The Hubble relation between distance and redshift is a purely cosmographic relation that depends only on the symmetries of a FLRW spacetime, but does not intrinsically make any dynamical assumptions. This suggests that it should be possible to estimate the parameters defining the Hubble relation without making any dynamical assumptions. To test this idea, we perform a number of inter-related cosmographic fits to the legacy05 and gold06 supernova datasets. Based on this supernova data, the "preponderance of evidence" certainly suggests an accelerating universe. However we would argue that (unless one uses additional dynamical and observational information) this conclusion is not currently supported "beyond reasonable doubt". As part of the analysis we develop two particularly transparent graphical representations of the redshift-distance relation -- representations in which acceleration versus deceleration reduces to the question of whether the relevant graph slopes up or down. Turning to the details of the cosmographic fits, three issues in particular concern us: First, the fitted value for the deceleration parameter changes significantly depending on whether one performs a chi^2 fit to the luminosity distance, proper motion distance or other suitable distance surrogate. Second, the fitted value for the deceleration parameter changes significantly depending on whether one uses the traditional redshift variable z, or what we shall argue is on theoretical grounds an improved parameterization y=z/(1+z). Third, the published estimates for systematic uncertainties are sufficiently large that they certainly impact on, and to a large extent undermine, the usual purely statistical tests of significance. We conclude that the supernova data should be treated with some caution.
Using mock data for the Hubble diagrams of type Ia supernovae (SNIa) and quasars (QSOs) generated based on the standard model of cosmology, and using the least-squares method based on the Markov-Chain-Monte-Carlo (MCMC) algorithm, we first put constraints on the cosmographic parameters in the context of the various model-independent cosmographic methods reconstructed from the Taylor $4^{th}$ and $5^{th}$ order expansions and the Pade (2,2) and (3,2) polynomials of the Hubble parameter, respectively. We then reconstruct the distance modulus in the framework of cosmographic methods and calculate…
We study observational constraints on the cosmographic functions up to the fourth derivative of the scale factor with respect to cosmic time, i.e., the so-called snap function, using the non-parametric method of Gaussian Processes. As observational data we use the Hubble parameter data. Also we use mock data sets to estimate the future forecast and study the performance of this type of data to constrain cosmographic functions. The combination between a non-parametric method and the Hubble parameter data is investigated as a strategy to reconstruct cosmographic functions. In addition, our resul…
In this work we study different types of dark energy (DE) models in the framework of the cosmographic approach, with emphasis on the Running Vacuum models (RVMs). We assess their viability using different information criteria and compare them with the so-called Ghost DE models (GDEs) as well as with the concordance $Λ$CDM model. We use the Hubble diagrams for Pantheon SnIa, quasars (QSOs), gamma-ray bursts (GRBs) as well as the data on baryonic acoustic oscillations (BAOs) in four different combinations. Upon minimizing the $χ^2$ function of the distance modulus in the context of the Markov Ch…
Cosmographic approach, a Taylor expansion of the Hubble function, has been used as a model-independent method to investigate the evolution of the universe in the presence of cosmological data. Apart from possible technical problems like the radius of convergence, there is an ongoing debates about the tensions appear when one investigates some high redshift cosmological data. In this work, we consider two common data sets namely SNIa (Pantheon sample) and the Hubble data to investigate advantages and disadvantages of the cosmographic approach. To do this, we obtain the evolution of cosmographic…
In this paper, we study the power-law $f(T)$ model using Hubble diagrams of type Ia supernovae (SNIa), quasars (QSOs), Gamma Ray Bursts (GRBs) and the measurements from baryonic acoustic oscillations (BAO) in the framework of the cosmographic method. Using mock data for SNIa, QSOs and GRBs generated based on the power-law $f(T)$ model, we show whether different cosmographic methods are suitable to reconstruct the distance modulus or not. In particular, we investigate the rational PADE polynomials $(3,2)$ and $(2,2)$ in addition to the fourth- and fifth- order Taylor series. We show that PADE $…
Redshift drift is the phenomenon whereby the observed redshift between an emitter and observer comoving with the Hubble flow in an expanding FLRW universe will slowly evolve -- on a timescale comparable to the Hubble time. There are nevertheless serious astrometric proposals for actually observing this effect. We shall however pursue a more abstract theoretical goal, and perform a general cosmographic analysis of this effect, eschewing (for now) dynamical considerations in favour of purely kinematic symmetry considerations and Taylor series expansions based on FLRW spacetimes. We shall develop…
We perform a comparative study of different types of dynamical dark energy models (DDES) using the cosmographic method. Among the models being examined herein we have the Running Vacuum models (RVMs), which have demonstrated considerable ability to fit the overall cosmological data at a level comparable to the standard cosmological model, $Λ$CDM, and capable of alleviating the $σ_8$ and $H_0$ tensions. At the same time we address a variety of Holographic dark energy models (HDEs) with different options for the time (redshift)-varying model parameter $c=c(z)$. We deal with the HDEs under the do…
The paper discusses a particular model of chameleon gravity where the scalar field has an exponential as $V=M^{4}\exp(\frac{αϕ}{M_{pl}})$ and an exponential coupling to the matter density component of the Universe as $ρ_{m}\exp(\frac{βϕ}{M_{pl}})$. We finds the relations between the four (in principle free) parameters of the model and the first five cosmographic parameters (which can be written in terms of the Hubble parameter and its first four derivatives). If such cosmographic parameter are known then the we present the algebraic relations which can be used to derive the free parameters in …
Redshift dependence and dipolar velocity corrections in cosmographic reconstructions through Type Ia supernova samples
Scuola Superiore Meridionale（高等南方学院）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Università di Camerino（卡梅里诺大学）；INAF, Osservatorio Astronomico di Brera（INAF布雷拉天文台）；INFN, Sezione di Perugia（INFN佩鲁贾分部）；Department of Nanoscale Science and Engineering, University at Albany SUNY（纽约州立大学奥尔巴尼分校纳米科学与工程系）；Al-Farabi Kazakh National University（法拉比哈萨克国立大学）；Dipartimento di Fisica, Università degli Studi di Torino（都灵大学物理系）；INFN, Sezione di Torino（INFN都灵分部）；INAF, Osservatorio Astrofisico di Torino（INAF都灵天文台）
In the context of cosmography approach and using the data of Hubble diagram for supernovae, quasars and gamma-ray bursts, we study some DE parametrizations and also the concordance $Λ$CDM universe. Using the different combinations of data sample including ({\it i}) supernovae (Pantheon), ({\it ii}) Pantheon + quasars and ({\it iii}) Pantheon + quasars + gamma-ray bursts and applying the minimization of $χ^2$ function of distance modulus of data samples in the context of Markov Chain Monte Carlo method, we first obtain the constrained values of the cosmographic parameters in model independent c…
The cosmographic approach is gaining considerable interest as a model-independent technique able to describe the late expansion of the universe. Indeed, given only the observational assumption of the cosmological principle, it allows to study the today observed accelerated evolution of the Hubble flow without assuming specific cosmological models. In general, cosmography is used to reconstruct the Hubble parameter as a function of the redshift, assuming an arbitrary fiducial value for the current matter density, $Ω_m$, and analysing low redshift cosmological data. Here we propose a different s…
We discuss the power of third-generation gravitational wave detectors to constrain cosmographic parameters in the case of electromagnetically bright standard sirens focusing on the specific case of the Einstein Telescope. We analyze the impact that the redshift source distribution, the number of detections and the observational error in the luminosity distance have on the inference of the first cosmographic parameters, and show that with a few hundreds detections the Hubble constant can be recovered at sub-percent level whereas the deceleration parameter at a few percent level, both with negli…
We present model independent reconstructions of quintessence and the Swampland conjectures (SC) using both Machine Learning (ML) and cosmography. In particular, we demonstrate how the synergies between theoretical analyses and ML can provide key insights on the nature of dark energy and modified gravity. Using the Hubble parameter $H(z)$ data from the cosmic chronometers we find that the ML and cosmography reconstructions of the SC are compatible with observations at low redshifts. Finally, including the growth rate data $fσ_8(z)$ we perform a model independent test of modified gravity cosmolo…
Cosmography is a powerful tool to investigate the Universe kinematic and then to reconstruct dynamics in a model-independent way. However, recent new measurements of supernovae Ia and quasars have populated the Hubble diagram up to high redshifts ($z \sim 7.5$) and the application of the traditional cosmographic approach has become less straightforward due to the large redshifts implied. Here we investigate this issue through an expansion of the luminosity distance-redshift relation in terms of "orthogonal" logarithmic polynomials. In particular we point out the advantages of a new procedure o…
Using a new sub-sample of observed strong gravitational lens systems, for the first time, we present the equation for the angular diameter distance in the $y$-redshift scenario for cosmography and use it to test the cosmographic parameters. In addition, we also use the observational Hubble data from cosmic chronometers and a Joint analysis of both data is performed. Among the most important conclusions are that this new analysis for cosmography using Strong Lensing Systems is equally competitive to constrain the cosmographic parameters as others presented in literature. Additionally, we presen…
The anisotropic expansion rate of the local Universe and its covariant cosmographic interpretation
University of the Western Cape（西开普敦大学）；National Institute for Theoretical & Computational Sciences（理论与计算科学国家研究所）；Aix Marseille Univ, Université de Toulon, CNRS, CPT（艾克斯-马赛大学、土伦大学、法国国家科学研究中心、CPT）；Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（台湾大学梁式宇宙学与粒子天体物理中心）；Queen Mary University of London（伦敦大学玛丽女王学院）
The standard cosmographic approach consists in performing a series expansion of a cosmological observable around $z=0$ and then using the data to constrain the cosmographic (or kinematic) parameters at present time. Such a procedure works well if applied to redshift ranges inside the $z$-series convergence radius ($z<1$), but can be problematic if we want to cover redshift intervals that fall outside the $z-$series convergence radius. This problem can be circumvented if we work with the $y-$redshift, $y=z/(1+z)$, or the scale factor, $a=1/(1+z)=1-y$, for example. In this paper, we use the scal…
We propose two model independent methods to obtain constraints on the transition and equivalence redshifts $z_{tr}$, $z_{eq}$. In particular, we consider $z_{tr}$ as the onset of cosmic acceleration, whereas $z_{eq}$ the redshift at which the densities of dark energy and pressureless matter are equated. With this prescription, we expand the Hubble and deceleration parameters up to two hierarchical orders and show a linear correlation between transition and equivalence, from which we propose exclusion plots where $z_{eq}$ is not allowed to span. To this end, we discuss how to build up cosmograp…
The distance modulus determined from Carmeli's cosmology fits the accelerating universe data of the high-redshift type Ia supernovae without dark matter
Mapping the redshift drift at various redshifts through cosmography
Scuola Superiore Meridionale（南方高等学院）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Università di Camerino, Divisione di Fisica（卡梅里诺大学物理系）；Department of Nanoscale Science and Engineering, University at Albany SUNY（奥尔巴尼州立大学纳米科学与工程系）；INAF, Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
Varying Gravity from a Modified Fractional Model: Observational Constraints and Slow-Fast Dynamics
Chiang Mai University（清迈大学）；CESNET；Universidad Católica del Norte（北方天主教大学）；North-West University（西北大学）；Durban University of Technology（德班理工大学）；Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）
Constraining Cosmological Parameters with Viscous Modified Chaplygin Gas and Generalized Cosmic Chaplygin Gas Models in Horava-Lifshitz Gravity: Utilizing Late-time Datasets
In this paper we present new constraints on the Hubble parameter $H_0$ using: (i) the available data on $H(z)$ obtained from cosmic chronometers (CCH); (ii) the Hubble rate data points extracted from the supernovae of Type Ia (SnIa) of the Pantheon compilation and the Hubble Space Telescope (HST) CANDELS and CLASH Multy-Cycle Treasury (MCT) programs; and (iii) the local HST measurement of $H_0$ provided by Riess et al. (2018), $H_0^{\rm HST}=(73.45\pm1.66)$ km/s/Mpc. Various determinations of $H_0$ using the Gaussian processes (GPs) method and the most updated list of CCH data have been recent…
The Hubble constant tension problem is analysed in the framework of a class of modified gravity, the so-called $F(R)$ gravity. To do so, we explore two models: an exponential and a power-law $F(R)$ gravities, which includes an early dark energy (EDE) term in the latter. These models can describe both an early time inflationary epoch and the late time accelerating expansion of the universe. We confront both models with recent observational data including the Pantheon Type Ia supernovae sample, the latest measurements of the Hubble parameter $H(z)$ from differential ages of galaxies (cosmic chro…
Recent low-redshift observations give value of the present-time Hubble parameter $H_{0}\simeq 74~\rm{km s}^{-1}\rm{Mpc}^{-1}$, roughly 10\% higher than the predicted value $H_{0}=67.4~\rm{km s}^{-1}\rm{Mpc}^{-1}$ from Planck's observations of the Cosmic Microwave Background radiation~(CMB) and the $Λ$CDM model. Phenomenologically, we show that by adding an extra component X with negative density in the Friedmann equation, it can relieve the Hubble tension without changing the Planck's constraint on the matter and dark energy densities. For the extra negative density to be sufficiently small, i…
Observations restrict the parameter space of Holographic Dark Energy (HDE) so that a turning point in the Hubble parameter $H(z)$ is inevitable. Concretely, cosmic microwave background (CMB), baryon acoustic oscillations (BAO) and Type Ia supernovae (SNE) data put the turning point in the future, but removing SNE results in an observational turning point at positive redshift. From the perspective of theory, not only does the turning point violate the Null Energy Condition (NEC), but as we argue, it may be interpreted as an evolution of the Hubble constant $H_0$ with redshift, which is at odds …
