Cosmographic Approach Research Articles

Cosmographic analysis of holographic nonzero torsion framework

In this paper, we use the cosmographic approach to discuss Friedmann space-time in the presence of torsion. For this, we explore equations of motion that explain creation in an isotropic and homogeneous cosmic backdrop with nonzero torsion. Here, we consider the energy density of holographic dark energy model [Formula: see text] where [Formula: see text] is a dimensionless parameter depending on redshift parameter [Formula: see text] is the reduced Planck mass and [Formula: see text] represents the holographic length scale. We examine this dark energy model with both constant and variable holographic length scales in terms of Hubble parameter to determine the best-fit scale. The interaction between dark sector components is taken to evaluate cosmographic parameters, like Hubble, equation of state, deceleration, jerk, snap, lerk and statefinder parameters. We consider four [Formula: see text] parametrizations, which are Chevallier–Polarski–Linder, Jassal–Bagla–Padmanabhan, Wetterich and Ma–Zhang for both cases. We obtain consistent results for specific choices of constant parameters in the underlying scenario.

A measurement of Hubble constant using cosmographic approach combining fast radio bursts and supernovae

ABSTRACT The Hubble constant (H0) is a crucial parameter in cosmology. Different cosmic observations have resulted in varying estimates results for H0, that is the well-known H0 tension. To address this issue, it is beneficial to use other data set to constrain H0. In this paper, via the cosmographic approach based on the Friedman–Lemaitre–Robertson–Walker (FLRW) metric to the dispersion measure (DM) of the intergalactic medium DMIGM(z) of fast radio bursts (FRBs), we obtain the Taylor expansion of 〈DMIGM(z)〉 in terms of redshift z. Utilizing the uncalibrated type Ia supernaove (SNe Ia) and 18 localized FRBs, we give the cosmological constraints, $H_0=65.5^{+6.4}_{-5.4}$ km s−1 Mpc−1 (68 per cent CL), cosmological deceleration parameter q0 = −0.50 ± 0.20 and the jerk parameter $j_0=-0.1^{+2.0}_{-2.5}$. To demonstrate the impact of parameter degeneracies on our analysis methods, we compare the results using three different forms of fIGM(z) and two different prior distributions of Ωb, 0. After that, we find that the uncertainty in H0 is not significantly affected by the width of the prior interval of fIGM(z) and Ωb, 0, but the mean value is influenced by the priors for fIGM(z) and Ωb, 0 due to parameter degeneracies with H0. Employing fIGM(z) that evolves with redshift, we obtain $H_0=69.0^{+6.7}_{-5.7}$ km s−1 Mpc−1. In addition, the mock analyses provide a posterior estimation of H0 with an accuracy of 4.6 per cent and higher precision for q0 and j0 in the near future.

Tensions with the flat ΛCDM model from high-redshift cosmography

ABSTRACT The longstanding search for the cosmological model that best describes the Universe has been made more intriguing since the recent discovery of the Hubble constant, H0, tension observed between the value of H0 from the Cosmic Microwave Background and from type Ia supernovae (SNe Ia). Hence, the commonly trusted flat Λ cold dark matter (ΛCDM) model is under investigation. In this scenario, cosmography is a very powerful technique to investigate the evolution of the Universe without any cosmological assumption, thus revealing tensions between observational data and predictions from cosmological models in a completely model-independent way. We here employ a robust cosmographic technique based on an orthogonal logarithmic polynomial expansion of the luminosity distance to fit quasars (QSOs) alone and QSOs combined with Gamma-Ray Bursts (GRBs), SNe Ia, and Baryon Acoustic Oscillations. To apply QSOs and GRBs as probes we use, respectively, the Risaliti–Lusso relation between ultraviolet and X-ray luminosities and the ‘Dainotti GRB 3D relation’ among the rest-frame end time of the X-ray plateau emission, its corresponding luminosity, and the peak prompt luminosity. We also correct QSOs and GRBs for selection biases and redshift evolution and we employ both the traditional Gaussian likelihood and the newly discovered best-fitting likelihoods for each probe investigated. This comprehensive analysis reveals a strong tension ($\gt 4 \, \sigma$) between our data sets and the flat ΛCDM model proving the power of both the cosmographic approach and high-redshift sources, such as QSOs and GRBs, which can probe the Universe at early epochs.

Revisiting cosmography via Gaussian process

In this paper, we revisit the kinematical state of our Universe via the cosmographic approach by using Gaussian process, where the minimum assumption is the cosmological principle, i.e. the Friedmann–Lemaître–Robertson–Walker metric. A obviously distinguished feature is that these cosmography parameters are free of any gravity theories and cosmological models. And Gaussian process is independent of any specific parameterized forms of function. Thus by transformations these generic cosmography parameters can be used to constrain a cosmological model and dark energy model directly at the kinematics level of our Universe. As a result, a series of cosmography parameters up to the fifth oder, i.e. the Hubble parameter H(z), the deceleration parameter q(z), the jerk parameter j(z), the snap parameter s(z) and the lerk parameter l(z), evolve with respect to the redshift z are reconstructed from the cosmic observations which include the recently released Pantheon+ SN Ia samples and the observational Hubble data H(z), also dubbed as cosmic chronometers. The result shows the transition redshift from a decelerated expansion to an accelerated expansion z_t=0.652^{+0.054}_{-0.043} which is consistent with the previous results.

Dependency of the cosmographic tension of standard model to statistical errors of observational data ‎

In this work, we study the standard model of cosmology in the context of cosmographic approach. We want to determine whether the cosmographic tension of the standard model that is reported in recent studies, depends on the statistical errors of the observational data or not. To do this, we produce three catalogues of mock data for the distance modulus of type Ia supernovae using a canonical value for matter density in the framework of standard model. In the first catalogue, the errors of mock data have been chosen equal to the errors of real data in Pantheon catalogue. In the second and third catalogues, the errors of mock data have been chosen equal to half and twice the real errors in Pantheon sample, respectively. In the next step, using the generated mock data, we minimize the least square function in the context of Markov Chain Monte Carlo method and put constraints on the cosmographic parameters in both model independent cosmographic approach and standard model. Our results show that decreasing the error of mock data can remove the cosmographic tension of the standard model. Also, the larger errors increase the deviation of standard model from cosmographic method. Hence, the cosmographic tension of the standard model which is recently reported by the Hubble diagrams of quasars and Gamma-Ray-Burst can be essentially due to large error bars of these observational data and so not a physical tension.

Neural networks and standard cosmography with newly calibrated high redshift GRB observations

Gamma-ray bursts (GRBs) detected at high redshift can be used to trace the cosmic expansion history. However, the calibration of their luminosity distances is not an easy task in comparison to Type Ia Supernovae (SNeIa). To calibrate these data, correlations between their luminosity and other observed properties of GRBs need to be identified, and we must consider the validity of our assumptions about these correlations over their entire observed redshift range. In this work, we propose a new method to calibrate GRBs as cosmological distance indicators using SNeIa observations with a machine learning architecture. As well we include a new data GRB calibrated sample using extended cosmography in a redshift range above z > 3.6. An overview of this machine learning technique was developed in [1] to study the evolution of dark energy models at high redshift. The aim of the method developed in this work is to combine two networks: a Recurrent Neural Network (RNN) and a Bayesian Neural Network (BNN). Using this computational approach, denoted RNN+BNN, we extend the network's efficacy by adding the computation of covariance matrices to the Bayesian process. Once this is done, the SNeIa distance-redshift relation can be tested on the full GRB sample and therefore used to implement a cosmographic reconstruction of the distance-redshift relation in different regimes. Thus, our newly-trained neural network is used to constrain the parameters describing the kinematical state of the Universe via a cosmographic approach at high redshifts (up to z ≈ 10), wherein we require a very minimal set of assumptions on the deep learning arquitecture itself that do not rely on dynamical equations for any specific theory of gravity.

Do current observations support transient acceleration of our universe?

In this paper, we have investigated a very natural question regarding the dynamics of the universe, namely, the possibility of its decelerating phase immediately after the present accelerating phase. To begin with, we have focused on the matter creation theory which is considered to be a viable alternative to dark energy and modified gravity models. Moreover, we have introduced the cosmographic approach which allows us to express the free parameters of a cosmological model in terms of the known cosmographic parameters. Assuming a generalized matter creation rate, we have discussed the theoretical bounds on the model parameters allowing the future deceleration of the universe. Moreover, using the observational bounds on the cosmographic parameters obtained from the low redshifts observational probes, we have also examined the chance of a decelerating phase of the universe. Finally, considering a variety of known cosmological models and parametrizations, we have tested the same possibility. Our analysis shows that the chance of a future decelerating expansion of the universe is highly dependent on the choice of the cosmological models and parametrizations and also on the observational data. Even though the future decelerating expansion is allowed in some cosmological frameworks, but we do not see any strong evidence in favor of this. Perhaps, the future cosmological surveys could offer some more information regarding the fate of the universe.

Cosmographic Parameters in Model-independent Approaches

Abstract The 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 debate about the tensions that appear when one investigates some high-redshift cosmological data. In this work, we consider two common data sets, namely, Type Ia supernovae (Pantheon sample) and the Hubble data, to investigate advantages and disadvantages of the cosmographic approach. To do this, we obtain the evolution of cosmographic functions using the cosmographic method, as well as two other well-known model-independent approaches, namely, the Gaussian process and the genetic algorithm. We also assume a ΛCDM model as the concordance model to compare the results of mentioned approaches. Our results indicate that the results of cosmography compared with the other approaches are not exact enough. Considering the Hubble data, which are less certain, the results of q 0 and j 0 obtained in cosmography provide a tension at more than 3σ away from the best result of ΛCDM. Assuming both of the data samples in different approaches, we show that the cosmographic approach, because it provides some biased results, is not the best approach for reconstruction of cosmographic functions, especially at higher redshifts.

Cosmographic approach to Running Vacuum dark energy models: New constraints using BAOs and Hubble diagrams at higher redshifts

Abstract 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 ΛCDM 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 χ2 function of the distance modulus in the context of the Markov Chain Monte Carlo method (MCMC), we put constraints on the current values of the standard cosmographic parameters in a model-independent way. It turns out that, in the absence of BAOs data, the various DE models generally exhibit cosmographic tensions with the observations at the highest redshifts (namely with the QSOs and GRBs data). However, if we include the robust observations from BAOs to our cosmographic sample, the ΛCDM and RVMs are clearly favored against the GDEs. Finally, judging from the perspective of the deviance information criterion (DIC), which enables us to compare models making use of the Markov chains of the MCMC method, we conclude that the RVMs are the preferred kind of DE models. We find it remarkable that these models, which had been previously shown to be capable of alleviating the σ8 and H0 tensions, appear now also as the most successful ones at the level of the cosmographic analysis.

Cosmography by orthogonalized logarithmic polynomials

Cosmography is a powerful tool for investigating the Universe kinematic and then for reconstructing the 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 ∼ 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 called orthogonalization, and we show that such an expansion provides a very good fit in the whole z = 0 ÷ 7.5 range to both real and mock data obtained assuming various cosmological models. Moreover, although the cosmographic series is tested well beyond its convergence radius, the parameters obtained expanding the luminosity distance–redshift relation for the Lambda cold dark matter (ΛCDM) model are broadly consistent with the results from a fit of mock data obtained with the same cosmological model. This provides a method for testing the reliability of a cosmographic function to study cosmological models at high redshifts, and it demonstrates that the logarithmic polynomial series can be used to test the consistency of the ΛCDM model with the current Hubble diagram of quasars and supernovae Ia. We confirm a strong tension (at > 4σ) between the concordance cosmological model and the Hubble diagram at z > 1.5. This tension is dominated by the contribution of quasars at z > 2 and also starts to be present in the few supernovae Ia observed at z > 1.

Tracing the cosmic history by Gauss-Bonnet gravity

Cosmic history can be traced considering further curvature contributions inside the gravitational action. Assuming that standard General Relativity can be extended by other curvature invariants, we discuss the possibility that an action containing higher-order curvature terms can fit, in principle, the whole universe evolution. In particular, a theory like $F(R,{\cal G})$, with $R$ the Ricci scalar and $\cal G$ the Gauss-Bonnet topological term, contains all the curvature invariants that, depending on the energy regime, can address inflation, matter dominated and dark energy regimes. In this paper, we investigate this possibility considering how $F(R,{\cal G})$ models can lead gravity from ultraviolet to infrared scales. Specifically, we will take into account a cosmographic approach for this purpose.

General cosmography model with spatial curvature

ABSTRACT We adopt a cosmographic approach in order to determine spatial curvature (i.e. ΩK), combining the latest release of cosmic chronometer (CC) data, the Pantheon sample of Type Ia supernovae observations and baryon acoustic oscillation measurements. We use the expanded transverse comoving distance DM($z$) as a basic function for deriving H($z$) and other cosmic distances. In this scenario, ΩK can be constrained only by CC data. To overcome the convergence issues at high-redshift domains, two methods are applied: the Padé approximants and the Taylor series in terms of the new redshift y = $z$/(1 + $z$). Adopting the Bayesian evidence, we find that there is positive evidence for the Padé approximant up to order (2,2) and weak evidence for the Taylor series up to third order against the ΛCDM + ΩK model. The constraint results show that a closed Universe is preferred by present observations under all the approximations used in this study. Also, the tension level of the Hubble constant H0 has less than 2σ significance between different approximations and the local distance ladder determination. For each assumed approximation, H0 is anticorrelated with ΩK and the sound horizon at the end of the radiation drag epoch, which indicates that the H0 tension problem can be slightly relaxed by introducing ΩK or any new physics that can reduce the sound horizon in the early Universe.

Connecting early and late epochs by f(z)CDM cosmography

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, Ωm, and analysing low redshift cosmological data. Here we propose a different strategy, linking together the parametric cosmographic behavior of the late universe expansion with the small scale universe. In this way, we do not need to assume any “a priori” values for the cosmological parameters, since these are constrained at early epochs using both the Cosmic Microwave Background Radiation (CMBR) and Baryonic Acoustic Oscillation (BAO) data. In other words, we want to develop a cosmographic approach without assuming any background model but considering a f(z)CDM model where the function f(z) is given by a suitable combination of polynomials capable of tracking the cosmic luminosity distance, replacing the cosmological constant Λ. In order to test this strategy, we describe the late expansion of the universe using the Pad'e polynomials. Specifically, we adopt a P(2,2) series, that is a promising rational series which guarantees a good convergence also at high redshift. This approach is discussed in the light of the recent H(z) values indicators, combined with Supernovae Pantheon sample, galaxy clustering and early universe data, as CMBR and BAO. We found an interesting dependence of the current matter density value with cosmographic parameters, proving the inaccuracy of setting the value of Ωm in cosmographic analyses. Furthermore, a non-negligible effect of the cosmographic parameters on the CMBR temperature anisotropy power spectrum is shown, and constraints by selected joint datasets are reported. Finally, we found that the cosmographic series, truncated at third order, shows a better χ2 best fit value then the vanilla ΛCDM model. This can be interpreted as the requirement that higher order corrections have to be considered to correctly describe low redshift data and remove the degeneration of the models.

Quantifying the evidence for the current speed-up of the Universe with low and intermediate-redshift data. A more model-independent approach

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 G'omez-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 the literature. The reconstructed functions are fully compatible with the predictions for the concordance model. In addition, we also discuss the confidence level at which we can claim that the Universe (assumed to be flat, homogeneous and isotropic) is currently accelerating. According to Jeffreys' scale and jargon, we find moderate evidence in favor of such speed-up using the data on SnIa+CCH, and very strong one when we also use data on BAOs. The measured current value of the deceleration parameter in the latter case reads q0∼ −0.60± 0.10, and for the deceleration-acceleration transition redshift we find zt∼ 0.80± 0.10. The former is ∼ 6σ away from 0. This is in stark contrast, for instance, with the ∼ 17σ that are found in the context of the flat ΛCDM even without including the BAOs data. This indicates that cosmography and Occam's razor criterion play a crucial role in this discussion, and that estimating the evidence for positive acceleration only in the framework of a particular cosmological model or parametrization is clearly insufficient.

Model-independent constraints on dark energy evolution from low-redshift observations

Knowing the late time evolution of the Universe and finding out the causes for this evolution are the important challenges of modern cosmology. In this work, we adopt a model-independent cosmographic approach and approximate the Hubble parameter considering the Pade approximation which works better than the standard Taylor series approximation for $z>1$. With this, we constrain the late time evolution of the Universe considering low-redshift observations coming from SNIa, BAO, $H(z)$, $H_{0}$ , strong-lensing time-delay as well as the Megamaser observations for angular diameter distances. We confirm the tensions with $\Lambda$CDM model for low-redshifts observations. The present value of the equation of state for the dark energy has to be phantom-like and for other redshifts, it has to be either phantom or should have a phantom crossing. For lower values of $\Omega_{m0}$, multiple phantom crossings are expected. This poses serious challenges for single, non-interacting scalar field models for dark energy. We derive constraints on the {\it statefinders} $(r,s)$ and these constraints show that a single dark energy model cannot fit data for the whole redshift range $0\leq z\leq 2$: in other words, we need multiple dark energy behaviors for different redshift ranges. Moreover, the constraint on sound speed for the total fluid of the Universe, and for the dark energy fluid (assuming them being barotropic), rules out the possibility of a barotropic fluid model for unified dark sector and barotropic fluid model for dark energy, as fluctuations in these fluids are unstable as $c_{s}^2 < 0$ due to constraints from low-redshift observations.

Constraints on kinematic parameters at z≠0

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 scale factor a as the variable of expansion. We expand the luminosity distance and the Hubble parameter around an arbitrary ã and use the Supernovae Ia (SNe Ia) and the Hubble parameter data to estimate H, q, j and s at z≠0 (ã≠1). We show that the last relevant term for both expansions is the third. Since the third order expansion of dL(z) has one parameter less than the third order expansion of H(z), we also consider, for completeness, a fourth order expansion of dL(z). For the third order expansions, the results obtained from both SNe Ia and H(z) data are incompatible with the ΛCDM model at 2σ confidence level, but also incompatible with each other. When the fourth order expansion of dL(z) is taken into account, the results obtained from SNe Ia data are compatible with the ΛCDM model at 2σ confidence level, but still remains incompatible with results obtained from H(z) data. These conflicting results may indicate a tension between the current SNe Ia and H(z) data sets.

Model-independent constraints on Lorentz invariance violation via the cosmographic approach

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 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 problem by using a model-independent approach. We calculate the time delay induced by LIV with the cosmic expansion history given in terms of cosmography, without assuming any particular cosmological model. Then, we constrain the possible LIV with the observational data, and find weak hints for LIV.

Searching for cosmological preferred axis using cosmographic approach

Recent released Planck data and other astronomical observations show that the universe may be anisotropic on large scales. This hints a cosmological privileged axis in our anisotropic expanding universe. This paper proceeds a modified redshift in anisotropic cosmological model as $ 1+\tilde{z}(t,\hat{\textbf{p}})=\frac{a(t_{0)}}{a(t)}(1-A(\hat{\textbf{n}}.\hat{\textbf{p}}))$ (where $A$ is the magnitude of anisotropy ,$\hat{\textbf{n}}$ is the direction of privileged axis, and $\hat{\textbf{p}}$ is the direction of each SNe Ia sample to galactic coordinates) along with anisotropic parameter $\delta=\frac{A(\hat{\textbf{n}}.\hat{\textbf{p}})}{1+A(\hat{\textbf{n}}.\hat{\textbf{p}})}$. The luminosity distance is expanded with model-independent cosmographic parameters as a function of modified redshift $\tilde{z}$. As the transformation matrix $M(n\times n)$ is obtained to convert the Taylor series coefficients of isotropic luminosity distance to corresponding anisotropic parameters. These results culminate the magnitude of anisotropy about $\mid A\mid \simeq 10^{-3}$ and the direction of preferred axis as $(l,b)=(297^{-34}_{+34},3^{-28}_{+28})$, which are consistent with other studies in $1-\sigma$ confidence level.

Is cosmography a useful tool for testing cosmology?

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 $\Lambda$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 results depending on the auxiliary variable used in the series expansion and is unable to rule out models or adequately reconstruct theories with higher-order derivatives in either the gravitational or matter sector. Consequently, in its present form, this method seems unable to provide reliable or useful results for cosmological applications.

Can f(R) gravity contribute to (dark) radiation?

We discuss the possibility that suitable modifications of gravity could account for some amount of the radiation we observe today, in addition to the possibility of explaining the present speed up of the universe. We start introducing and reviewing cosmological reconstruction methods for metric f(R) theories of gravity that can be considered as one of the straightforward modifications of Einstein's gravity as soon as f(R)≠ R. We then take into account two possible f(R) models which could give rise to (dark) radiation. Constraints on the models are found by using the Planck Collaboration 2015 data within a cosmographic approach and by obtaining the matter power spectrum of those models. The conclusion is that f(R) gravity can only contribute minimally to the (dark) radiation to avoid departures from the observed matter power spectrum at the smallest scales (of the order of 0.01Mpc−1), i.e., precisely those scales that exited the horizon at the radiation dominated epoch. This result could strongly contribute to select reliable f(R) models.