Evidence for a fast evolution of the UV luminosity function beyond redshift 6 from a deep HAWK-I survey of the GOODS-S field
M. Castellano, A. Fontana, K. Boutsia, A. Grazian, L. Pentericci, R. Bouwens, M. Dickinson, M. Giavalisco, P. Santini, S. Cristiani, F. Fiore, S. Gallozzi, E. G… 展开作者
M. Castellano, A. Fontana, K. Boutsia, A. Grazian, L. Pentericci, R. Bouwens, M. Dickinson, M. Giavalisco, P. Santini, S. Cristiani, F. Fiore, S. Gallozzi, E. Giallongo, R. Maiolino, F. Mannucci, N. Menci, A. Moorwood, M. Nonino, D. Paris, A. Renzini, P. Rosati, S. Salimbeni, V. Testa, E. Vanzella
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Accepted for publication in Astronomy & Astrophysics
We perform a deep search for galaxies in the redshift range 6.5<z<7.5, to measure the evolution of the number density of luminous galaxies in this redshift range and derive useful constraints on the evolution of their Luminosity Function. We present here the first results of an ESO Large Program, that exploits the unique combination of area and sensitivity provided in the near-IR by the camera Hawk-I at the VLT. We have obtained two Hawk-I pointings on the GOODS South field for a total of 32 observing hours, covering ~90 arcmin2. The images reach Y=26.7 mags for the two fields. We have used public ACS images in the z band to select z-dropout galaxies with the colour criteria Z-Y>1, Y-J<1.5 and Y-K<2. The other public data in the UBVRIJHK bands are used to reject possible low redshift interlopers. The output has been compared with extensive Monte Carlo simulations to quantify the observational effects of our selection criteria as well as the effects of photometric errors. We detect 7 high quality candidates in the magnitude range Y=25.5-26.7. This interval samples the critical range for M* at z>6 (M_1500 ~- 19.5 to -21.5). After accounting for the expected incompleteness, we rule out at a 99% confidence level a Luminosity Function constant from z=6 to z=7, even including the effects of cosmic variance. For galaxies brighter than M_1500=-19.0 we derive a luminosity density rho_UV=1.5^{+2.0}_{-0.9} 10^25 erg/s/Hz/Mpc3, implying a decrease by a factor 3.5 from z=6 to z~6.8. On the basis of our findings, we make predictions for the surface densities expected in future surveys surveys, based on ULTRA-VISTA, HST-WFC3 or JWST-NIRCam, evaluating the best observational strategy to maximise their impact.
(Abridged) We present here the second half of an ESO Large Programme, which exploits the unique combination of area and sensitivity provided in the near-IR by the camera Hawk-I at the VLT. We have obtained - 30 observing hours with Hawk-I in the Y-band of two high galactic latitude fields. We combined the Y-band data with deep J and K Hawk-I observations, and with FORS1/FORS2 U, B, V, R, I, and Z observations to select z-drop galaxies having Z - Y > 1, no optical detection and flat Y - J and Y - K colour terms. We detect 8 high-quality candidates in the magnitude range Y = 25.5 - 26.5 that we …
We aim to place new, strengthened constraints on the luminosity function (LF) of H-alpha emitting galaxies at redshift z=2.2, and to further constrain the instantaneous star-formation rate density of the universe (rho*). We have used the new HAWK-I instrument at ESO-VLT to obtain extremely deep narrow-band (line; NB2090) and broad-band (continuum; Ks) imaging observations. The target field is in the GOODS-South, providing us with a rich multi-wavelength auxiliary data set, which we utilise for redshift confirmation and to estimate dust content. We use this new data to measure the faint-end slo…
We point out a new possibility to determine the average redshift distribution of a large sample of gravitational wave standard sirens, without spectroscopic follow-ups. It is based on the cross correlation between the luminosity-distance space large scale structure (LSS) traced by standard sirens, and the redshift space LSS traced by galaxies in preexisting electromagnetic wave observations. We construct an unbiased and model independent estimator $E_z$ to realize this possibility. We demonstrate with BBO and Euclid that, $0.1\%$ accuracy in redshift determination can be achieved. This method …
We present the results of our search for high-redshift Lyman-break galaxies over the GOODS-South field. We use HST-ACS data in B, V, i' & z', VLT-ISAAC J and Ks, Spitzer-IRAC 3.6, 4.5, 5.8 and 8.0 micron data in conjunction with the new HAWK-I Y-band science verification data to search for dropout galaxies in the redshift range 6<z<9. We survey ~119 arcmin^2 to Y_AB=25.7 (5sigma), of which 37.5 arcmin^2 reaches Y_AB=25.9. Candidate z' and Y drop-outs were selected on the basis of a colour cut of (Y-J)_{AB}>0.75 mag and (z'-Y)_{AB}>1.0 mag respectively. We find no robust Y-drops (z~9) brighter …
This paper presents a new grid-based method for investigating the evolution of the steep-spectrum radio luminosity function, with the aim of quantifying the high-redshift cut-off suggested by previous work. To achieve this, the Combined EIS-NVSS Survey of Radio Sources (CENSORS) has been developed; this is a 1.4 GHz radio survey, containing 135 sources complete to a flux density of 7.2 mJy, selected from the NRAO VLA Sky Survey (NVSS) over 6 deg^2 of the ESO Imaging Survey (EIS) Patch D. The sample is currently 73% spectroscopically complete, with the remaining redshifts estimated via the K-z …
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…
We present a model to understand the redshift evolution of the UV luminosity and stellar mass functions of Lyman Break Galaxies. Our approach is based on the assumption that the luminosity and stellar mass of a galaxy is related to its dark matter halo assembly and gas infall rate. Specifically, galaxies experience a burst of star formation at the halo assembly time, followed by a constant star formation rate, representing a secular star formation activity sustained by steady gas accretion. Star formation from steady gas accretion is the dominant contribution to the galaxy UV luminosity at all…
The determination of luminosity function (LF) of gamma-ray bursts (GRBs) is of an important role for the cosmological applications of the GRBs, which is however hindered seriously by some selection effects due to redshift measurements. In order to avoid these selection effects, we suggest to calculate pseudo-redshifts for Swift GRBs according to the empirical L-E_p relationship. Here, such a $L-E_p$ relationship is determined by reconciling the distributions of pseudo- and real redshifts of redshift-known GRBs. The values of E_p taken from Butler's GRB catalog are estimated with Bayesian stati…
We investigate the dependence of the Fanaroff-Riley (FR) 1/2 dichotomy of radio galaxies on their luminosities and redshifts. Because of a very strong redshift-luminosity correlation (Malmquist bias) in a flux-limited sample, any redshift-dependent effect could appear as a luminosity related effect and vice versa. A question could then arise - do all the morphological differences seen in the two classes (FR 1 and 2 types) of sources, usually attributed to the differences in their luminosities, could as well be primarily a redshift-dependent effect? A sharp break in luminosity, seen among the t…
We extend existing methods for using cross-correlations to derive redshift distributions for photometric galaxies, without using photometric redshifts. The model presented in this paper simultaneously yields highly accurate and unbiased redshift distributions and, for the first time, redshift-dependent luminosity functions, using only clustering information and the apparent magnitudes of the galaxies as input. In contrast to many existing techniques for recovering unbiased redshift distributions, the output of our method is not degenerate with the galaxy bias b(z), which is achieved by modelli…
The Dominion Radio Astrophysical Observatory Deep Field polarization study has been matched with the Spitzer Wide-Area Infrared Extragalactic survey of the European Large Area Infrared Space Observatory Survey North 1 field. We have used VLA observations with a total intensity rms of 87 microJy beam^-1 to match SWIRE counterparts to the radio sources. Infrared color analysis of our radio sample shows that the majority of polarized sources are elliptical galaxies with an embedded active galactic nucleus. Using available redshift catalogs, we found 429 radio sources of which 69 are polarized wit…
By cross-correlating large samples of galaxy clusters with publicly available radio source catalogs, we construct the volume-averaged radio luminosity function (RLF) in clusters of galaxies, and investigate its dependence on cluster redshift and mass. In addition, we determine the correlation between the cluster mass and the radio luminosity of the brightest source within 50 kpc from the cluster center. We use two cluster samples: the optically selected maxBCG cluster catalog and a composite sample of X-ray selected clusters. The radio data come from the VLA NVSS and FIRST surveys. We use scal…
We show that with the simple assumption of no correlation between the Ly-alpha equivalent width and the UV luminosity of a galaxy, the observed distribution of high redshift galaxies in an equivalent width - absolute UV magnitude plane can be reproduced. We further show that there is no dependence between Ly-alpha equivalent width and Ly-alpha luminosity in a sample of Ly-alpha emitters. The test was expanded to Lyman-break galaxies and again no dependence was found. Simultaneously, we show that a recently proposed lack of large equivalent width, UV bright galaxies (Ando et al. 2006) can be ex…
The beginning of the cosmological phase bearing the direct kinematic imprints of supernovae dimming may significantly vary within different models of late-time cosmology, even if such models are able to fit present SNe data at a comparable level of statistical accuracy. This effect -- useful in principle to discriminate among different physical interpretations of the luminosity-redshift relation -- is illustrated here with a pedagogical example based on the LTB geometry.
Determinations of the UV luminosity function of AGN at high redshifts are important for constraining the AGN contribution to reionization and understanding the growth of supermassive black holes. Recent inferences of the luminosity function suffer from inconsistencies arising from inhomogeneous selection and analysis of AGN data. We address this problem by constructing a sample of more than 80,000 colour-selected AGN from redshift z=0 to 7.5. While this sample is composed of multiple data sets with spectroscopic redshifts and completeness estimates, we homogenise these data sets to identical c…
The standard $Λ$CDM model is recently reported to deviate from the high-redshift Hubble diagram of type Ia supernovae (SNe) and quasars (QSOs) at $\sim4σ$ confidence level. In this work, we combine the PAge approximation (a nearly model-independent parameterization) and a high-quality QSO sample to search for the origins of the deviation. By visualizing the $Λ$CDM model and the marginalized $3σ$ constraints of SNe+QSOs into PAge space, we confirm that the SNe+QSOs constraints in both flat and non-flat PAge cases are in remarkable tension with the standard $Λ$CDM cosmology. Next, we investigate…
We present a semi-analytical model of star formation which explains simultaneously the observed UV luminosity function of high redshift Lyman break galaxies (LBGs) and luminosity functions of Lyman-alpha emitters. We consider both models that use the Press-Schechter (PS) and Sheth-Tormen (ST) halo mass functions to calculate the abundances of dark matter halos. The Lyman-alpha luminosity functions at z < 4 are well reproduced with only <10% of the LBGs emitting Lyman-alpha lines with rest equivalent width greater than the limiting equivalent width of the narrow band surveys. However, the obser…
We have identified 469 MgII doublet systems having W_r >= 0.02 Å in 252 Keck/HIRES and UVES/VLT quasar spectra over the redshift range 0.1 < z < 2.6. Using the largest sample yet of 188 weak MgII systems (0.02 Å <= W_r < 0.3 Å), we calculate their absorber redshift path density, dN/dz. We find clear evidence of evolution, with dN/dz peaking at z ~ 1.2, and that the product of the absorber number density and cross section decreases linearly with increasing redshift; weak MgII absorbers seem to vanish above z ~ 2.7. If the absorbers are ionized by the UV background, we estimate number densities …
We apply Bayesian statistics with prior probabilities of galaxy surface luminosity (SL) to improve photometric redshifts. We apply the method to a sample of 1266 galaxies with spectroscopic redshifts in the GOODS North and South fields at 0.1 < z < 2.0. We start with spectrophotometric redshifts (SPZs) based on Probing Evolution and Reionization Spectroscopically grism spectra, which cover a wavelength range of 6000-9000A, combined with (U)BViz(JHK) broadband photometry in the GOODS fields. The accuracy of SPZ redshifts is estimated to be σ(Δ(z))=0.035 with an systematic offset of -0.026, wher…
The low luminosity QSO (LLQSO) sample consists of type 1 active galactic nuclei (AGN) up to a redshift of z=0.06 in the Hamburg/ESO QSO survey. Its purpose is to study how the brightest AGN in the nearby universe evolve with respect to AGN activity and host properties as a function of redshift. We show that our sample lies well between the NUclei of GAlaxies (NUGA) sample and the Palomar Green (PG) QSO sample in terms of redshift, gas masses and luminosities and seems to connect them. The continuous growth in mass, luminosity and, linked to this, the AGN activity over the samples has either a …
There are many kinds of models which describe the dynamics of dark energy (DE). Among all we adopt an equation of state (EoS) which varies as a function of time. We adopt Markov Chain Monte Carlo method to constrain the five parameters of our models. As a consequence, we can show the characteristic behavior of DE during the evolution of the universe. We constrain the EoS of DE with use of the avairable data of gamma-ray bursts and type Ia supernovae (SNe Ia) concerning the redshift-luminosity distance relations. As a result, we find that DE is quintessence-like in the early time and phantom-li…
The star-forming emission line galaxies (ELGs) with strong [OII] doublet are one of the main spectroscopic targets for the ongoing and upcoming fourth generation galaxy redshift surveys. In this work, we measure the [OII] luminosity $L_{\mathrm{[OII]}}$ and the near-ultraviolet band absolute magnitude $M_{\mathrm{NUV}}$ for a large sample of galaxies in the redshift range of $0.6\leq z <1.45$ from the Public Data Release 2 (PDR-2) of the VIMOS Public Extragalactic Redshift Survey (VIPERS). We aim to construct the intrinsic relationship between the $L_{\mathrm{[OII]}}$ and $M_{\mathrm{NUV}}$ th…
We measure the luminosity and color dependence and the redshift evolution of galaxy clustering in the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Ninth Data Release. We focus on the projected two-point correlation function (2PCF) of subsets of its CMASS sample, which includes about 260,000 galaxies over ~3,300 sq. deg in the redshift range 0.43<z<0.7. To minimize the selection effect on galaxy clustering, we construct well-defined luminosity and color subsamples by carefully accounting for the CMASS galaxy selection cuts. The 2PCF of the whole CMASS sample, if approxim…
We present the first far-infrared luminosity function in the AKARI Deep Field South, a premier deep field of the AKARI Space Telescope, using spectroscopic redshifts obtained with AAOmega. To date, we have found spectroscopic redshifts for 389 galaxies in this field and have measured the local (z < 0.25) 90 micron luminosity function using about one-third of these redshifts. The results are in reasonable agreement with recent theoretical predictions.
We show that the star-forming regions in high-redshift luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs) and submillimeter galaxies (SMGs) have similar physical scales to those in local normal star-forming galaxies. To first order, their higher infrared (IR) luminosities result from higher luminosity surface density. We also find a good correlation between the IR luminosity and IR luminosity surface density in starburst galaxies across over five orders of magnitude of IR luminosity from local normal galaxies to z ~ 2 SMGs. The intensely star-forming regions of local ULIRGs are si…
Intrinsic galaxy shape and angular momentum alignments can arise in cosmological large-scale structure due to tidal interactions or galaxy formation processes. Cosmological hydrodynamical simulations have recently come of age as a tool to study these alignments and their contamination to weak gravitational lensing. We probe the redshift and luminosity evolution of intrinsic alignments in Horizon-AGN between z=0 and z=3 for galaxies with an r-band absolute magnitude of <-20. Alignments transition from being radial at low redshifts and high luminosities, dominated by the contribution of elliptic…
We construct a three-dimensional and redshift-evolutionary X-ray and ultraviolet ($L_X-L_{UV}$) luminosity relation for quasars from the powerful statistic tool called copula, and find that the constructed $L_X-L_{UV}$ relation from copula is more viable than the standard one and the observations favor the redshift-evolutionary relation more than $3σ$. The Akaike and Bayes information criterions indicate that the quasar data support strongly the three-dimensional $L_X-L_{UV}$ relation. Our results show that the quasars can be regarded as a reliable indicator of the cosmic distance if the $L_X-…
We present new observational determinations of the evolution of the 2-10keV X-ray luminosity function (XLF) of AGN. We utilise data from a number of surveys including both the 2Ms Chandra Deep Fields and the AEGIS-X 200ks survey, enabling accurate measurements of the evolution of the faint end of the XLF. We combine direct, hard X-ray selection and spectroscopic follow-up or photometric redshift estimates at z<1.2 with a rest-frame UV colour pre-selection approach at higher redshifts to avoid biases associated with catastrophic failure of the photometric redshifts. Only robust optical counterp…
Proposed space-based gravitational-wave detectors such as BBO and DECIGO can detect ~10^6 neutron-star binaries and determine luminosity distance to the binaries with a high precision. Combining the luminosity distance and electromagnetically-derived redshift, one would be able to probe cosmological expansion out to high redshift. In this paper, we show that the Hubble parameter as a function of redshift can be directly measured with monopole and dipole components of the luminosity distance on the sky. As a result, the measurement accuracies of the Hubble parameter in each redshift bin up to z…
We present the galaxy optical luminosity function for the redshift range 0.05<z<0.75 from the AGN and Galaxy Evolution Survey (AGES), a spectroscopic survey of 7.6 sq. deg. in the Bootes field of the NOAO Deep Wide-Field Survey. Our statistical sample is comprised of 12,473 galaxies with known redshifts down to I=20.4 (AB). Our results at low redshift are consistent with those from SDSS; at higher redshift, we find strong evidence for evolution in the luminosity function, including differential evolution between blue and red galaxies. We find that the luminosity density evolves as (1+z)^(0.54+…
We demonstrate that deep good-seeing VLT/HAWK-I $K_\mathrm{s}$ images complemented with $g$+$z$-band photometry can yield a sensitivity for weak lensing studies of massive galaxy clusters at redshifts \mbox{$0.7\lesssim z \lesssim 1.1$}, which is almost identical to the sensitivity of HST/ACS mosaics of single-orbit depth. Key reasons for this good performance are the excellent image quality frequently achievable for $K_\mathrm{s}$ imaging from the ground, a highly effective photometric selection of background galaxies, and a galaxy ellipticity dispersion that is noticeably lower than for opti…
The main goal of this study is to investigate the LF of a sample of 142 X-ray selected clusters, with spectroscopic redshift confirmation and a well defined selection function, spanning a wide redshift and mass range, and to test the LF dependence on cluster global properties, in a homogeneous and unbiased way. Our study is based on the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) photometric galaxy catalogue,associated with photometric redshifts. We constructed LFs inside a scaled radius using a selection in photometric redshift around the cluster spectroscopic redshift in order to r…
After recalling a general non-perturbative expression for the luminosity-redshift relation holding in a recently proposed "geodesic light-cone" gauge, we show how it can be transformed to phenomenologically more convenient gauges in which cosmological perturbation theory is better understood. We present, in particular, the complete result on the luminosity-redshift relation in the Poisson gauge up to second order for a fairly generic perturbed cosmology, assuming that appreciable vector and tensor perturbations are only generated at second order. This relation provides a basic ingredient for t…
We present the generalization of previously published results, about the perturbed redshift and the luminosity-redshift relation up to second order in perturbation theory, for the case of the Poisson gauge and in the presence of anisotropic stress. The results are therefore valid for general dark energy models and (most) modified gravity models. We use an innovative approach based on the recently proposed "geodesic light-cone" gauge. We then compare our finding with other results, which recently appeared in the literature, for the particular case of vanishing anisotropic stress. Arriving at a …
Luminosity correlations of long Gamma-ray bursts (GRB) are extensively proposed as an effective complementarity to trace the Hubble diagram of Universe at high redshifts, which is of great importance to explore properties of dark energy. Recently, several empirical luminosity correlations have been statistically proposed from GRB observations. However, to treat GRB as the distance indicator, there are two key issues: the redshift evolution of luminosity correlations and their calibrations. In this paper, we choose the Amati relation, the correlation between the peak spectra energy and the equi…
Using a recently proposed gauge invariant formulation of light-cone averaging, together with adapted "geodesic light-cone" coordinates, we show how an "induced backreaction" effect emerges, in general, from correlated fluctuations in the luminosity distance and covariant integration measure. Considering a realistic stochastic spectrum of inhomogeneities of primordial (inflationary) origin we find that both the induced backreaction on the luminosity-redshift relation and the dispersion are larger than naively expected. On the other hand the former, at least to leading order and in the linear pe…
We present the hard-band ($2-10\,\mathrm{keV}$) X-ray luminosity function (HXLF) of $0.5-2\,\mathrm{keV}$ band selected AGN at high redshift. We have assembled a sample of 141 AGN at $3<z\lesssim5$ from X-ray surveys of different size and depth, in order to sample different regions in the $ L_X - z$ plane. The HXLF is fitted in the range $\mathrm{logL_X\sim43-45}$ with standard analytical evolutionary models through a maximum likelihood procedure. The evolution of the HXLF is well described by a pure density evolution, with the AGN space density declining by a factor of $\sim10$ from $z=3$ to …
We post-process galaxies in the IllustrisTNG simulations with SKIRT radiative transfer calculations to make predictions for the rest-frame near-infrared (NIR) and far-infrared (FIR) properties of galaxies at $z\geq 4$. The rest-frame $K$- and $z$-band galaxy luminosity functions from TNG are overall consistent with observations, despite a $\sim 0.5\,\mathrm{dex}$ underprediction at $z=4$ for $M_{\rm K}\lesssim -25$ and $M_{\rm z}\lesssim -24$. Predictions for the JWST MIRI observed galaxy luminosity functions and number counts are given. Based on theoretical estimations, we show that the next-…
Revealing what fraction of galaxies harbor AGN is central in understanding black hole accretion history of the Universe. However, optical and soft X-ray surveys miss the most highly obscured AGNs. Infrared (IR), instead, is more robust against absorption. Previous IR photometric surveys, however, only had 4 or 5 filters in mid-IR. Our AKARI North Ecliptic Pole (NEP) wide field sample has 18 filters in mid-IR (9 from AKARI, 4 from WISE, and 5 from Spitzer), for the first time, allowing a sophisticated mid-IR SED fitting diagnosis for a statistical number of sources (89178 over 5.4 deg$^2$). By …
The redshift-luminosity distributions for well-defined galaxies and quasars in the Sloan Digital Sky Survey (SDSS) are compared for the two redshift-distance relations of a Hubble redshift and a de Sitter redshift. Assuming a Hubble redshift, SDSS data can be interpreted as luminosity evolution following the Big Bang. In contrast, given a de Sitter redshift, the intrinsic brightness of objects at all redshifts is roughly the same. In a de Sitter universe, 95 per cent of SDSS galaxies and quasars fall into a magnitude range of only 2.8, and 99.7 per cent are within 5.4 mag. The comparable Hubbl…
We present a semi-analytical model of high redshift galaxy formation. In our model the star formation inside a galaxy is regulated by the feedback from supernova (SNe) driven outflows. We derive a closed analytical form for star formation rate in a single galaxy taking account of the SNe feedback in a self-consistent manner. We show that our model can explain the observed correlation between the stellar mass and the circular velocity of galaxies from dwarf galaxies to massive galaxies of $10^{12} M_\odot$. For small mass dwarf galaxies additional feedback other than supernova feedback is neede…
Type 1a supernova magnitudes are used to fit cosmological parameters under the assumption the model will fit the observed redshift dependence. We test this assumption with the Union 2.1 compilation of 580 sources. Several independent tests find the existing model fails to account for a significant correlation of supernova color and redshift. The correlation of magnitude residuals relative to the $ΛCDM$ model and $color \times redshift$ has a significance equivalent to 13 standard deviations, as evaluated by randomly shuffling the data. Extending the existing $B-V$ color correction to a relatio…
The luminosity function for quasars (QSOs) is usually fitted by a Schechter function. The dependence of the number of quasars on the redshift, both in the low and high luminosity regions, requires the inclusion of a lower and upper boundary in the Schechter function. The normalization of the truncated Schechter function is forced to be the same as that for the Schechter function, and an analytical form for the average value is derived. Three astrophysical applications for QSOs are provided: deduction of the parameters at low redshifts, behavior of the average absolute magnitude at high redshif…
Gamma-ray bursts (GRBs) detected at high redshift can be used to trace the Hubble diagram of the Universe. However, the distance calibration of GRBs is not as easily as that of type Ia supernovae (SNe Ia). For the calibrating method based on the empirical luminosity correlations, there is an underlying assumption that the correlations should be universal over the whole redshift range. In this paper, we investigate the possible redshift dependence of six luminosity correlations with a completely model-independent deep learning method. We construct a network combining the Recurrent Neural Networ…
The correlation between the peak spectra energy ($E_p$) and the equivalent isotropic energy ($E_{\rm iso}$) of long gamma-ray bursts (GRBs), the so-called Amati relation, is often used to constrain the high-redshift Hubble diagram. Assuming Lambda cold dark matter ($Λ$CDM) cosmology, Wang et al. found a $\gtrsim 3σ$ tension in the data-calibrated Amati coefficients between low- and high-redshift GRB samples. To reduce the impact of fiducial cosmology, we use the Parameterization based on cosmic Age (PAge), an almost model-independent framework to trace the cosmological expansion history. We fi…
