arXiv subjects

Tong-Jie Zhang

Publications and source records attributed to Tong-Jie Zhang.

At least 127 records · Page 7Linked to original sources

arXiv2012

Optimizing the Recovery of Fisher Information in the Dark Matter Power Spectrum

We combine two Gaussianization techniques - Wavelet Non-Linear Wiener Filter (WNLWF) and density reconstruction - to quantify the recovery of Fisher information that is lost in the gravitational collapse. We compute a displacement fields, in analogy with the Zel'dovich approximation, and apply a Wavelet Non-Linear Wiener Filter that decomposes the reconstructed density fields into a Gaussian and a non-Gaussian component. From a series of 200 realizations of N-body simulations, we compute the recovery performance for density fields obtained with both dark matter particles and haloes. We find that the height of the Fisher information trans-linear plateau is increased by more than an order of magnitude at k > 1.0h/Mpc for particles, whereas either technique alone offers an individual recovery boost of only a factor of three to five. We conclude that these two techniques work in a symbiosis, as their combined performance is stronger than the sum of their individual contribution. When applied to the halo catalogues, we find that the reconstruction has only a weak effect on the recovery of Fisher Information, while the non-linear wavelet filter boosts the information by about a factor offive. We also observe that non-Gaussian Poisson noise saturates the Fisher information, and that shot noise subtracted measurements exhibit a milder information recovery.

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arXiv2012

Reconstructing the History of Energy Condition Violation from Observational Data

We study the likelihood of energy condition violations in the history of the Universe. Our method is based on a set of functions that characterize energy condition violation. FLRW cosmological models are built around these "indication functions". By computing the Fisher matrix of model parameters using type Ia supernova and Hubble parameter data, we extract the principal modes of these functions' redshift evolution. These modes allow us to obtain general reconstructions of energy condition violation history independent of the dark energy model. We find that the data suggest a history of strong energy condition violation, but the null and dominant energy conditions are likely to be fulfilled. Implications for dark energy models are discussed.

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arXiv2012

Constraints on Lema\^ıtre-Tolman-Bondi models from Observational Hubble Parameter data

We use the observational Hubble parameter data (OHD), both the latest observational dataset (Stern et al. 2010, referred to as SJVKS) and the simulated datasets, to constrain Lema\^ıtre-Tolman-Bondi (LTB) void models. The necessity of the consistency check on OHD itself in the LTB cosmology is stressed. Three voids are chosen as test models and are constrained using the Union2 dataset of SN Ia as well as OHD. Despite their different parametrization, the results from our test models show some indicating similarities, e.g., the best-fit voids obtained from OHD are all considerably broader than those from SN Ia. Due to the small size of the SJVKS dataset, the constraints are not conclusive. The constraining power of the future OHD observations are therefore investigated, through a Figure of Merit (FoM) analysis based on the Monte Carlo simulated data. We found that, in the case that the future OHD become more consistent with SN Ia, the results from the test models are almost unanimous: 1) as many as 32 OHD data points at the SJVKS-like uncertainty level are needed to give a higher FoM than the Union2 dataset of SN Ia; 2) precise observation helps reduce this required number; 3) increasing the survey depth does not always increase the FoM. On the other hand, if the future OHD and the Union2 dataset keep favor different voids, in a similar manner as they do at present, the 1σ confidence regions obtained from the two probes should finally separate. We test this conjecture and found that, the minimum observational requirement (the size of the dataset, the uncertainty level and the survey depth) for this inconsistency to emerge depends strongly on the void model.

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arXiv2011

Information Content in the Angular Power Spectrum of Weak Lensing: Wavelet Method

We quantify the performance of a non-linear Wiener filter, constructed in wavelet space, at recovering some of the Fisher information that was lost in the weak lensing convergence field. The proposed method consists in a separation of the original field into the sum of a Gaussian and a non-Gaussian contribution. After filtering an ensemble of such fields, which are obtained from $N$-body simulations, we find that we can recapture about four times more Fisher information, an effect that can potentially improve by a significant amount the constraining power of weak lensing surveys on cosmological parameters, including the dark energy equation of state $ω$. We compare this performance with that of the logarithmic mapping and find that the wavelet method can recover up to three times more information.

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arXiv2011

Quadrature algorithms to the luminosity distance with a time-dependent dark energy model

In our previous work, we have proposed two methods for computing the luminosity distance d_{L}^Λ in LCDM model. In this paper, two effective quadrature algorithms, known as Romberg Integration and composite Gaussian Quadrature, are presented to calculate the luminosity distance d_{L}^{CPL} in the Chevallier-Polarski-Linder parametrization(CPL) model. By comparing the efficiency and accuracy of the two algorithms, we find that the second is more promising. Moreover, we develop another strategy adapted for approximating d_{L}^Λ in flat LCDM universe. To some extent, our methods can make contributions to the recent numerical stimulation for the investigation of dark energy cosmology.

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arXiv2011

Morphology of Galaxy Clusters: A Cosmological Model-Independent Test of the Cosmic Distance-Duality Relation

Aiming at comparing different morphological models of galaxy clusters, we use two new methods to make a cosmological model-independent test of the distance-duality (DD) relation. The luminosity distances come from Union2 compilation of Supernovae Type Ia. The angular diameter distances are given by two cluster models (De Filippis et al. and Bonamente et al.). The advantage of our methods is that it can reduce statistical errors. Concerning the morphological hypotheses for cluster models, it is mainly focused on the comparison between elliptical $β$-model and spherical $β$-model. The spherical $β$-model is divided into two groups in terms of different reduction methods of angular diameter distances, i.e. conservative spherical $β$-model and corrected spherical $β$-model. Our results show that the DD relation is consistent with the elliptical $β$-model at $1σ$ confidence level (CL) for both methods, whereas for almost all spherical $β$-model parameterizations, the DD relation can only be accommodated at $3σ$ CL, particularly for the conservative spherical $β$-model. In order to minimize systematic uncertainties, we also apply the test to the overlap sample, i.e. the same set of clusters modeled by both De Filippis et al. and Bonamente et al.. It is found that the DD relation is compatible with the elliptically modeled overlap sample at $1σ$ CL, however for most of the parameterizations, the DD relation can not be accommodated even at $3σ$ CL for any of the two spherical $β$-models. Therefore it is reasonable that the marked triaxial ellipsoidal model is a better geometrical hypothesis describing the structure of the galaxy cluster compared with the spherical $β$-model if the DD relation is valid in cosmological observations.

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arXiv2011

Constraints on $Λ(t)$CDM models as holographic and agegraphic dark energy with the observational Hubble parameter data

The newly released observational $H(z)$ data (OHD) is used to constrain $Λ(t)$CDM models as holographic and agegraphic dark energy. By the use of the length scale and time scale as the IR cut-off including Hubble horizon (HH), future event horizon (FEH), age of the universe (AU), and conformal time (CT), we achieve four different $Λ(t)$CDM models which can describe the present cosmological acceleration respectively. In order to get a comparison between such $Λ(t)$CDM models and standard $Λ$CDM model, we use the information criteria (IC), $Om(z)$ diagnostic, and statefinder diagnostic to measure the deviations. Furthermore, by simulating a larger Hubble parameter data sample in the redshift range of $0.1<z<2.0$, we get the improved constraints and more sufficient comparison. We show that OHD is not only able to play almost the same role in constraining cosmological parameters as SNe Ia does but also provides the effective measurement of the deviation of the DE models from standard $Λ$CDM model. In the holographic and agegraphic scenarios, the results indicate that the FEH is more preferable than HH scenario. However, both two time scenarios show better approximations to $Λ$CDM model than the length scenarios.

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arXiv2011

Power of Observational Hubble Parameter Data: a Figure of Merit Exploration

We use simulated Hubble parameter data in the redshift range 0 \leq z \leq 2 to explore the role and power of observational H(z) data in constraining cosmological parameters of the ΛCDM model. The error model of the simulated data is empirically constructed from available measurements and scales linearly as z increases. By comparing the median figures of merit calculated from simulated datasets with that of current type Ia supernova data, we find that as many as 64 further independent measurements of H(z) are needed to match the parameter constraining power of SNIa. If the error of H(z) could be lowered to 3%, the same number of future measurements would be needed, but then the redshift coverage would only be required to reach z = 1. We also show that accurate measurements of the Hubble constant H_0 can be used as priors to increase the H(z) data's figure of merit.

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arXiv2011

Constraints on the Dark Side of the Universe and Observational Hubble Parameter Data

This paper is a review on the observational Hubble parameter data that have gained increasing attention in recent years for their illuminating power on the dark side of the universe --- the dark matter, dark energy, and the dark age. Currently, there are two major methods of independent observational H(z) measurement, which we summarize as the "differential age method" and the "radial BAO size method". Starting with fundamental cosmological notions such as the spacetime coordinates in an expanding universe, we present the basic principles behind the two methods. We further review the two methods in greater detail, including the source of errors. We show how the observational H(z) data presents itself as a useful tool in the study of cosmological models and parameter constraint, and we also discuss several issues associated with their applications. Finally, we point the reader to a future prospect of upcoming observation programs that will lead to some major improvements in the quality of observational H(z) data.

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arXiv2010

Increasing the Fisher Information Content in the Matter Power Spectrum by Non-linear Wavelet Weiner Filtering

We develop a purely mathematical tool to recover some of the information lost in the non-linear collapse of large-scale structure. From a set of 141 simulations of dark matter density fields, we construct a non-linear Weiner filter in order to separate Gaussian and non-Gaussian structure in wavelet space. We find that the non-Gaussian power is dominant at smaller scales, as expected from the theory of structure formation, while the Gaussian counterpart is damped by an order of magnitude on small scales. We find that it is possible to increase the Fisher information by a factor of three before reaching the translinear plateau, an effect comparable to other techniques like the linear reconstruction of the density field.

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arXiv2010

Numerical Strategies of Computing the Luminosity Distance

We propose two efficient numerical methods of evaluating the luminosity distance in the spatially flat ΛCDM universe. The first method is based on the Carlson symmetric form of elliptic integrals, which is highly accurate and can replace numerical quadratures. The second method, using a modified version of Hermite interpolation, is less accurate but involves only basic numerical operations and can be easily implemented. We compare our methods with other numerical approximation schemes and explore their respective features and limitations. Possible extensions of these methods to other cosmological models are also discussed.

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arXiv2010

Constraints on smoothness parameter and dark energy using observational $H(z)$ data

The universe, with large-scale homogeneity, is locally inhomogeneous, clustering into stars, galaxies and larger structures. Such property is described by the smoothness parameter $α$ which is defined as the proportion of matter in the form of intergalactic medium. If we take consideration of the inhomogeneities in small scale, there should be modifications of the cosmological distances compared to a homogenous model. Dyer and Roeder developed a second-order ordinary differential equation (D-R equation) that describes the angular diameter distance-redshift relation for inhomogeneous cosmological models. Furthermore, we may obtain the D-R equation for observational $H(z)$ data (OHD). The density-parameter $Ω_{\rm M}$, the state of dark energy $ω$, and the smoothness-parameter $α$ are constrained by a set of OHD in a spatially flat $Λ$CDM universe as well as a spatially flat XCDM universe. By using of $χ^2$ minimization method we get $α=0.81^{+0.19}_{-0.20}$ and $Ω_{\rm M}=0.32^{+0.12}_{-0.06}$ at $1σ$ confidence level. If we assume a Gaussian prior of $Ω_{\rm M}=0.26\pm0.1$, we get $α=0.93^{+0.07}_{-0.19}$ and $Ω_{\rm M}=0.31^{+0.06}_{-0.05}$. For XCDM model, $α$ is constrained to $α\geq0.80$ but $ω$ is weakly constrained around -1, where $ω$ describes the equation of the state of the dark energy ($p_{\rm X}=ωρ_{\rm X}$). We conclude that OHD constrains the smoothness parameter more effectively than the data of SNe Ia and compact radio sources.

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arXiv2010

Thermodynamical properties of the Undulant Universe

Recent observations show that our universe is accelerating by dark energy, so it is important to investigate the thermodynamical properties of it. The Undulant Universe is a model with equation of state $ω(a)=-\cos(b\ln a)$ for dark energy, where we show that there neither the event horizon nor the particle horizon exists. However, as a boundary of keeping thermodynamical properties, the apparent horizon is a good holographic screen. The Universe has a thermal equilibrium inside the apparent horizon, so the Unified First Law and the Generalized Second Law of thermodynamics are satisfied. As a thermodynamical whole, the evolution of the Undulant Universe behaves very well in the current phase. However, when considering the unification theory, the failure of conversation law at the epoch of the matter dominated or near singularity need some more consideration for the form of the Undulant Universe.

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arXiv2010

Cosmological Constraints on the Undulant Universe

We use the redshift Hubble parameter $H(z)$ data derived from relative galaxy ages, distant type Ia supernovae (SNe Ia), the Baryonic Acoustic Oscillation (BAO) peak, and the Cosmic Microwave Background (CMB) shift parameter data, to constrain cosmological parameters in the Undulant Universe. We marginalize the likelihood functions over $h$ by integrating the probability density $P\propto e^{-χ^2/2}$. By using the Markov Chain Monte Carlo (MCMC) technique, we obtain the best fitting results and give the confidence regions on the $b-Ω_{\rm m0}$ plane. Then we compare their constraints. Our results show that the $H(z)$ data play a similar role with the SNe Ia data in cosmological study. By presenting the independent and joint constraints, we find that the BAO and CMB data play very important roles in breaking the degeneracy compared with the $H(z)$ and SNe Ia data alone. Combined with the BAO or CMB data, one can improve the constraints remarkably. The SNe Ia data sets constrain $Ω_{\rm m0}$ much tighter than the $H(z)$ data sets, but the $H(z)$ data sets constrain $b$ much tighter than the SNe Ia data sets. All these results show that the Undulant Universe approaches the $Λ\rm$CDM model. We expect more $H(z)$ data to constrain cosmological parameters in future.

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arXiv2010

Cosmological constraints from Radial Baryon Acoustic Oscillation measurements and Observational Hubble data

We use the Radial Baryon Acoustic Oscillation (RBAO) measurements, distant type Ia supernovae (SNe Ia), the observational $H(z)$ data (OHD) and the Cosmic Microwave Background (CMB) shift parameter data to constrain cosmological parameters of $Λ$CDM and XCDM cosmologies and further examine the role of OHD and SNe Ia data in cosmological constraints. We marginalize the likelihood function over $h$ by integrating the probability density $P\propto e^{-χ^{2}/2}$ to obtain the best fitting results and the confidence regions in the $Ω_{m}-Ω_Λ$ plane.With the combination analysis for both of the {\rm $Λ$}CDM and XCDM models, we find that the confidence regions of 68.3%, 95.4% and 99.7% levels using OHD+RBAO+CMB data are in good agreement with that of SNe Ia+RBAO+CMB data which is consistent with the result of Lin et al's work. With more data of OHD, we can probably constrain the cosmological parameters using OHD data instead of SNe Ia data in the future.

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arXiv2010

Statefinder diagnosis for the Palatini $f(R)$ gravity theories

The Palatini $f(R)$ gravity, is able to probably explain the late time cosmic acceleration without the need for dark energy, is studied. In this paper, we investigate a number of $f(R)$ gravity theories in Palatini formalism by means of statefinder diagnosis. We consider two types of $f(R)$ theories: (i) $f(R)=R+αR^{m}-βR^{-n}$ and (ii) $f(R)=R+αln R+β$. We find that the evolutionary trajectories in the $s-r$ and $q-r$ planes for various types of the Palatini $f(R)$ theories reveal different evolutionary properties of the universe. Additionally, we use the observational $H(z)$ data to constrain models of $f(R)$ gravity.

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arXiv2009

Signatures of the Baryon Acoustic Oscillations on the Convergence Power Spectrum of Weak lensing by Large Scale Structure

We employ an analytical approach to investigate the signatures of Baryon Acoustic Oscillations (BAOs) on the convergence power spectrum of weak lensing by large scale structure. It is shown that the BAOs wiggles can be found in both of the linear and nonlinear convergence power spectra of weak lensing at about $40\le l\le600$, but they are weaker than that of matter power spectrum. Although the statistical error for LSST are greatly smaller than that of CFHT and SNAP survey especially at about $30<l<300$, they are still larger than the their maximum variations of BAOs wiggles. Thus, the detection of BAOs with the ongoing and upcoming surveys such as LSST, CFHT and SNAP survey confront a technical challenge.

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arXiv2008

Reconstruction of Gas Temperature and Density Profiles of the Galaxy Cluster RX J1347.5-1145

We use observations of Sunyaev-Zel'dovich effect and X-ray surface brightness to reconstruct the radial profiles of gas temperature and density under the assumption of a spherically symmetric distribution of the gas. The method of reconstruction, first raised by Silk & White, depends directly on the observations of the Sunyaev-Zel'dovich effect and the X-ray surface brightness, without involving additional assumptions such as the equation of state of the gas or the conditions of hydrostatic equilibrium. We applied this method to the cluster RX J1347.5-1145, which has both the Sunyaev-Zel'dovich effect and X-ray observations with relative high precision. It is shown that it will be an effective method to obtain the gas distribution in galaxy clusters. Statistical errors of the derived temperature and density profiles of gas were estimated according to the observational uncertainties.

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