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 the cosmodynamical parameters can be fitted and then employ them to analyse the kinematics via its generic cosmographic parameters? By all means, without experimenting the problem of truncation of the series that all cosmography proposals in the literature argue. In this work we present a generic EoS depending solely on the form of $f_i(z)$ and its derivative is found, where this function can be any polynomial (mimicking a dark energy-like term) that allow the dynamics of a specific cosmological density. We test our generic EoS with standard cosmological models and with polynomials proposals as Padé and Chebyshev approximants. Interesting enough, a Padé (2,2) approximant has been considered inside a $f(z)$CDM-like model showing a transition in $z=1$. Also, we found that this is not assured since models with these characteristics have degeneracy and truncation problems that experiment a divergence at this redshift limit. To explore our results, also we present a new supernovae sample trained via a deep learning tool called Recurrent-Bayesian (RNN+BNN) network that can solve problems as overfitting at lower redshifts and increase the density of data points in this region, which can help to discern between cosmographies at 2-$σ$ of precision.
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…
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…
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…
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…
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…
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 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 larges…
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…
The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parameterize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé seri…
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 …
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.
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 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 …
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…
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…
In this work, we study two scenarios of the Universe filled by a perfect fluid following the traditional dark energy and a viscous fluid as dark matter. In this sense, we explore the simplest case for the viscosity in the Eckart formalism, a constant, and then, a polynomial function of the redshift. We constrain the phase-space of the model parameters by performing a Bayesian analysis based on Markov Chain Monte Carlo method and using the latest data of the Hubble parameter (OHD), Type Ia Supernovae (SNIa) and Strong Lensing Systems. The first two samples cover the region $0.01<z<2.36$. Based …
Based on the cosmological principle only, the method of describing the evolution of the Universe, called cosmography, is in fact a kinematics of cosmological expansion. The effectiveness of cosmography lies in the fact that it allows, based on the results of observations, to perform a rigid selection of models that do not contradict the cosmological principle. It is important that the introduction of new components (dark matter, dark energy or even more mysterious entities) will not affect the relationship between the kinematic characteristics (cosmographic parameters) This paper shows that wi…
The parameters of any model that satisfies the cosmological principle (the universe is homogeneous and isotropic on large scale), can be expressed through cosmographic parameters. In this paper, we perform this procedure for the Cardassian model. We demonstrate a number of advantages of the approach used before traditional methods.
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…
We use cosmography to present constraints on the kinematics of the Universe without postulating any underlying theoretical model a priori. To this end, we use a Markov Chain Monte Carlo 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. The cosmographic approach to our analysis is revisited and extended for new notions of redshift presented as alternatives to the redshift z. Furthermore, we introduce a new set of fitting parameters describing the kinematical ev…
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 investigate the prospects for determining the accelerating history of the Universe from upcoming measurements of the expansion rate $H(z)$. In our analyses, we use Monte Carlo simulations based on $w$CDM models to generate samples with different characteristics and calculate the evolution of the deceleration parameter $q(z)$. We show that a cosmographic (and, therefore, model-independent) evidence for cosmic acceleration ($q(z<z_t) < 0$, where $z_t$ is the transition redshift) will only be possible with an accuracy in $H(z)$ data greater than the expected in current planned surveys. A brief…
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…
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…
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…
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…
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…
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…
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…
Constraining the dark energy equation of state, $w_x(z)$, is one of the main issues of current and future cosmological surveys. In practice, this requires making assumptions about the evolution of $w_x$ with redshift $z$, which can be manifested in a choice of a specific parametric form where the number of cosmological parameters play an important role in the observed cosmic acceleration. Since any attempt to constrain the EoS requires fixing some prior in one form or the other, settling a method to constrain cosmological parameters is of great importance. In this paper, we provide a straightf…
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 …
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 …
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 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…
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…
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…
We consider high-redshift $f(R)$ cosmography adopting the technique of polynomial reconstruction. In lieu of considering Taylor treatments, which turn out to be non-predictive as soon as $z>1$, we take into account the Padé rational approximations which consist in performing expansions converging at high redshift domains. Particularly, our strategy is to reconstruct $f(z)$ functions first, assuming the Ricci scalar to be invertible with respect to the redshift $z$. Having the thus-obtained $f(z)$ functions, we invert them and we easily obtain the corresponding $f(R)$ terms. We minimize error p…
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 reconstruct in this paper the deceleration and jerk parameters as functions of the cosmological redshift from data on cosmic chronometers (CCH), baryon acoustic oscillations (BAOs), and the Pantheon+MCT compilation of supernovae of Type Ia (SnIa). The reconstruction is carried out with the Weighted Function Regression method, previously introduced by Gómez-Valent & Amendola (2018). It improves the usual cosmographic approach by automatically implementing Occam's razor criterion. This makes our procedure to be more free of model and parametrization dependencies than many other analyses in th…
The present work deals with a combined test of the so-called Fractional Action Cosmology (FAC) on the example of a specific model obtained by the author earlier. In this model, the effective cosmological term is proportional to the Hubble parameter squared through the so-called kinematic induction. The reason of studying this cosmological model could be explained by its ability to describe two periods of accelerated expansion, that is in agreement with the recent observations and the cosmological inflation paradigm. First of all, we put our model through the theoretical tests that gives a gene…
In the paper we check whether the contribution of $(-)(1+z)^6$ type in the Friedmann equation can be tested. We consider some astronomical tests to constrain the density parameters in such models. We describe different interpretations of such an additional term: geometric effects of Loop Quantum Cosmology, effects of braneworld cosmological models, non-standard cosmological models in metric-affine gravity, and models with spinning fluid. Kinematical (or geometrical) tests based on null geodesics are insufficient to separate individual matter components when they behave like perfect fluid and s…
