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 kinematic contamination of the cosmological signal. We also show that the redshift drift directly impacts the change of flux. Thus apart from the redshift drift, measurements of the flux drift will provide an additional tool of detecting the expansion of the universe, including its acceleration. We discuss the strategies of detecting the flux drift and show that by including the flux drift signal to the redshift drift signal we boost the chances of a direct detection of the expansion of the Universe. We show that if only the stability of flux is at the level of $ΔF/F \sim 10^{-6}$ then the SKA1-mid Array should be able to detect these effects, before the ETL and the full SKA. Thus, by including the flux drift into the SKA1-mid Array's analysis pipeline, we could be able to provide by mid-2030s a direct evidence of the expansion of the universe including its accelerating phase.
We investigate the effect of the redshift drift in strong gravitational lensing. The redshift drift produces a time variation of $i)$ the apparent position of a lensed source and $ii)$ the time delay among incoming signals from different images. We dub these effects as angular drift and time delay drift, respectively, and analyze their relevance in cosmology.
We derive some basic equations related to the redshift drift and we show how some dark energy (DE) properties can be retrieved from it. We consider in particular three kinds of DE models which exhibit a characteristic signature in their redshift drift while no such signature would be present in their luminosity-distances: a sudden change of the equation of state parameter w_{DE} at low redshifts, oscillating DE and finally an equation of state with spikes at low redshifts. Accurate redshift drift measurements would provide interesting complementary probes for some of these models and for model…
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 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 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.
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…
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…
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 …
We discuss how dynamical dark energy universes with exotic singularities may be distinguished from the standard $Λ$CDM model on the basis of their redshift drift signal, for which measurements both in the acceleration phase and in the deep matter era will be provided by forthcoming astrophysical facilities. Two specific classes of exotic singularity models are studied: sudden future singularity models and finite scale factor singularity models. In each class we identify the models which can mimic $Λ$CDM and play the role of dark energy as well as models for which redshift drift signals are sig…
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 …
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）
We derive a redshift drift formula for the spherically symmetric inhomogeneous pressure Stephani universes which are complementary to the spherically symmetric inhomogeneous density Lemaître-Tolman-Bondi models. We show that there is a clear difference between redshift drift predictions for these two models as well as between the Stephani models and the standard $Λ$CDM Friedmann models. The Stephani models have positive drift values at small redshift and behave qualitatively (but not quantitatively) as the $Λ$CDM models at large redshift, while the drift for LTB models is always negative. This…
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…
An expression for the average redshift drift in a statistically homogeneous and isotropic dust universe is given. The expression takes the same form as the expression for the redshift drift in FLRW models. It is used for a proof-of-principle study of the effects of backreaction on redshift drift measurements by combining the expression with two-region models. The study shows that backreaction can lead to positive redshift drift at low redshifts, exemplifying that a positive redshift drift at low redshifts does not require dark energy. Moreover, the study illustrates that models without a dark …
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…
We study the redshift drift, i.e., the time derivative of the cosmological redshift in the Lemaître-Tolman-Bondi (LTB) solution in which the observer is assumed to be located at the symmetry center. This solution has often been studied as an anti-Copernican universe model to explain the acceleration of cosmic volume expansion without introducing the concept of dark energy. One of decisive differences between LTB universe models and Copernican universe models with dark energy is believed to be the redshift drift. The redshift drift is negative in all known LTB universe models, whereas it is pos…
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 derive a redshift drift formula within the framework of varying speed of light (VSL) theory using the specific ansatz for the variability of $c(t) = c_0 a^n(t)$. We show that negative values of the parameter $n$, which correspond to diminishing value of the speed of light during the evolution of the universe, effectively rescales dust matter to become little negative pressure matter, and the cosmological constant to became phantom. Positive values of $n$ (growing $c(t)$) make VSL model to become more like Cold Dark Matter (CDM) model. Observationally, there is a distinction between the VSL …
The redshift drift of objects moving in the Hubble flow has been proposed as a powerful model-independent probe of the underlying cosmology. A measurement of the first and second order redshift derivatives appears to be well within the reach of upcoming surveys using ELT-HIRES and the SKA Phase 2 array. Here we show that an unambiguous prediction of the R_h=ct cosmology is zero drift at all redshifts, contrasting sharply with all other models in which the expansion rate is variable. For example, multi-year monitoring of sources at redshift z=5 with the ELT-HIRES is expected to show a velocity …
Earlier studies have conjectured that redshift drift is described by spatially averaged quantities and thus becomes positive if the average expansion of the Universe accelerates. This conclusion is reevaluated here by considering exact light propagation in a simple toy-model with average accelerated expansion. The toy-model and light propagation setup is explicitly designed for concordance between spatial averages and averages along light rays. While it is verified that redshift-distance relations are well described by average quantities in this setup, it is found that the redshift drift is no…
Redshift Drift fluctuations from N-body simulations
Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；INAF – Osservatorio Astronomico di Trieste（意大利国家天体物理研究所的的里雅斯特天文台）；IFPU – Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；INFN – Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
We consider the redshift drift and position drift associated with astrophysical sources in a formalism that is suitable for describing emitters and observers of light in an arbitrary spacetime geometry, while identifying emitters of a given null-geodesic bundle that arrives at the observer worldline. We then restrict the situation to the special case of a Lemaitre-Tolman-Bondi (LTB) geometrical structure, and solve for light rays propagating through the structure with arbitrary impact parameters, i.e., with arbitrary angles of entry into the LTB structure. The redshift drift signal emitted by …
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 analyze the science reach of a next generation galaxy redshift survey such as BigBOSS to fit simultaneously for time varying dark energy equation of state and time- and scale-dependent gravity. The simultaneous fit avoids potential bias from assuming $Λ$CDM expansion or general relativity and leads to only modest degradation in constraints. Galaxy bias, fit freely in redshift bins, is self calibrated by spectroscopic measurements of redshift space distortions and causes little impact. The combination of galaxy redshift, cosmic microwave background, and supernova distance data can deliver 5-…
Models of inhomogeneous universes constructed with exact solutions of Einstein's General Relativity have been proposed in the literature with the aim of reproducing the cosmological data without any need for a dark energy component. Besides large scale inhomogeneity models spherically symmetric around the observer, Swiss-cheese models have also been studied. Among them, Swiss-cheeses where the inhomogeneous patches are modeled by different particular Szekeres solutions have been used for reproducing the apparent dimming of the type Ia supernovae (SNIa). However, the problem of fitting such mod…
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 study cosmological constraints on the various accelerating models of the universe using the time evolution of the cosmological redshift of distant sources. The important characteristic of this test is that it directly probes the expansion history of the universe. In this work we analyze the various models of the universe which can explain the late time acceleration, within the framework of General Theory of Relativity (GR) (XCDM, scalar field potentials) and beyond GR (f(R) gravity model).
Future redshift-drift measurements (also known as Sandage-Loeb signal) will be crucial to probe the so called "redshift desert", thus providing a new tool for cosmological studies. In this paper we quantify the ability of a future measurement of the Sandage-Loeb signal by a CODEX-like spectrograph to constrain a phenomenological parametrization of dynamical dark energy, specifically by obtaining constraints on $w_0$ and $w_a$. We also demonstrate that if used alongside CMB data, the Sandage-Loeb measurements will be able to break degeneracies between expansion parameters, thus greatly improvin…
Redshift drift provides a direct kinematic measurement of cosmic acceleration but it occurs with a characteristic time scale of a Hubble time. Thus redshift observations with a challenging precision of $10^{-9}$ require a 10 year time span to obtain a signal-to-noise of 1. We discuss theoretical and experimental approaches to address this challenge, potentially requiring less observer time and having greater immunity to common systematics. On the theoretical side we explore allowing the universe, rather than the observer, to provide long time spans; speculative methods include radial baryon ac…
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）
Dark energy affects the Hubble expansion rate (namely, the expansion history) $H(z)$ by an integral over $w(z)$. However, the usual observables are the luminosity distances or the angular diameter distances, which measure the distance-redshift relation. Actually, dark energy affects the distances (and the growth factor) by a further integration over functions of $H(z)$. Thus, the direct measurements of the Hubble parameter $H(z)$ at different redshifts are of great importance for constraining the properties of dark energy. In this paper, we show how the typical dark energy models, for example,…
Since the advent of the accelerated expanding homogeneous universe model, some other explanations for the supernova Ia dimming have been explored, among which there are inhomogeneous models constructed with exact $Λ= 0$ solutions of Einstein's equations. They have been used either as one patch or to build Swiss-cheese models. The most studied ones have been the Lemaître-Tolman-Bondi (LTB) models. However, these models being spatially spherical, they are not well designed to reproduce the large scale structures which exhibit clusters, filaments and non spherical voids. This is the reason why Sz…
As the Universe expands, the redshift of distant sources changes with time. Here we discuss gravitational lensing phenomena that are consequence of the redshift drift between lensed source, gravitational lens, and observer. When the source is located very close to the drifting caustics, a pair of images could occur (or disappear) because of the cosmological expansion. Furthermore, lensing systems act as signal converters of the redshift drift. The angular position, magnification, distortion, and time delay of already existing multiple images change. We estimate the expected frequency of these …
In this work, using the Gaussian process, we explore the potentiality of future gravitational wave (GW) measurements to probe cosmic opacity at high redshifts through comparing its opacity-free luminosity distance (LD) with the opacity-dependent one from the combination of Type Ia supernovae (SNIa) and gamma-ray bursts (GRBs). The GW data, SNIa and GRB data are simulated from the measurements of the future Einstein Telescope, the actual Pantheon compilation and the latest observation of GRBs compiled by L. Amati {\it et al}, respectively. A nonparametric method is proposed to probe the spatial…
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…
The drift in the redshift of objects passively following the cosmological expansion has long been recognized as a key model-independent probe of cosmology. Here, we study the cosmological relevance of measurements of time or redshift derivatives of this drift, arguing that the combination of first and second redshift derivatives is a powerful test of the $Λ$CDM cosmological model. In particular, the latter can be obtained numerically from a set of measurements of the drift at different redshifts. We show that, in the low-redshift limit, a measurement of the derivative of the drift can provide …
Exact inhomogeneous solutions of Einstein's equations have been used in the literature to build models reproducing the cosmological data without dark energy. However, owing to the degrees of freedom pertaining to these models, it is necessary to get rid of the degeneracy often exhibited by the problem of distinguishing between them and accelerating universe models. We give an overview of redshift drift in inhomogeneous cosmologies, and explain how it serves to this purpose. One class of models which fits the data is the Szekeres Swiss-cheese class where non-spherically symmetric voids exhibit …
Our proper acceleration with respect to the Cosmic Microwave Background results in a real-time change of the angular position of distant extragalactic sources. The cosmological component of this aberration drift signal, the non-inertial motion generated by the large-scale distribution of matter, can in principle be detected by future high-precision astrometric experiments. It will provide interesting consistency tests of the standard model of cosmology, set independent constraints on the amplitude of the Hubble constant and the linear growth rate of cosmic structures, and be instrumental in se…
An interesting test on the nature of the Universe is to measure the global spatial curvature of the metric in a model independent way, at a level of $|Ω_k|<10^{-4}$, or, if possible, at the cosmic variance level of the amplitude of the CMB fluctuations $|Ω_k|\approx10^{-5}$. A limit of $|Ω_k|<10^{-4}$ would yield stringent tests on several models of inflation. Further, improving the constraint by an order of magnitude would help in reducing "model confusion" in standard parameter estimation. Moreover, if the curvature is measured to be at the value of the amplitude of the CMB fluctuations, it …
The evolution of the expansion rate of the Universe results in a drift in the redshift of distant sources over time. A measurement of this drift would provide us with a direct probe of expansion history. The Lyman alpha forest has been recognized as the best candidate for this experiment, but the signal would be weak and it will take next generation large telescopes coupled with ultra-stable high resolution spectrographs to reach the cm/s resolution required. One source of noise that has not yet been assessed is the transverse motion of Lyman alpha absorbers, which varies the gravitational pot…
We consider the question of determining the optical drift effects in general relativity, i.e. the rate of change of the apparent position, redshift, Jacobi matrix, angular distance and luminosity distance of a distant object as registered by an observer in an arbitrary spacetime. We present a fully relativistic and covariant approach, in which the problem is reduced to a hierarchy of ODE's solved along the line of sight. The 4-velocities and 4-accelerations of the observer and the emitter and the geometry of the spacetime along the line of sight constitute the input data. We build on the stand…
We perform a comprehensive redshift-space distortion analysis based on cosmic voids in the large-scale distribution of galaxies observed with the Sloan Digital Sky Survey. To this end, we measure multipoles of the void-galaxy cross-correlation function and compare them with standard model predictions in cosmology. Merely considering linear-order theory allows us to accurately describe the data on the entire available range of scales and to probe void-centric distances down to about $2h^{-1}{\rm Mpc}$. Common systematics, such as the Fingers-of-God effect, scale-dependent galaxy bias, and nonli…
Detecting the change of a cosmological object's redshift due to the time evolution of the Universal expansion rate is an ambitious experiment that will be attempted with future telescope facilities. In this paper, we describe the ACCELERATION programme, which aims to study the properties of the most underdense regions of the Universe. One of the highlight goals of this programme is to prepare for the redshift drift measurement. Using the EAGLE cosmological hydrodynamic simulations, we estimate the peculiar acceleration of gas in galaxies and in the Lya forest. We find that star-forming 'cold n…
Two recently proposed techniques, involving the measurement of the cosmic parallax and redshift drift, provide novel ways of directing probing (over a time-span of several years) the background metric of the universe and therefore shed light on the dark energy conundrum. The former makes use of upcoming high-precision astrometry measurements to either observe or put tight constraints on cosmological anisotropy for off-center observers, while the latter employs high-precision spectroscopy to give an independent test of the present acceleration of the universe. In this paper, we show that both m…
In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of th…
`Ether-drift' experiments have played a crucial role for the origin of relativity. Though, a recent re-analysis shows that those original measurements where light was still propagating in gaseous systems, differently from the modern experiments in vacuum and in solid dielectrics, indicate a small universal anisotropy which is naturally interpreted in terms of a non-local thermal gradient. We argue that this could possibly be the effect, on weakly bound gaseous matter, of the temperature gradient due to the Earth's motion within the Cosmic Background Radiation (CBR). Therefore, a check with mod…
