Cosmography is an ideal tool to investigate the cosmic expansion history of the Universe in a model-independent way. The equations of motion in modified theories of gravity are usually very complicated; cosmography may select practical models without imposing arbitrary choices a priori. We use the model-independent way to derive $f(z)$ and its derivatives up to fourth order in terms of measurable cosmographic parameters. We then fit those functions into the luminosity distance directly. We perform the MCMC analysis by considering three different sets of cosmographic functions. Using the largest supernovae Ia Pantheon sample, we derive the constraints on the Hubble constant $H_0$ and the cosmographic functions, and find that the former two terms in Taylor expansion of luminosity distance work dominantly in $f(Q)$ gravity.
In this work we use cosmography to alleviate the degeneracy among cosmological models, proposing a way to parameterize matter and dark energy in terms of cosmokinematics quantities. The recipe of using cosmography allows to expand observable quantities in Taylor series and to directly compare those expansions with data. We adopt this strategy and we propose a fully self-consistent parametrization of the total energy density driving the late time universe speed up. Afterwards, we describe a feasible \emph{cosmographic dark energy model}, in which matter is fixed whereas dark energy evolves by m…
Cosmography represents an important branch of cosmology which aims to describe the universe without the need of postulating \emph{a priori} any particular cosmological model. All quantities of interest are expanded as a Taylor series around here and now, providing in principle, a way of directly matching with cosmological data. In this way, cosmography can be regarded a model-independent technique, able to fix cosmic bounds, although several issues limit its use in various model reconstructions. The main purpose of this review is to focus on the key features of cosmography, emphasising both th…
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…
Cosmography has been referred to as a solution to the inverse scattering problem, which is reasonable since it allows us to calculate cosmological bounds from data samplers by performing an expansion of the cosmological observables around present time. Nevertheless, this approach is not properly an inverse scattering solution since the method only circumvents the problem to fit the equation of state (EoS) parameters (model-dependent) by replacing it with their fit of its cosmographic parameters (with a polynomial series-dependence). Therefore, can we construct a new cosmography approach where …
We study the possibility to extract model independent information about the dynamics of the universe by using Cosmography. We intend to explore it systematically, to learn about its limitations and its real possibilities. Here we are sticking to the series expansion approach on which Cosmography is based. We apply it to different data sets: Supernovae Type Ia (SNeIa), Hubble parameter extracted from differential galaxy ages, Gamma Ray Bursts (GRBs) and the Baryon Acoustic Oscillations (BAO) data. We go beyond past results in the literature extending the series expansion up to the fourth order …
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 …
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…
Being based on the only assumption that the universe is homogenous and isotropic on large scales, cosmography is an ideal tool to investigate the cosmic expansion history in a almost model-independent way. Fitting the data on the luminosity distance and Baryon Acoustic Oscillations allows to determine the confidence ranges for the cosmographic parameters hence giving some quantitative constraints that a whatever theory has to fulfill. As an application, we consider here the case of teleparallel gravity (TEGR) also referred to as f(T)-gravity. To this end, we first work out analytical expressio…
Currently, in order to explain the accelerated expansion phase of the universe, several alternative approaches have been proposed, among which the most common are dark energy models and alternative theories of gravity. Although these approaches rest on very different physical aspects, it has been shown that both are in agreement with the data in the current status of cosmological observations, thus leading to an enormous degeneration between these models. So until evidences of higher experimental accuracy are available, more conservative model independent approaches are a useful tool for break…
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…
We perform a cosmographic analysis using several cosmological observables such as the luminosity distance moduli, the volume distance, the angular diameter distance and the Hubble parameter. These quantities are determined using different data sets: Supernovae type Ia and Gamma Ray Bursts, the Baryonic Acoustic Oscillations, the cosmic microwave background power spectrum and the Hubble parameter as measured from surveys of galaxies. This data set allows to put constraints on the cosmographic expansion with unprecedented precision. We also present forecasts for the coefficients of the kinematic…
We constrain the parameters describing the kinematical state of the universe using a cosmographic approach, which is fundamental in that it requires a very minimal set of assumptions (namely to specify a metric) and does not rely on the dynamical equations for gravity. On the data side, we consider the most recent compilations of Supernovae and Gamma Ray Bursts catalogues. This allows to further extend the cosmographic fit up to $z = 6.6$, i.e. up to redshift for which one could start to resolve the low z degeneracy among competing cosmological models. In order to reliably control the cosmogra…
The problem of reproducing dark energy effects is reviewed here with particular interest devoted to cosmography. We summarize some of the most relevant cosmological models, based on the assumption that the corresponding barotropic equations of state evolve as the universe expands, giving rise to the accelerated expansion. We describe in detail the $Λ$CDM ($Λ$-Cold Dark Matter) and $ω$CDM models, considering also some specific examples, e.g., Chevallier-Polarsky-Linder, the Chaplygin gas and the Dvali-Gabadadze-Porrati cosmological model. Finally, we consider the cosmological consequences of $f…
The cosmographic approach, which only relies upon the homogeneity and isotropy of the Universe on large scales, has become an essential tool in dealing with an increasing number of theoretical possibilities for explaining the late-time acceleration of the Universe, ranging from Modified Gravity theories to Dark Energy alternatives passing from testing the cosmological concordance Lambda-CDM model. Despite its generality, we show that this method has a number of shortcomings when trying to adequately reconstruct theories with higher-order derivatives in either the gravitational or the matter se…
Cosmography is a powerful tool to investigate the Universe kinematic and then to reconstruct dynamics in a model-independent way. However, recent new measurements of supernovae Ia and quasars have populated the Hubble diagram up to high redshifts ($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…
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…
We develop a cosmographic framework for analysing redshift drift signals of nearby sources model-independently, i.e., without making assumptions about the metric description of the Universe. We show that the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) prediction is altered nontrivially by regional anisotropies and inhomogeneities. In particular, we find that the position drift of the sources is nontrivially linked to the redshift drift signal. The redshift drift signal for nearby sources might be formulated in terms of an effective deceleration parameter, which reduces to the FLRW deceleratio…
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）
The cosmographic technique is a powerful model-independent tool for distinguishing between competing cosmological scenarios. The key strengths and weaknesses of standard cosmography are discussed in view of healing the convergence problem endangering the high-redshift expansions of cosmological distances. We focus especially on rational cosmographic approximations to reconstruct the dark energy behaviour under the $f(R)$, $f(T)$ and $f(Q)$ gravity frameworks. Based on observational constraints over the cosmographic series, we investigate the origin of cosmic acceleration and the possibility of…
Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the $Λ$CDM model, based on General Relativity and standard model of particles, are discussed in view of the most recent observational constraints. The motivations for considering extensions and modifications of General Relativity are taken into account, with particular attention to $f(R)$ and $f(T)$ theories of gravity where dynamics is represented by curvature or torsion field respectively. The features of $f(R)$ models…
In light of the statistical performance of cosmological observations, in this work we present the cosmography in $f(T,B)$ gravity. In this scenario we found a cosmological viable standard case that allows to reduce the degeneracy between several $f(T,B)$ models already proposed in the literature. Furthermore, we constrain this model using Pantheon SNeIa compilation, Cosmic Chronometers and a newly GRB calibrated data sample. We found that with an appropriate strategy for including the cosmographic parameter, we do produce a viable cosmology with our model within $f(T,B)$ gravity.
We address the issue of constraining the class of $f(\mathcal{R})$ able to reproduce the observed cosmological acceleration, by using the so called cosmography of the universe. We consider a model independent procedure to build up a $f(z)$-series in terms of the measurable cosmographic coefficients; we therefore derive cosmological late time bounds on $f(z)$ and its derivatives up to the fourth order, by fitting the luminosity distance directly in terms of such coefficients. We perform a Monte Carlo analysis, by using three different statistical sets of cosmographic coefficients, in which the …
In this paper, using a significantly improved version of the model-independent, cosmographic approach to cosmology (John, M. V. 2004, ApJ, 614, 1), we address an important question: Was there a decelerating past for the universe? To answer this, the Bayes's probability theory is employed, which is the most appropriate tool for quantifying our knowledge when it changes through the acquisition of new data. The cosmographic approach helps to sort out the models in which the universe was always accelerating from those in which it decelerated for at least some time in the period of interest. Bayesi…
Investigating the accelerated expansion of the universe with cosmography is a best method to constraint cosmological models. In this work, in the $F(G)$ modified gravity framework, we obtain equations of motion in a flat FRW metric. Then we reconstruct the present day values of $F(G)$ and its derivatives with the cosmographic parameters on the only assumption that the universe is homogenous and isotropic on large scale. Also we investigate the conditions of cosmologically viable $F(G)$ gravity models with the fiducial data set values.
We use cosmography to present constraints on the kinematics of the Universe, without postulating any underlying theoretical model. To this end, we use a Monte Carlo Markov Chain analysis to perform comparisons to the supernova Ia Union 2 compilation, combined with the Hubble Space Telescope measurements of the Hubble constant, and the Hubble parameter datasets. We introduce a sixth order cosmographic parameter and show that it does not enlarge considerably the posterior distribution when comparing to the fifth order results. We also propose a way to construct viable parameter variables to be u…
Closing the Cosmographic Hierarchy: Dynamical Attractors from Inflation to Reheating
University of Cape Town（开普敦大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（理论与计算科学国家研究所）；University of Lethbridge（莱斯布里奇大学）；South African Astronomical Observatory（南非天文台）；Centre for Space Research, North-West University（西北大学空间研究中心）
Cosmography is used in cosmological data processing in order to constrain the kinematics of the universe in a model-independent way, providing an objective means to evaluate the agreement of a model with observations. In this paper, we extend the conventional methodology of cosmography employing Taylor expansions of observables by an alternative approach using Padé approximations. Due to the superior convergence properties of Padé expansions, it is possible to improve the fitting analysis to obtain numerical values for the parameters of the cosmographic series. From the results, we can derive …
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 useful tool to constrain cosmological models, in particular dark energy models. In the case of modified theories of gravity, where the equations of motion are generally quite complicated, cosmography can contribute to select realistic models without imposing arbitrary choices a priori. Indeed, its reliability is based on the assumptions that the universe is homogeneous and isotropic on large scale and luminosity distance can be "tracked" by the derivative series of the scale factor a(t). We apply this approach to induced gravity brane-world models where an f(R)-term is present…
We propose a strategy to infer the transition redshift $z_{da}$, which characterizes the passage through the universe decelerated to accelerated phases, in the framework $f(R)$ gravities. To this end, we numerically reconstruct $f(z)$, i.e. the corresponding $f(R)$ function re-expressed in terms of the redshift $z$ and we show how to match $f(z)$ with cosmography. In particular, we relate $f(z)$ and its derivatives to the cosmographic coefficients, i.e. $H_0, q_0$ and $j_0$ and demonstrate that its corresponding evolution may be framed by means of an effective logarithmic dark energy term $Ω_X…
We examine the observational viability of a class of $f(\mathcal{R})$ gravity cosmological models. Particular attention is devoted to constraints from the recent observational determination of the redshift of the cosmological deceleration-acceleration transition. Making use of the fact that the Ricci scalar is a function of redshift $z$ in these models, $\mathcal {R=R}(z)$, and so is $f(z)$, we use cosmography to relate a $f(z)$ test function evaluated at higher $z$ to late-time cosmographic bounds. First, we consider a model independent procedure to build up a numerical $f(z)$ by requiring th…
A method to set constraints on the parameters of extended theories of gravitation is presented. It is based on the comparison of two series expansions of any observable that depends on H(z). The first expansion is of the cosmographical type, while the second uses the dependence of H with z furnished by a given type of extended theory. When applied to f(R) theories together with the redshift drift, the method yields limits on the parameters of two examples (the theory of Hu and Sawicki (2007), and the exponential gravity introduced by Linder (2009)) that are compatible with or more stringent th…
We propose a novel approach for parameterizing the luminosity distance, based on the use of rational "Padé" approximations. This new technique extends standard Taylor treatments, overcoming possible convergence issues at high redshifts plaguing standard cosmography. Indeed, we show that Padé expansions enable us to confidently use data over a larger interval with respect to the usual Taylor series. To show this property in detail, we propose several Padé expansions and we compare these approximations with cosmic data, thus obtaining cosmographic bounds from the observable universe for all case…
Cosmography is a phenomenological and relatively model-independent approach to cosmology, where physical quantities are expanded as a Taylor series in the cosmological redshift, or in related variables. Here we apply this methodology to constrain possible cosmological variations of the fine-structure constant, $α$. Two peculiarities of this case are the existence of high-redshift data, and the fact that one term in the series is directly and tightly constraint by local laboratory tests with atomic clocks. We use this atomic clock data, together with direct model-independent high-resolution ast…
Covariant cosmography in the presence of local structures: comparing exact solutions and perturbation theory
National Institute for Theoretical & Computational Sciences（国家理论与计算科学研究所）；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，理论物理中心）；Department of Physics & Astronomy, Queen Mary University of London（伦敦玛丽女王大学物理与天文系）；Department of Physics & Astronomy, University of the Western Cape（西开普大学物理与天文系）
It is nowadays accepted that the universe is undergoing a phase of accelerated expansion as tested by the Hubble diagram of Type Ia Supernovae (SNeIa) and several LSS observations. Future SNeIa surveys and other probes will make it possible to better characterize the dynamical state of the universe renewing the interest in cosmography which allows a model independent analysis of the distance - redshift relation. On the other hand, fourth order theories of gravity, also referred to as $f(R)$ gravity, have attracted a lot of interest since they could be able to explain the accelerated expansion …
Since Lorentz invariance plays an important role in modern physics, it is of interest to test the possible Lorentz invariance violation (LIV). The time-lag (the arrival time delay between light curves in different energy bands) of Gamma-ray bursts (GRBs) has been extensively used to this end. However, to our best knowledge, one or more particular cosmological models were assumed {\it a priori} in (almost) all of the relevant works in the literature. So, this makes the results on LIV in those works model-dependent and hence not so robust in fact. In the present work, we try to avoid this proble…
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）
Model-independent methods in cosmology has become an essential tool in order to deal with an increasing number of theoretical alternatives for explaining the late-time acceleration of the Universe. In principle, this provides a way of testing the Cosmological Concordance (or $Λ$CDM) model under different assumptions and ruling out whole classes of competing theories. One such model-independent method is the so-called cosmographic approach, which relies only on the homogeneity and isotropy of the Universe on large scales. We show that this method suffers from many shortcomings, providing biased…
Modeling of matter bounce in $f(R,T)$ gravity has been presented with no violation of the null energy condition. Only a closed universe with negative pressure is allowed in good agreement with some recent observations which favor a universe with positive curvature. Our results agree with some recent works in which a combination of positive curvature and vacuum energy leads to non-singular bounces with no violation of the null energy condition. The stability of the model has been discussed. The cosmographic parameters are developed for the derived model to explain the accelerated expansion of t…
We perform a number of inter-related cosmographic fits to the legacy05 and gold06 supernova datasets. We pay particular attention to the influence of both statistical and systematic uncertainties, and also to the extent to which the choice of distance scale and manner of representing the redshift scale affect the cosmological parameters. While the "preponderance of evidence" certainly suggests an accelerating universe, we would argue that (based on the supernova data) this conclusion is not currently supported "beyond reasonable doubt". As part of the analysis we develop two particularly trans…
The challenging issue of determining the correct $f(R)$ among several possibilities is here revised by means of numerical reconstructions of the modified Friedmann equations around the redshift interval $z\in[0,1]$. Frequently, a severe degeneracy between $f(R)$ approaches occurs, since different paradigms correctly explain present time dynamics. To set the initial conditions on the $f(R)$ functions, we involve the use of the so called cosmography of the Universe, i.e. the technique of fixing constraints on the observable Universe by comparing expanded observables with current data. This power…
In this paper we propose an alternative cosmography by considering Horava-Lifshitz gravity as a model of quantum gravity to search for quantum effects at the cosmological level. For our analyses we consider current late universe surveys and a Gravitational Waves forecast from Einstein Telescope. We found naturally a non-flat scenario with $Ω_k =-0.021^{+0.023}_{-0.029}$ with $H_0 = 71.904^{+1.406}_{-1.347}$, without showing the standard reported $3.4$-$σ$ inconsistency. Furthermore, we obtained a specific value for the Ho\v rava parameter $ω\approx -3.8\times 10^{-14}$, which can be interprete…
Mapping the expansion history of the universe is a compelling task of physical cosmology, especially in the context of the observational evidence for the recent acceleration of the universe, which demonstrates that canonical theories of cosmology and particle physics are incomplete and that there is new physics still to be discovered. Cosmography is a phenomenological approach to cosmology, where (with some caveats) physical quantities are expanded as a Taylor series in the cosmological redshift $z$, or analogous parameters such as the rescaled redshift $y=z/(1+z)$ or the logarithmic redshift …
Modified gravity, known as $f(R)$ gravity, has presently been applied to Cosmology as a realistic alternative to dark energy. For this kind of gravity the expansion of the Universe may accelerate while containing only baryonic and cold dark matter. The aim of the present investigation is to place cosmographic constraints on the class of theories of the form $f(R)=R - α/R^n$ within the Palatini approach. Although extensively discussed in recent literature and confronted with several observational data sets, cosmological tests are indeed inconclusive about the true signal of $n$ in this class of…
In the context of $f(\mathcal{R})$ gravity, dark energy is a geometrical fluid with negative equation of state. Since the function $f(\mathcal{R})$ is not known \emph{a priori}, the need of a model independent reconstruction of its shape represents a relevant technique to determine which $f(\mathcal{R})$ model is really favored with respect to others. To this aim, we relate cosmography to a generic $f(\mathcal R)$ and its derivatives in order to provide a model independent investigation at redshift $z \sim 0$. Our analysis is based on the use of three different cosmological distance definition…
We review different dark energy cosmologies. In particular, we present the $Λ$CDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the $Λ$CDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies fo…
