Francisco S. N. Lobo, Jose Pedro Mimoso, Matt Visser
备注：
V1: 24 pages. V2: 25 pages, 2 references added, no physics changes; V3: Now 24 Pages; this version closely resembles the final published version. (Reformatted; some discussion added; several references added.)
Redshift drift is the phenomenon whereby the observed redshift between an emitter and observer comoving with the Hubble flow in an expanding FLRW universe will slowly evolve -- on a timescale comparable to the Hubble time. There are nevertheless serious astrometric proposals for actually observing this effect. We shall however pursue a more abstract theoretical goal, and perform a general cosmographic analysis of this effect, eschewing (for now) dynamical considerations in favour of purely kinematic symmetry considerations and Taylor series expansions based on FLRW spacetimes. We shall develop various exact results and series expansions for the redshift drift (and its derivative) in terms of the present day Hubble, deceleration, jerk, snap, crackle, and pop parameters, as well as the present day redshift of the source. In particular, potential observation of this redshift drift effect is intimately related to the universe exhibiting a nonzero deceleration parameter.
Using mock data for the Hubble diagrams of type Ia supernovae (SNIa) and quasars (QSOs) generated based on the standard model of cosmology, and using the least-squares method based on the Markov-Chain-Monte-Carlo (MCMC) algorithm, we first put constraints on the cosmographic parameters in the context of the various model-independent cosmographic methods reconstructed from the Taylor $4^{th}$ and $5^{th}$ order expansions and the Pade (2,2) and (3,2) polynomials of the Hubble parameter, respectively. We then reconstruct the distance modulus in the framework of cosmographic methods and calculate…
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 $Λ$CDM 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 $χ^2$ function of the distance modulus in the context of the Markov Ch…
Redshift dependence and dipolar velocity corrections in cosmographic reconstructions through Type Ia supernova samples
Scuola Superiore Meridionale（高等南方学院）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Università di Camerino（卡梅里诺大学）；INAF, Osservatorio Astronomico di Brera（INAF布雷拉天文台）；INFN, Sezione di Perugia（INFN佩鲁贾分部）；Department of Nanoscale Science and Engineering, University at Albany SUNY（纽约州立大学奥尔巴尼分校纳米科学与工程系）；Al-Farabi Kazakh National University（法拉比哈萨克国立大学）；Dipartimento di Fisica, Università degli Studi di Torino（都灵大学物理系）；INFN, Sezione di Torino（INFN都灵分部）；INAF, Osservatorio Astrofisico di Torino（INAF都灵天文台）
Cosmographic approach, a Taylor expansion of the Hubble function, has been used as a model-independent method to investigate the evolution of the universe in the presence of cosmological data. Apart from possible technical problems like the radius of convergence, there is an ongoing debates about the tensions appear when one investigates some high redshift cosmological data. In this work, we consider two common data sets namely SNIa (Pantheon sample) and the Hubble data to investigate advantages and disadvantages of the cosmographic approach. To do this, we obtain the evolution of cosmographic…
We develop a cosmographic framework for analysing redshift drift signals of nearby sources model-independently, i.e., without making assumptions about the metric description of the Universe. We show that the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) prediction is altered nontrivially by regional anisotropies and inhomogeneities. In particular, we find that the position drift of the sources is nontrivially linked to the redshift drift signal. The redshift drift signal for nearby sources might be formulated in terms of an effective deceleration parameter, which reduces to the FLRW deceleratio…
We study observational constraints on the cosmographic functions up to the fourth derivative of the scale factor with respect to cosmic time, i.e., the so-called snap function, using the non-parametric method of Gaussian Processes. As observational data we use the Hubble parameter data. Also we use mock data sets to estimate the future forecast and study the performance of this type of data to constrain cosmographic functions. The combination between a non-parametric method and the Hubble parameter data is investigated as a strategy to reconstruct cosmographic functions. In addition, our resul…
In this paper, we study the power-law $f(T)$ model using Hubble diagrams of type Ia supernovae (SNIa), quasars (QSOs), Gamma Ray Bursts (GRBs) and the measurements from baryonic acoustic oscillations (BAO) in the framework of the cosmographic method. Using mock data for SNIa, QSOs and GRBs generated based on the power-law $f(T)$ model, we show whether different cosmographic methods are suitable to reconstruct the distance modulus or not. In particular, we investigate the rational PADE polynomials $(3,2)$ and $(2,2)$ in addition to the fourth- and fifth- order Taylor series. We show that PADE $…
The anisotropic expansion rate of the local Universe and its covariant cosmographic interpretation
University of the Western Cape（西开普敦大学）；National Institute for Theoretical & Computational Sciences（理论与计算科学国家研究所）；Aix Marseille Univ, Université 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 and Particle Astrophysics, National Taiwan University（台湾大学梁式宇宙学与粒子天体物理中心）；Queen Mary University of London（伦敦大学玛丽女王学院）
The cosmographic approach is gaining considerable interest as a model-independent technique able to describe the late expansion of the universe. Indeed, given only the observational assumption of the cosmological principle, it allows to study the today observed accelerated evolution of the Hubble flow without assuming specific cosmological models. In general, cosmography is used to reconstruct the Hubble parameter as a function of the redshift, assuming an arbitrary fiducial value for the current matter density, $Ω_m$, and analysing low redshift cosmological data. Here we propose a different s…
Mapping the redshift drift at various redshifts through cosmography
Scuola Superiore Meridionale（南方高等学院）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Università di Camerino, Divisione di Fisica（卡梅里诺大学物理系）；Department of Nanoscale Science and Engineering, University at Albany SUNY（奥尔巴尼州立大学纳米科学与工程系）；INAF, Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
Cosmography is a powerful tool to investigate the Universe kinematic and then to reconstruct dynamics in a model-independent way. However, recent new measurements of supernovae Ia and quasars have populated the Hubble diagram up to high redshifts ($z \sim 7.5$) and the application of the traditional cosmographic approach has become less straightforward due to the large redshifts implied. Here we investigate this issue through an expansion of the luminosity distance-redshift relation in terms of "orthogonal" logarithmic polynomials. In particular we point out the advantages of a new procedure o…
It is well known that positive values of redshift drift is a signature of dark energy within the conventionally studied Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) universe models. Here we show -- without making assumptions on the metric tensor of the Universe -- that redshift drift is a promising direct probe of violation of the strong energy condition within the theory of general relativity.
We consider redshift drift in a general space-time as expressed in terms of physically interpretable multipole series. An important realisation from the derived results is that redshift drift cannot in general be thought of as a direct probe of the average expansion rate of the Universe due to the presence of structure along the light beams from the astrophysical sources to the observer. We also predict the general presence of a dipolar and a quadrupolar offset in the detection of redshift drift for observers placed in locally anisotropic environments.
The redshift drift, the change of cosmological redshift with time, is a direct consequence of the expansion of the Universe. Thus the measurement of the cosmological redshift drift will offer a direct test of our models of cosmology. The magnitude of the effect is very small, i.e. the spectral shift is of order of $10^{-10} - 10^{-9}$ over the period of a decade, but the next generation facilities such as ELT and SKA will be able to directly detect the expansion of our Universe by the year 2040. In this paper we focus on detectebility of this effect, including strategies of overcoming the kine…
High precision astrometry now enables to measure the time drift of astrophysical observables in real time, hence providing new ways to probe different cosmological models. This article presents a general derivation of the redshift and direction drifts for general observers. It is then applied to the standard cosmological framework of a Friedmann-Lemaitre space- time including all effects at first order in the cosmological perturbations, as well as in the class of spatially anisotropic universe models of the Bianchi I family. It shows that for a general observer, the direction drift splits into…
The redshift drift is a model-independent probe of fundamental cosmology, but choosing a fiducial model one can also use it to constrain the model parameters. We compare the constraining power of redshift drift measurements by the Extremely Large Telescope (ELT), as studied by Liske {\it et al.} (2008), with that of two recently proposed alternatives: the cosmic accelerometer of Eikenberry {\it et al.} (2020), and the differential redshift drift of Cooke (2020). We find that the cosmic accelerometer with a 6-year baseline leads to weaker constraints than those of the ELT (by $60\%$), but with …
Mapping the expansion history of the universe is a compelling task of physical cosmology, especially in the context of the observational evidence for the recent acceleration of the universe, which demonstrates that canonical theories of cosmology and particle physics are incomplete and that there is new physics still to be discovered. Cosmography is a phenomenological approach to cosmology, where (with some caveats) physical quantities are expanded as a Taylor series in the cosmological redshift $z$, or analogous parameters such as the rescaled redshift $y=z/(1+z)$ or the logarithmic redshift …
In the present article 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 t…
The apparent angular size of the shadow of a black hole in an expanding Universe is redshift-dependent. Since cosmological redshifts change with time - known as the redshift drift - all redshift-dependent quantities acquire a time-dependence, and a fortiori so do black hole shadows. We find a mathematical description of the black hole shadow drift and show that the amplitude of this effect is of order $10^{-16}$ per day for M87$^{\star}$. While this effect is small, we argue that its non-detection can be used to constrain the accretion rate around supermassive black holes, as well as a novel p…
The redshift drift (also known as the Sandage Test) is a model-independent probe of fundamental cosmology, enabling us to watch the universe expand in real time, and thereby to confirm (or not) the recent acceleration of the universe without any model-dependent assumptions. On the other hand, by choosing a fiducial model one can also use it to constrain the model parameters, thereby providing a consistency test for results obtained with other probes. The drift can be measured by the Extremely Large Telescope and also by the full SKA. Recently two alternative measurement methods have been propo…
The cosmological redshift drift could lead to the next step in high-precision cosmic geometric observations, becoming a direct and irrefutable test for cosmic acceleration. In order to test the viability and possible properties of this effect, also called Sandage-Loeb (SL) test, we generate a model independent mock data set so as to compare its constraining power with that of the future mock data sets of Type Ia Supernovae (SNe) and Baryon Acoustic Oscillations (BAO). The performance of those data sets is analyzed by testing several cosmological models with the Markov chain Monte Carlo (MCMC) …
We provide a formula for estimating the redshift and its secular change (redshift drift) in Lemaître-Tolman-Bondi (LTB) spherically symmetric universes. We compute the scaling of the redshift drift for LTB models that predict Hubble diagrams indistinguishable from those of the standard cosmological model, the flat $Λ$ Cold Dark Matter ($Λ$CDM) model. We show that the redshift drift for these degenerate LTB models is typically different from that predicted in the $Λ$CDM scenario. We also highlight and discuss some unconventional redshift-drift signals that arise in LTB universes and give them d…
Due to the expansion of our Universe, the redshift of distant objects changes with time. Although the amplitude of this redshift drift is small, it will be measurable with a decade-long campaigns on the next generation of telescopes. Here we present an alternative view of the redshift drift which captures the expansion of the universe in single epoch observations of the multiple images of gravitationally lensed sources. Considering a sufficiently massive lens, with an associated time delay of order decades, simultaneous photons arriving at a detector would have been emitted decades earlier in …
We assess the dominant low-redshift anisotropic signatures in the distance-redshift relation and redshift drift signals. We adopt general-relativistic irrotational dust models allowing for gravitational radiation -- the `quiet universe models' -- which are extensions of the silent universe models. Using cosmological simulations evolved with numerical relativity, we confirm that the quiet universe model is a good description on scales larger than those of collapsing structures. With this result, we reduce the number of degrees of freedom in the fully general luminosity distance and redshift dri…
Cosmological observations usually map our present-day past light cone. However, it is also possible to compare different past light cones. This is the concept behind the redshift drift, a model-independent probe of fundamental cosmology. In simple physical terms, this effectively allows us to watch the Universe expand in real time. While current facilities only allow sensitivities several orders of magnitude worse than the expected signal, it should be possible to detect it with forthcoming ones. Here we discuss the potential impact of measurements by three such facilities: the Extremely Large…
We construct an alternative uniformly accelerated reference frame based on the 3+1 formalism in adapted coordinates. In this frame, time-dependent redshift drift exists between co-moving observers, which differs from that in Rindler coordinates. This phenomenon can be tested in laboratory and improve our understanding of non-inertial frames.
Nonlinear Relativistic Effects on Cosmological Redshift Drift
Università di Pisa（比萨大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Pisa（意大利国家核物理研究所比萨分部）；Università LUM（卢姆大学）；Universidade Estadual de Londrina（隆德里纳州立大学）
We derive a generalized luminosity distance versus redshift relation for a linearly perturbed FLRW (Friedmann-Lemaitre-Robertson-Walker) metric with two scalar mode excitations. We use two equivalent approaches, based on the Jacobi map and the van Vleck determinant respectively. We apply the resultant formula to two simple models - an exact FLRW universe and an approximate FLRW universe perturbed by a single scalar mode sinusoidally varying with time. For both models we derive a cosmographic expansion for d_L in terms of z. We comment on the interpretation of our results and their possible app…
