The 2002 discovery of the "Amati Relation" of GRB spectra created the possibility that this and other correlations of GRB phenomenology might be used to make GRBs into standard candles. One recurring apparent difficulty with this program has been that some of the primary observational quantities to be fit as "data" - the isotropic-equivalent prompt energy $E_{iso}$ and the collimation-corrected "total" prompt energy energy $E_γ$ - depend for their construction on the very cosmological models that they are supposed to help constrain. This is the so-called "circularity problem" of standard candle GRBs. This paper is intended to point out that the circularity problem is not in fact a problem at all, except to the extent that it amounts to a self-inflicted wound. It arises essentially because of an unfortunate choice of data variables, such as $E_{iso}$, which are unnecessarily model-dependent. If, instead, the empirical correlations of GRB phenomenology which are formulated in source-variables are {\it mapped to the primitive observational variables} (such as fluence) and compared to the observations in that space, then all circularity disappears. I also indicate here a set of procedures for encoding high-dimensional empirical correlations in a "Gaussian Tube" smeared model that includes both the correlation and its intrinsic scatter, and how that source-variable model may easily be mapped to the space of primitive observables and fashioned into a likelihood. I discuss the projections of such Gaussian tubes into sub-spaces, which may be used to incorporate data from GRB events that may lack some element of the data (for example, GRBs without ascertained jet-break times). In this way, a large set of inhomogeneously observed GRBs may be assimilated into a single analysis, so long as each possesses at least two correlated data attributes.
Standard candles are one of the most important tools to study the universe. In this paper, the constraints of standards candles on the cosmological parameters are estimated for different cases. The dependence of the constraints on the intrinsic scatter of the luminosity relation and the redshift distribution of the standard candles is specifically investigated. The results, especially for the constraints on the components of the universe, clearly show that constraints from standard candles at different redshifts have different degeneracy orientations, thus standard candles with a wide redshift…
The origin of prompt emission from gamma ray bursts remains to be an open question. Correlated prompt optical and gamma-ray emission observed in a handful of GRBs strongly suggests a common emission region, but failure to adequately fit the broadband GRB spectrum prompted the hypothesis of different emission mechanisms for the low- and high-energy radiations. We demonstrate that our multi-component model for GRB gamma-ray prompt emission provides an excellent fit to GRB 110205A from optical to gamma-ray energies. Our results show that the optical and highest gamma-ray emissions have the same s…
Gamma-ray bursts (GRBs) are widely proposed as an effective probe to trace the Hubble diagram of the Universe in high redshift range. However, the calibration of GRBs is not as easy as that of type-Ia supernovae (SNe Ia). Most calibrating methods at present make use one or some of the empirical luminosity correlations, e.g., Amati relation. One of the underlying assumptions of these calibrating methods is that the empirical correlation is universal over all redshifts. In this paper, we check to what extent this assumption holds. Assuming that SNe Ia exactly trace the Hubble diagram of the Univ…
Gamma-ray bursts (GRBs) are among the most powerful sources in the universe. In the recent years, GRBs have been proposed as a complementary probe to type Ia supernovae (SNIa). However, as is well known, there is a circularity problem in the use of GRBs to study cosmology. In this work, based on the Padé approximant, we propose a new cosmology-independent method to calibrate GRBs. We consider a sample consisting of 138 long Swift GRBs and obtain 79 calibrated long GRBs at high-redshift $z>1.4$ (named Mayflower sample) which can be used to constrain cosmological models without the circularity p…
We compare the cosmology of conformal gravity (CG), (Mannheim 2006), to $Λ$CDM. CG cosmology has repulsive matter and radiation on cosmological scales, while retaining attractive gravity at local scales. Mannheim (2003) finds that CG agrees with $Λ$CDM for supernova data at redshifts $z<1$. We use GRBs and quasars as standard candles to contrast these models in the redshift range $0<z<8$. We find CG deviates significantly from $Λ$CDM at high redshift and that $Λ$CDM is favoured by the data with $Δχ^2=48$. Mannheim's model has a bounded dark energy contribution, but we identify a $λ$ fine-tunin…
Dirac, in 1937 proposed the variation of coupling constants derived from his large number hypothesis. Efforts have continued since then to constrain their variation by various methods. We briefly discuss several methods used for the purpose while focusing primarily on the use of supernovae type 1a, quasars, and gamma-ray bursts (GRBs) as cosmological probes for determining cosmological distances. Supernovae type Ia (SNeIa) are considered the best standard candles since their intrinsic luminosity can be determined precisely from their light curves. However, they have only been observed up to ab…
Long duration Gamma-Ray Bursts (LGRBs) may serve as standard candles to constrain cosmological parameters by probing the Hubble diagram well beyond the range of redshift currently accessible using type-Ia supernovae. The standardization of GRBs is based on phenomenological relations between two or more parameters found from spectral modeling, of which one is strongly dependent on the cosmological model. The Amati relation links the source-frame energy ${E_{\mathrm{i,p}}}$ at which the prompt gamma-ray spectral energy distribution $νF_ν$ peaks, and the isotropic-equivalent bolometric energy ${E…
We perform unbiased tests for the clumpiness of universe by confronting the Zel'dovich-Kantowski-Dyer-Roeder luminosity distance which describes the effect of local inhomogeneities on the propagation of light with the observational one estimated from measurements of standard candles, i.e., type Ia supernovae (SNe Ia) and gamma-ray bursts (GRBs). Methodologically, we first determine the light-curve fitting parameters which account for distance estimation in SNe Ia observations and luminosity/energy relations which are responsible for distance estimation of GRBs in the global fit to reconstruct …
Tightening Cosmological Constraints Within and Beyond $Λ$CDM Using Gamma-Ray Bursts Calibrated with Type Ia Supernovae
INAF - Osservatorio Astronomico di Capodimonte（意大利国家天体物理研究所卡波迪蒙特天文台）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天文与天体物理研究院）；Department of Astronomy, Beijing Normal University（北京师范大学天文系）；INAF - Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；Università di Camerino（卡梅里诺大学）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Istituto Nazionale di Fisica Nucleare, Sezione di Perugia（意大利国家核物理研究所佩鲁贾分部）；SUNY Polytechnic（纽约州立理工大学）；Al-Farabi Kazakh National University（阿里-法拉比哈萨克国立大学）；ICRANet（国际相对论天体物理中心网络）
GRB satellites are relatively inefficient detectors of dim hard bursts because they trigger on photon counts, which are number-biased against hard photons. Therefore, for example, given two bursts of identical peak luminosity near the detection threshold, a dim soft burst will be preferentially detected over a dim hard burst. This detector bias can create or skew an apparent correlation where increasingly hard GRBs appear increasingly bright. Although such correlations may be obfuscated by a middle step where GRBs need to be bright enough to have their actual redshifts determined, it is found …
Constraints on the original Cardassian model and the modified polytropic Cardassian model are examined from the recently derived 42 gamma-ray bursts (GRBs) data calibrated with the method avoiding the circularity problem. The results show that GRBs can be an optional observation to constrain on the Cardassian models. Combining the GRBs data with the newly derived size of baryonic acoustic oscillation peak from the Sloan Digital Sky Survey (SDSS), and the position of first acoustic peak of the Cosmic Microwave Background radiation (CMB) from Wilkinson Microwave Anisotropy Probe (WMAP), we find …
The correlation between the peak photon energy of the internal spectrum Ep,i and isotropic equivalent radiated energy Eiso (the Amati relation) is explored in a scalar field model of dark energy. Using an updated data set of 109 high redshift GRBs, we show that the correlation parameters only weakly depend on the cosmological model. Once the parameters of Amati relation have been determined we use this relation to construct a fiducial GRBs Hubble diagram that extends up to redshifts ~ 8. Moreover we apply a local regression technique to estimate, in a model independent way, the distance modulu…
Standard candles can probe the evolution of dark energy in a large redshift range. But the cosmic opacity can degrade the quality of standard candles. In this paper, we use the latest observations, including type Ia supernovae (SNe Ia) from JLA sample and Hubble parameters, to probe the opacity of the universe. In order to avoid the cosmological dependence of SNe Ia luminosity distances, a joint fitting of the SNe Ia light-curve parameters, cosmological parameters and opacity is used. In order to explore the cosmic opacity at high redshifts, the latest gamma-ray bursts (GRBs) are used. At high…
We here propose a new model-independent technique to overcome the circularity problem affecting the use of Gamma-Ray Bursts (GRBs) as distance indicators through the use of $E_{\rm p}$--$E_{\rm iso}$ correlation. We calibrate the $E_{\rm p}$--$E_{\rm iso}$ correlation and find the GRB distance moduli that can be used to constrain dark energy models. We use observational Hubble data to approximate the cosmic evolution through Bézier parametric curve obtained through the linear combination of Bernstein basis polynomials. In so doing, we build up a new data set consisting of 193 GRB distance modu…
We present a sample of 74 Gamma-Ray Bursts (GRBs) from the Fermi-GBM catalogue for which we compute the distance moduli and use them to constrain effective dark energy models. To overcome the circularity problem affecting GRBs as distance indicators, we calibrate the Amati relation of our sample with a cosmology-independent technique. Specifically, we use the latest observational Hubble parameter data, including associated systematics, to approximate the cosmic expansion through a Bezier parametric curve. We subsequently obtain the distance moduli of the GRBs and include the data in a suite of…
Gamma-ray bursts (GRBs) have been regarded as standard candles at very high redshift for cosmology research. We have proposed a new method to calibrate GRB distance indicators with Type Ia supernova (SNe Ia) data in a completely cosmology-independent way to avoid the circularity problem that had limited the direct use of GRBs to probe cosmology [N. Liang, W. K. Xiao, Y. Liu, and S. N. Zhang, Astrophys. J. 685, 354 (2008).]. In this paper, a simple method is provided to combine GRB data into the joint observational data analysis to constrain cosmological models; in this method those SNe Ia data…
Gamma-ray bursts (GRBs), as a possible probe to extend the Hubble diagram to high redshifts, have attracted much attention recently. In this paper, we select two samples of GRBs that have a plateau phase in X-ray afterglow. One is short GRBs with plateau phases dominated by magnetic dipole (MD) radiations. The other is long GRBs with gravitational-wave (GW) dominated plateau phases. These GRBs can be well standardized using the correlation between the plateau luminosity $L_0$ and the end time of plateau $t_b$. The so-called circularity problem is mitigated by using the observational Hubble par…
Gamma-ray bursts (GRBs) are a potential tool to probe high-redshift universe. However, the circularity problem enforces people to find model-independent methods to study the luminosity correlations of GRBs. Here, we present a new method which uses gravitational waves as standard sirens to calibrate GRB luminosity correlations. For the third-generation ground-based GW detectors (i.e., Einstein Telescope), the redshifts of gravitational wave (GW) events accompanied electromagnetic counterparts can reach out to $\sim 4$, which is more distant than type Ia supernovae ($z\lesssim 2$). The Amati rel…
Cosmological probes at any redshift are necessary to reconstruct consistently the cosmic history. Studying properly the tension on the Hubble constant, $H_0$, obtained by Supernovae Type Ia (SNe Ia) and the Planck measurements of the Cosmic Microwave Background Radiation would require complete samples of distance indicators at any epoch. Gamma-Ray Bursts (GRBs) are necessary for the aforementioned task because of their huge luminosity that allows us to extend the cosmic ladder at very high redshifts. However, using GRBs alone as standard candles is challenging because their luminosity varies w…
Gamma-Ray Bursts (GRBs), can be employed as standardized candles, extending the distance ladder beyond Supernovae Type Ia (SNe Ia, $z=2.26$). We standardize GRBs using the 3D fundamental plane relation (the Dainotti relation) among the rest-frame end time of the X-ray plateau emission, its corresponding luminosity, and the peak prompt luminosity. Combining SNe Ia and GRBs, we constrain $Ω_{\text{M}}= 0.299 \pm 0.009$ assuming a flat $Λ$CDM cosmology with and without correcting GRBs for selection biases and redshift evolution. Using a 3D optical Dainotti correlation, we find this sample is as e…
Measuring cosmic dipole with the GRB luminosity-time relation
Aix Marseille Univ, Universite de Toulon, CNRS, CPT（艾克斯-马赛大学、土伦大学、法国国家科学研究中心、CPT）；Leung Center for Cosmology & Particle Astrophysics, National Taiwan University（台湾大学梁天文与粒子天体物理中心）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；National Astronomical Observatory of Japan（日本国立天文台）；The Graduate University for Advanced Studies, SOKENDAI（综合研究大学院大学（SOKENDAI））；Space Science Institute（空间科学研究所）；Center for Astrophysics, University of Nevada, Las Vegas（内华达大学拉斯维加斯分校天体物理学中心）
It has previously been discovered that there is a universal power law behavior exhibited by the late X-ray emission (LXRE) of a "golden sample" (GS) of six long energetic GRBs, when observed in the rest-frame of the source. This remarkable feature, independent of the different isotropic energy (E_iso) of each GRB, has been used to estimate the cosmological redshift of some long GRBs. This analysis is extended here to a new class of 161 long GRBs, all with E_iso > 10^52 erg. These GRBs are indicated as binary-driven hypernovae (BdHNe) in view of their progenitors: a tight binary system composed…
Gamma Ray Bursts (GRBs) are the most energetic sources in the universe and among the farthest known astrophysical sources. These features make them appealing candidates as standard candles for cosmological applications so that studying the physical mechanisms for the origin of the emission and correlations among their observable properties is an interesting task. We consider here the luminosity L*X - break time Ta* (hereafter LT) correlation and investigate whether there are systematics induced by selection effects or redshift dependent calibra- tion. We perform this analysis both for the full…
We propose how to calibrate long gamma-ray burst (GRB) correlations employing intermediate redshift data sets, instead of limiting to $z\simeq0$ catalogs. To do so, we examine the most updated observational Hubble data (OHD) and baryonic acoustic oscillations (BAO). We exploit the model-independent technique of Bézier polynomial interpolation, alleviating de facto the well-known circularity problem affecting GRB correlations. To get constraints on cosmic parameters, using Markov chain Monte Carlo Metropolis algorithm, we distinguish the influence on BAO scale, $r_{\rm s}$, Hubble constant $H_0…
Several interesting luminosity correlations among gamma-ray burst (GRB) variables have been recently discussed extensively. In this paper, we derive the six luminosity correlations ($\tlag-L$, $V-L$, $\epkk-L$, $\epkk-E_γ$, $\trt-L$, $\epkk-E_{γ, \mathrm{iso}}$) from the light curves and spectra of the latest 116 long GRBs, including the time lag ($\tlag$) between low and high photon energy light curves, the variability ($V$) of the light curve, the peak energy of the spectrum ($\epkk$), and the minimum rise time ($\trt$) of the peaks. We find that the intrinsic scatter of the $V-L$ correlatio…
Multi-Model Framework for Reconstructing Gamma-Ray Burst Light Curves
Panjab University（潘杰布大学）；Swinburne University of Technology（斯威本科技大学）；National Astronomical Observatory of Japan（日本国立天文台）；The Graduate University for Advanced Studies (SOKENDAI)（高级研究院（SOKENDAI））；Space Science Institute（空间科学研究所）；University of Nevada（内华达大学）；PSIT College（PSIT学院）；University of Wroclaw（弗罗茨瓦夫大学）；Visveswaraya Technological University（维斯韦萨瓦亚理工大学）；KNIT Sultanpur（苏丹布尔国家工程学院）；Indian Institute of Science（印度科学学院）；Vishwakarma Government Engineering College（维什瓦卡尔马政府工程学院）；Indian Institute of Science Educ（印度科学教育学院）
In this paper, we continue to build support for the proposal to use gamma-ray bursts (GRBs) as standard candles in constructing the Hubble Diagram at redshifts beyond the current reach of Type Ia supernova observations. We confirm that correlations among certain spectral and lightcurve features can indeed be used as luminosity indicators, and demonstrate from the most up-to-date GRB sample appropriate for this work that the $Λ$CDM model optimized with these data is characterized by parameter values consistent with those in the concordance model. Specifically, we find that $(Ω_m,Ω_Λ)\approx (0.…
