to any dispersion-supported stellar system, and we demonstrate its use by studying the Local Group dwarf spheroidal (dSph) galaxy Draco. We use existing kinematic data at larger radii and also present 12 new radial velocities within the central 13 pc obtained with the VIRUS-W integral field spec…
In the present work we suggest new and more generalized parameterizations for the Equation of State, EoS, of dark energy, maintaining the basic structure of two-parameters CPL-model, but covering both the past and the future of the cosmic history, without divergences and consistently with the current observational data. We propose two generalizations, starting from the extended MZp-model by Ma and Zhang, 2011, the $ξ$MZp-model and the DFp-model. The potential advantages of using these new formulations is their extended range of validity, mainly in the future, to determine possible future scena…
A comparative study of a set of parametric dark energy models is performed by studying the evolution of dark energy both in the past and future epochs. In addition, the age of the universe and time till the distant future $(a=1000)$ are estimated. The validity of generalized second law of thermodynamic in different parametric models is also ascertained.
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 r…
We study the cosmological evolution for a scalar field dark matter model, by considering a parameterization of the evolution equations that allow us to unify in a single parameter a family of potentials: quadratic (free case), trigonometric (Axion-like case), and hyperbolic. After exploring the cosmological dynamics of this model, we perform a statistical analysis to study the viability of such model in comparison with the standard Cold Dark Matter model. We found that the free case is preferred over the other scalar field potentials, but in any case all of them are disfavored by the cosmologi…
The present thesis is devoted to the non-parametric reconstruction of some cosmological parameters using diverse observational datasets. The Universe is assumed to be spatially homogeneous and isotropic, thus described by the FLRW metric. The first chapter provides a brief introduction to cosmology and focuses on the reconstruction methods. An assessment of the cosmic distance-duality relation is discussed in chapter 2. In chapter 3, a non-parametric reconstruction of the cosmological jerk parameter is carried out. Chapter 4 explores the possibility of a non-gravitational interaction in the co…
The cosmological jerk parameter $j$ is reconstructed in a non-parametric way from observational data independent of a fiducial cosmological model. From this kinematical quantity, the equation of state parameter for composite matter distribution is also found out. The result shows that there is a deviation from the $Λ$CDM model close to $z=1.5$, at the $3σ$ confidence level.
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 present a parametric strong lensing analysis of three massive clusters. Our aim is to probe the inner shape of dark matter haloes, in particular the existence of a core. We adopt the following working hypothesis: any group/cluster scale dark matter clump introduced in the modelling should be associated with a luminous counterpart. We also adopt some additional well motivated priors in the analysis, even if this degrades the quality of the fit, quantified using the RMS between the observed and model generated images. In particular, in order to alleviate the degeneracy between the smooth unde…
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.
Current results from the Lyman alpha forest assume that the primordial power spectrum of density perturbations follows a simple power law form, with running. We present the first analysis of Lyman alpha data to study the effect of relaxing this strong assumption on primordial and astrophysical constraints. We perform a large suite of numerical simulations, using them to calibrate a minimally parametric framework for describing the power spectrum. Combined with cross-validation, a statistical technique which prevents over-fitting of the data, this framework allows us to reconstruct the power sp…
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…
We study dark energy through the viewpoints of parametric and nonparametric analyses of late-time cosmological data. We consider four Hubble parameter priors reflecting the Hubble tension and make use of two phenomenological functions, namely, a normalized dark energy density and a compactified dark energy equation of state. We predict the shape of both functions and present new constraints on the dark energy equation of state. The results hint at dark energy evolution regardless of the choice of the method and of the priors. The fact that similar evolutions for the dark energy densities are f…
A parametric reconstruction of the jerk parameter, the third order derivative of the scale factor expressed in a dimensionless way, has been discussed. Observational constraints on the model parameters have been obtained by Maximum Likelihood Analysis of the models using Supernova Distance Modulus data (SNe), Observational Hubble Data (OHD), Baryon Acoustic Oscillation (BAO) data and CMB shift parameter data (CMBShift). The present value of the jerk parameter has been kept open to start with, but the plots of various cosmological parameter like deceleration parameter $q(z)$, jerk parameter $j(…
We present a method to estimate the lensing potential from massive galaxy clusters for given observational X-ray data. The concepts developed and applied in this work can easily be combined with other techniques to infer the lensing potential, e.g. weak gravitational lensing or galaxy kinematics, to obtain an overall best fit model for the lensing potential. After elaborating on the physical details and assumptions the method is based on, we explain how the numerical algorithm itself is implemented with a Richardson-Lucy algorithm as a central part. Our reconstruction method is tested on simul…
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 present a comparison between approximated methods for the construction of mock catalogs based on the halo-bias mapping technique. To this end, we use as reference a high resolution $N$-body simulation of 3840$^3$ dark matter particles on a 400$h^{-1}\rm{Mpc}$ cube box from the Multidark suite. In particular, we explore parametric versus non-parametric bias mapping approaches and compare them at reproducing the halo distribution in terms of the two and three point statistics down to $\sim 10^8\,{\rm M}_{\odot}\,h^{-1}$ halo masses. Our findings demonstrate that the parametric approach remain…
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…
Context: In the past decade, sensitive, resolved Sunyaev-Zel'dovich (SZ) studies of galaxy clusters have become common. Whereas many previous SZ studies have parameterized the pressure profiles of galaxy clusters, non-parametric reconstructions will provide insights into the thermodynamic state of the intracluster medium (ICM). Aims: We seek to recover the non-parametric pressure profiles of the high redshift ($z=0.89$) galaxy cluster CLJ 1226.9+3332 as inferred from SZ data from the MUSTANG, NIKA, Bolocam, and Planck instruments, which all probe different angular scales. Methods: Our non-para…
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 …
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…
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 …
Non-parametric reconstruction methods, such as Gaussian process (GP) regression, provide a model-independent way of estimating an underlying function and its uncertainty from noisy data. We demonstrate how GP-reconstruction can be used as a consistency test between a given data set and a specific model by looking for structures in the residuals of the data with respect to the model's best-fit. Applying this formalism to the Planck temperature and polarisation power spectrum measurements, we test their global consistency with the predictions of the base $Λ$CDM model. Our results do not show any…
The present work is based on a parametric reconstruction of the deceleration parameter $q(z)$ in a model for the spatially flat FRW universe filled with dark energy and non-relativistic matter. In cosmology, the parametric reconstruction technique deals with an attempt to build up a model by choosing some specific evolution scenario for a cosmological parameter and then estimate the values of the parameters with the help of different observational datasets. In this paper, we have proposed a logarithmic parametrization of $q(z)$ to probe the evolution history of the universe. Using the type Ia …
We present a non-parametric measure of the ellipticity and the alignment of the dark matter halos in Abell 901/902 supercluster. This super-cluster is a system of four separate peaks in a $0.5^{\circ}\times0.5^{\circ}$ field of view. We map the mass distribution of each individual peak using an improved version of Particle Based Lensing (PBL) and measure the ellipticity of the dark matter halos associated with two of the peaks directly from the mass map and by fitting them to a singular isothermal ellipse. The parametric and non-parametric measurements are consistent for A901b while the positi…
We consider nonlinear redshift-dependent equation of state parameters as dark energy models in a spatially flat Friedmann-Lemaître-Robertson-Walker universe. To depict the expansion history of the universe in such cosmological scenarios, we take into account the large scale behaviour of such parametric models and fit them using a set of latest observational data with distinct origin that includes cosmic microwave background radiation, Supernove Type Ia, baryon acoustic oscillations, redshift space distortion, weak gravitational lensing, Hubble parameter measurements from cosmic chronometers an…
Perturbative quantities, such as the growth rate ($f$) and index ($γ$), are powerful tools to distinguish different dark energy models or modified gravity theories even if they produce the same cosmic expansion history. In this work, without any assumption about the dynamics of the Universe, we apply a non-parametric method to current measurements of the expansion rate $H(z)$ from cosmic chronometers and high-$z$ quasar data and reconstruct the growth factor and rate of linearised density perturbations in the non-relativistic matter component. Assuming realistic values for the matter density p…
Vector bosons heavier than $10^{-22}$ eV can be viable dark matter candidates with distinctive experimental signatures. Ultralight dark matter generally requires a non-thermal origin to achieve the observed density, while still behaving like a pressureless fluid at late times. We show that such a production mechanism naturally occurs for vectors whose mass originates from a dark Higgs. If the dark Higgs has a large field value after inflation, the energy in the Higgs field can be efficiently transferred to vectors through parametric resonance. Computing the resulting abundance and spectra requ…
We investigate theoretical and observational aspects of a time-dependent parameterization for the dark energy equation of state (EoS) $w(z)$, which is a well behaved function of the redshift $z$ over the entire cosmological evolution, i.e., $z \in [-1,\infty)$. By using a theoretical algorithm of constructing the quintessence potential directly from the effective EoS parameter, we derive and discuss the general features of the resulting potential for this $w(z)$ function. Since the parameterization here discussed allows us to divide the parametric plane in defined regions associated to distinc…
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.
The tomographic Alcock-Paczynski (AP) method can result in tight cosmological constraints by using small and intermediate clustering scales of the large scale structure (LSS) of the galaxy distribution. By focusing on the redshift dependence, the AP distortion can be distinguished from the distortions produced by the redshift space distortions (RSD). In this work, we combine the tomographic AP method with other recent observational datasets of SNIa+BAO+CMB+$H_0$ to reconstruct the dark energy equation-of-state $w$ in a non-parametric form. The result favors a dynamical DE at $z\lesssim1$, and …
We investigate the cosmological stability of light bosonic dark matter carrying a tiny electric charge. In the wave-like regime of high occupation numbers, annihilation into gauge bosons can be drastically enhanced by parametric resonance. The millicharged particle can either be minimally coupled to photons or its electromagnetic interaction can be mediated via kinetic mixing with a massless hidden photon. In the case of a direct coupling current observational constraints on the millicharge are stronger than those arising from parametric resonance. For the (theoretically preferred) case of kin…
We present a new method for determining the local dark matter density using kinematic data for a population of tracer stars. The Jeans equation in the $z$-direction is integrated to yield an equation that gives the velocity dispersion as a function of the total mass density, tracer density, and the tilt term that describes the coupling of vertical and radial motions. We then fit a dark matter mass profile to tracer density and velocity dispersion data to derive credible regions on the vertical dark matter density profile. Our method avoids numerical differentiation, leading to lower numerical …
In the context of a Hubble tension problem that is growing in its statistical significance, we reconsider the effectiveness of non-parametric reconstruction techniques which are independent of prescriptive cosmological models. By taking cosmic chronometers, Type Ia Supernovae and baryonic acoustic oscillation data, we compare and contrast two important reconstruction approaches, namely Gaussian processes (GP) and the \textbf{Lo}cally w\textbf{e}ighted \textbf{S}catterplot \textbf{S}moothing together with \textbf{Sim}ulation and \textbf{ex}trapolation method (LOESS-Simex or LS). In the context …
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.
The accelerated cosmic expansion could be due to dark energy within general relativity (GR), or modified gravity. It is of interest to differentiate between them, by using both the expansion history and the growth history. In the literature, it was proposed that the growth index $γ$ is useful to distinguish these two scenarios. In this work, we consider the non-parametric reconstruction of the growth index $γ$ as a function of redshift $z$ from the latest observational data as of July 2018 via Gaussian Processes. We find that $f(R)$ theories and dark energy models within GR (especially $Λ$CDM)…
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…
We investigate the impact of uncertainty in the velocity distribution of dark matter on direct detection experiments. We construct an multinomial prior with a hyperparameter $β$ that describes the strength of our belief in an isotropic Maxwell-Boltzmann velocity distribution. By varying $β$, we interpolate between a halo-independent and halo-dependent analysis. We present a novel approximation for the marginalisation of this prior that is applicable to any counting experiment. With this formula, we investigate the impact of the uncertainty in limits from XENON1T. For dark matter masses greater…
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…
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…
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 …
