Integrated Sachs-Wolfe Signal Research Articles

Evidence for a high-zISW signal from supervoids in the distribution of eBOSS quasars

ABSTRACTThe late-time integrated Sachs-Wolfe (ISW) imprint of $R\gtrsim 100~h^{-1}\, \mathrm{Mpc}$ superstructures is sourced by evolving large-scale potentials due to a dominant dark energy component in the ΛCDM model. The aspect that makes the ISW effect distinctly interesting is the repeated observation of stronger-than-expected imprints from supervoids at z ≲ 0.9. Here we analyse the un-probed key redshift range 0.8 < z < 2.2 where the ISW signal is expected to fade in ΛCDM, due to a weakening dark energy component, and eventually become consistent with zero in the matter dominated epoch. On the contrary, alternative cosmological models, proposed to explain the excess low-z ISW signals, predicted a sign-change in the ISW effect at z ≈ 1.5 due to the possible growth of large-scale potentials that is absent in the standard model. To discriminate, we estimated the high-z ΛCDM ISW signal using the Millennium XXL mock catalogue, and compared it to our measurements from about 800 supervoids identified in the eBOSS DR16 quasar catalogue. At 0.8 < z < 1.2, we found an excess ISW signal with AISW ≈ 3.6 ± 2.1 amplitude. The signal is then consistent with the ΛCDM expectation (AISW = 1) at 1.2 < z < 1.5 where the standard and alternative models predict similar amplitudes. Most interestingly, we also observed an opposite-sign ISW signal at 1.5 < z < 2.2 that is in 2.7σ tension with the ΛCDM prediction. Taken at face value, these recurring hints for ISW anomalies suggest an alternative growth rate of structure in low-density environments at $\sim 100~h^{-1}\, \mathrm{Mpc}$ scales.

Stacked CMB lensing and ISW signals around superstructures in the DESI Legacy Survey

ABSTRACTThe imprints of large-scale structures on the Cosmic Microwave Background (CMB) can be studied via the CMB lensing and Integrated Sachs–Wolfe (ISW) signals. In particular, the stacked ISW signal around supervoids has been claimed in several works to be anomalously high. In this study, we find cluster and void superstructures using four tomographic redshift bins with 0 < z < 0.8 from the DESI Legacy Survey and measure the stacked CMB lensing and ISW signals around them. To compare our measurements with ΛCDM model predictions, we construct a mock catalogue with matched galaxy number density and bias and apply the same photo-z uncertainty as the data. The consistency between the mock and the data is verified via the stacked galaxy density profiles around the superstructures and their quantity. The corresponding lensing convergence and ISW maps are then constructed and compared. The stacked lensing signal agrees with data well except at the highest redshift bin in density peaks, where the mock prediction is significantly higher, by approximately a factor of 1.3. The stacked ISW signal is generally consistent with the mock prediction. We do not obtain a significant signal from voids, AISW = −0.10 ± 0.69, and the signal from clusters, AISW = 1.52 ± 0.72, is at best weakly detected. However, these results are strongly inconsistent with previous claims of ISW signals at many times the level of the ΛCDM prediction. We discuss the comparison of our results with past work in this area and investigate possible explanations for this discrepancy.

Searching for Integrated Sachs–Wolfe Effect from Fermi-LAT diffuse γ-ray map

Abstract In this paper, we estimate the cross-correlation power spectra between the Planck 2018 cosmic microwave background (CMB) temperature anisotropy map and the unresolved γ -ray background (UGRB) from the 9-years Fermi-Large Area Telescope (LAT) data. In this analysis, we use up to nine energy bins over a wide energy range of [0.631, 1000] GeV from the Fermi-LAT UGRB data. Firstly, we find that the Fermi data with the energy ranges [1.202, 2.290] GeV and [17.38, 36.31] GeV show the positive evidence for the Integrated Sachs-Wolfe (ISW) effect at 1 . 8 σ confidence level, and the significance would be increased to 2 . 7 σ when using these two energy bins together. Secondly, we apply the single power-law model to normalize the amplitude and use all the nine Fermi energy bins to measure the significance of the ISW effect, we obtained A amp = 0 . 95 ± 0 . 53 (68% C.L.). For the robustness test, we implement a null hypothesis by randomizing the Fermi mock maps of nine energy bins and obtain the non-detection of ISW effect, which confirms that the ISW signal comes from the Fermi-LAT diffuse γ -ray data and is consistent with the standard Λ CDM model prediction essentially. We use a cross-correlation coefficient to show the relation between different energy bins. Furthermore, we vary the cut ranges | b | of galactic plane on the mask of Fermi map and carefully check the consequent influence on the ISW signal detection.

Cross-correlating Planck with VST ATLAS LRGs: a new test for the ISW effect in the Southern hemisphere

ABSTRACT The integrated Sachs–Wolfe (ISW) effect probes the late-time expansion history of the Universe, offering direct constraints on dark energy. Here, we present our measurements of the ISW signal at redshifts of $\bar{z}=0.35$, 0.55, and 0.68, using the cross-correlation of the Planck cosmic microwave background temperature map with ∼0.5 million luminous red galaxies (LRGs) selected from the VST ATLAS survey. We then combine these with previous measurements based on WMAP and similar SDSS LRG samples, providing a total sample of ∼2.1 million LRGs covering ∼12 000 deg2 of sky. At $\bar{z}=0.35$ and $\bar{z}=0.55$, we detect the ISW signal at 1.2σ and 2.3σ (or 2.6σ combined), in agreement with the predictions of lambda cold dark matter (ΛCDM). We verify these results by repeating the measurements using the BOSS LOWZ and CMASS, spectroscopically confirmed LRG samples. We also detect the ISW effect in three magnitude limited ATLAS + SDSS galaxy samples extending to z ≈ 0.4 at ∼2σ per sample. However, we do not detect the ISW signal at $\bar{z}=0.68$ when combining the ATLAS and SDSS results. Further tests using spectroscopically confirmed eBOSS LRGs at this redshift remain inconclusive due to the current low sky coverage of the survey. If the ISW signal is shown to be redshift dependent in a manner inconsistent with the predictions of ΛCDM, it could open the door to alternative theories such as modified gravity. It is therefore important to repeat the high-redshift ISW measurement using the completed eBOSS sample, as well as deeper upcoming surveys such as DESI and LSST.

Cosmic variance mitigation in measurements of the integrated Sachs-Wolfe effect

The cosmic microwave background (CMB) is sensitive to the recent phase of accelerated cosmic expansion through the late-time integrated Sachs-Wolfe (ISW) effect, which manifests as secondary temperature fluctuations on large angular scales. However, the large cosmic variance from primary CMB fluctuations limits the usefulness of this effect in constraining dark energy or modified gravity. In this paper, we propose a novel method to separate the ISW signal from the primary signal using gravitational lensing, based on the fact that the ISW signal is, to a good approximation, not gravitationally lensed. We forecast how well we can isolate the ISW signal for different experimental configurations, and discuss various applications, including modified gravity, large-scale CMB anomalies, and measurements of local-type primordial non-Gaussianity. Although not within reach of current experiments, the proposed method is a unique way to remove the cosmic variance of the primary signal, allowing for better CMB-based constraints on late-time phenomena than previously thought possible.

Measuring the ISW effect with next-generation radio surveys

The late-time integrated Sachs-Wolfe (ISW) signal in the CMB temperature anisotropies is an important probe of dark energy when it can be detected by cross-correlation with large-scale structure surveys. Because of their huge sky area, surveys in the radio are well-suited to ISW detection. We show that 21cm intensity mapping and radio continuum surveys with the SKA in Phase~1 promise a $\sim5\sigma$ detection if we use tomography, with a similar forecast for the precursor EMU survey. In SKA Phase~2, the 21cm galaxy redshift survey and the continuum survey could deliver a $\sim6\sigma$ detection. Our analysis of the radio surveys aims for theoretical accuracy on large scales. Firstly, we include all the effects on the radio surveys from observing on the past lightcone: redshift-space distortions and lensing magnification can have a significant impact on the ISW signal to noise ratio, while Doppler and other relativistic distortions are not significant. Secondly, we use the full information in the observable galaxy angular power spectra $C_\ell(z,z')$, by avoiding the Limber approximation and by including all cross-correlations between redshift bins in the covariance. Without these cross-bin correlations, the ISW signal to noise ratio is biased.

Constraining cosmology with the cosmic microwave and infrared backgrounds correlation

We explore the use of the cosmic infrared background (CIB) as a tracer of the large scale structures for cross-correlating with the cosmic microwave background (CMB) and exploit the integrated Sachs–Wolfe (ISW) effect. We used an improved linear CIB model from our previous work and derived the theoretical CIB×ISW cross-correlation for different Planck HFI frequencies (217, 353, 545 and 857 GHz) and IRAS (3000 GHz). As expected, we predict a positive cross-correlation between the CIB and the CMB whose amplitude decreases rapidly at small scales. We perform a signal-to-noise ratio (S/N) analysis of the predicted cross-correlation. In the ideal case when the cross-correlation is obtained over 70% (40%) of the sky without residual contaminants (e.g. galactic dust) in maps, the S/N ranges from 4.2 to 5.6 (3.2 to 4.3); the highest S/N comes from 857 GHz. A Fisher matrix analysis shows that an ISW signal detected with a S/N this high on the 40% sky can considerably improve the constraints on the cosmological parameters; constraints on the equation of state of the dark energy especially are improved by 80%. We then performed a more realistic analysis considering the effect of residual galactic dust contamination in CIB maps. We calculated the dust power spectra for different frequencies and sky fractions that dominate the CIB power spectra at the lower multipoles we are interested in. Considering a conservative 10% residual level of galactic dust in the CIB power spectra, we observe that the S/N drops drastically, which makes it very challenging to detect the ISW. To determine the capability of current maps to detect the ISW effect through this method, we measured the cross-correlation of the CIB and the CMB Planck maps on the so-called GASS field, which covers an area of ∼11% in the southern hemisphere. We find that with such a small sky fraction and the dust residuals in the CIB maps, we do not detect any ISW signal, and the measured cross-correlation is consistent with zero. To avoid degrading the S/N for the ISW measurement by more than 10% on the 40% sky, we find that the dust needs to be cleaned up to the 0.01% level on the power spectrum.

On the ISW-cluster cross-correlation in future surveys

We investigate the cosmological information contained in the cross-correlation between the Integrated Sachs-Wolfe (ISW) of the Cosmic Microwave Background (CMB) anisotropy pattern and galaxy clusters from future wide surveys. Future surveys will provide cluster catalogues with a number of objects comparable with galaxy catalogues currently used for the detection of the ISW signal by cross-correlation with the CMB anisotropy pattern. By computing the angular power spectra of clusters and the corresponding cross-correlation with CMB, we perform a signal-to-noise ratio (SNR) analysis for the ISW detection as expected from the eROSITA and the Euclid space missions. We discuss the dependence of the SNR of the ISW-cluster cross-correlation on the specifications of the catalogues and on the reference cosmology. We forecast that the SNRs for ISW-cluster cross-correlation are alightly smaller compared to those which can be obtained from future galaxy surveys but the signal is expected to be detected at high significance, i.e. more than $> 3\,\sigma$. We also forecast the joint constraints on parameters of model extensions of the concordance $\Lambda$CDM cosmology by combining CMB and the ISW-cluster cross-correlation.

Integrated Sachs-Wolfe map reconstruction in the presence of systematic errors

The decay of gravitational potentials in the presence of dark energy leads to an additional, late-time contribution to anisotropies in the cosmic microwave background (CMB) at large angular scales. The imprint of this so-called integrated Sachs-Wolfe (ISW) effect to the CMB angular power spectrum has been detected and studied in detail, but reconstructing its spatial contributions to the CMB $\textit{map}$, which would offer the tantalizing possibility of separating the early- from the late-time contributions to CMB temperature fluctuations, is more challenging. Here we study the technique for reconstructing the ISW map based on information from galaxy surveys and focus in particular on how its accuracy is impacted by the presence of photometric calibration errors in input galaxy maps, which were previously found to be a dominant contaminant for ISW signal estimation. We find that both including tomographic information from a single survey and using data from multiple, complementary galaxy surveys improve the reconstruction by effectively self-calibrating the estimator against spurious power contributions from calibration errors. A high-fidelity reconstruction further requires one to account for the contribution of calibration errors to the observed galaxy power spectrum in the model used to construct the ISW estimator. We find that if the photometric calibration errors in galaxy surveys can be independently controlled at the level required to obtain unbiased dark energy constraints, then it is possible to reconstruct ISW maps with excellent accuracy using a combination of maps from two galaxy surveys with properties similar to Euclid and SPHEREx.

ISW-galaxy cross correlation: a probe of dark energy clustering and distribution of dark matter tracers

Cross correlation of the Integrated Sachs-Wolfe signal (ISW) with the galaxy distribution in late time is a promising tool for constraining the dark energy properties. Here, we study the effect of dark energy clustering on the ISW-galaxy cross correlation and demonstrate the fact that the bias parameter between the distribution of the galaxies and the underlying dark matter introduces a degeneracy and complications. We argue that as the galaxy's host halo formation time is different from the observation time, we have to consider the evolution of the halo bias parameter. It will be shown that any deviation from ΛCDM model will change the evolution of the bias as well. Therefore, it is deduced that the halo bias depends strongly on the sub-sample of galaxies which is chosen for cross correlation and that the joint kernel of ISW effect and the galaxy distribution has a dominant effect on the observed signal. In this work, comparison is made specifically between the clustered dark energy models using two samples of galaxies. The first one is a sub-sample of galaxies from Sloan Digital Sky Survey, chosen with the r-band magnitude 18 < r < 21 and the dark matter halo host of mass M ∼1012M⊙ and formation redshift of zf ∼ 2.5. The second one is the sub-sample of Luminous Red galaxies with the dark matter halo hosts of mass M ∼ 1013M⊙ and formation redshift of zf ∼ 2.0. Using the evolved bias we improve the χ2 for the ΛCDM which reconciles the ∼1σ-2σ tension of the ISW-galaxy signal with ΛCDM prediction. Finally, we study the parameter estimation of a dark energy model with free parameters w0 and wa in the equation of state wde = w0 +waz/(1+z) with the constant bias parameter and also with an evolved bias model with free parameters of galaxy's host halo mass and the halo formation redshift.

Reconstructing the integrated Sachs-Wolfe map with galaxy surveys

The Integrated Sachs-Wolfe (ISW) effect is a large-angle modulation of the cosmic microwave background (CMB), generated when CMB photons traverse evolving potential wells associated with large scale structure (LSS). Recent efforts have been made to reconstruct maps of the ISW signal using information from surveys of galaxies and other LSS tracers, but investigation into how survey systematics affect their reliability has so far been limited. Using simulated ISW and LSS maps, we study the impact of galaxy survey properties and systematic errors on the accuracy of reconstructed ISW signal. We find that systematics that affect the observed distribution of galaxies along the line of sight, such as photo-z and bias-evolution related errors, have a relatively minor impact on reconstruction quality. In contrast, however, we find that direction-dependent calibration errors can be very harmful. Specifically, we find that in order to avoid significant degradation of our reconstruction quality statistics, direction-dependent number density fluctuations due to systematics must be controlled so that their variance is smaller than $10^{-6}$ (which corresponds to a 0.1% calibration). Additionally, we explore the implications of our results for attempts to use reconstructed ISW maps to shed light on the origin of large-angle CMB alignments. We find that there is only a weak correlation between the true and reconstructed angular momentum dispersion, which quantifies alignment, even for reconstructed ISW maps which are fairly accurate overall.

On the recovery of ISW fluctuations using large-scale structure tracers and CMB temperature and polarization anisotropies

In this work we present a method to extract the signal induced by the integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB). It makes use of the Linear Covariance-Based filter introduced by Barreiro et al., and combines CMB data with any number of large-scale structure (LSS) surveys and lensing information. It also exploits CMB polarization to reduce cosmic variance. The performance of the method has been thoroughly tested with simulations taking into account the impact of non-ideal conditions such as incomplete sky coverage or the presence of noise. In particular, three galaxy surveys are simulated, whose redshift distributions peak at low ($z \simeq 0.3$), intermediate ($z \simeq 0.6$) and high redshift ($z \simeq 0.9$). The contribution of each of the considered data sets as well as the effect of a mask and noise in the reconstructed ISW map is studied in detail. When combining all the considered data sets (CMB temperature and polarization, the three galaxy surveys and the lensing map), the proposed filter successfully reconstructs a map of the weak ISW signal, finding a perfect correlation with the input signal for the ideal case and around 80 per cent, on average, in the presence of noise and incomplete sky coverage. We find that including CMB polarization improves the correlation between input and reconstruction although only at a small level. Nonetheless, given the weakness of the ISW signal, even modest improvements can be of importance. In particular, in realistic situations, in which less information is available from the LSS tracers, the effect of including polarisation is larger. For instance, for the case in which the ISW signal is recovered from CMB plus only one survey, and taking into account the presence of noise and incomplete sky coverage, the improvement in the correlation coefficient can be as large as 10 per cent.

Combined constraints on deviations of dark energy from an ideal fluid fromEuclidandPlanck

Cosmological fluids are commonly assumed to be distributed in a spatially homogeneous way, while their internal properties are described by a perfect fluid. As such, they influence the Hubble-expansion through their respective densities and equation of state parameters. The subject of this paper is an investigation of the fluid-mechanical properties of a dark energy fluid, which is characterised by its sound speed and its viscosity apart from its equation of state. In particular, we compute the predicted spectra for the integrated Sachs-Wolfe effect for our generalised fluid, and compare them with the corresponding predictions for weak gravitational lensing and galaxy clustering, which had been computed in previous work. We perform statistical forecasts and show that the integrated Sachs-Wolfe signal obtained by cross correlating Euclid galaxies with Planck temperatures, when joined to galaxy clustering and weak lensing observations, yields a percent sensitivity on the dark energy sound speed and viscosity. We prove that the iSW effect provides strong degeneracy breaking for low sound speeds and large differences between the sound speed and viscosity parameters.

The integrated Sachs–Wolfe signal from BOSS superstructures

Cosmic structures leave an imprint on the microwave background radiation through the integrated Sachs-Wolfe effect. We construct a template map of the linear signal using the SDSS-III Baryon Acoustic Oscillation Survey at redshift 0.43 < z < 0.65. We verify the imprint of this map on the Planck CMB temperature map at the 97% confidence level and show consistency with the density-temperature cross-correlation measurement. Using this ISW reconstruction as a template we investigate the presence of ISW sources and further examine the properties of the Granett-Neyrinck-Szapudi supervoid and supercluster catalogue. We characterise the three-dimensional density profiles of these structures for the first time and demonstrate that they are significant structures. Model fits demonstrate that the supervoids are elongated along the line-of-sight and we suggest that this special orientation may be picked out by the void-finding algorithm in photometric redshift space. We measure the mean temperature profiles in Planck maps from public void and cluster catalogues. In an attempt to maximise the stacked ISW signal we construct a new catalogue of super-structures based upon local peaks and troughs of the gravitational potential. However, we do not find a significant correlation between these structures and the CMB temperature.

The bispectrum of cosmic string temperature fluctuations including recombination effects

We calculate the cosmic microwave background temperature bispectrum from cosmic strings, including the contributions from the last scattering surface, using a well-established Gaussian model for the string energy-momentum correlation functions, and a simplified model for the cosmic fluid. We check our approximation for the integrated Sachs-Wolfe (ISW) contribution against the bispectrum obtained from the full sky map of the cosmic string ISW signal used by the Planck team, obtaining good agreement. We validate our model for the last scattering surface contribution by comparing the predicted temperature power spectrum with that obtained from a full Boltzmann code treatment applied to the Unconnected Segment Model of a string network. We find that including the last scattering contribution has only a small impact on the upper limit on the string tension resulting from the bispectrum at Planck resolutions, and argue that the bispectrum is unlikely to be competitive with the power spectrum at any resolution.

Mapping the integrated Sachs-Wolfe effect

On large scales, the anisotropies in the cosmic microwave background (CMB) reflect not only the primordial field but also the energy gain when photons traverse decaying gravitational potentials of large scales structure, the Integrated Sachs-Wolfe (ISW) effect. Decomposing the anisotropy signal into a primordial piece and an ISW component is more urgent than ever as cosmologists strive to understand the Universe on the largest of scales. Here we present a likelihood technique for extracting the ISW signal from measurements of the CMB, the distribution of galaxies, and maps of gravitational lensing. We test this technique first to simulated data and then we apply it to the combination of temperature anisotropies, the lensing map made by the Planck satellite, and the NVSS galaxy survey. We also show projections for upcoming surveys.

The Jubilee ISW Project - II. Observed and simulated imprints of voids and superclusters on the cosmic microwave background

We examine the integrated Sachs-Wolfe (ISW) imprint of voids and superclusters on the cosmic microwave background. We first study results from the Jubilee $N$-body simulation. From Jubilee, we obtain the full-sky ISW signal from structures out to redshift $z=1.4$ and a mock luminous red galaxy (LRG) catalogue. We confirm that the expected signal in the concordance \Lambda CDM model is very small and likely to always be much smaller than the anisotropies arising at the last scattering surface. Any current detections of such an imprint must, therefore, predominantly arise from something other than an ISW effect in a \Lambda CDM universe. Using the simulation as a guide, we then look for the signal using a catalogue of voids and superclusters from the Sloan Digital Sky Survey. We find a result that is consistent with the \Lambda CDM model, i.e. a signal consistent with zero.

Can a supervoid explain the cold spot?

The discovery of a void of size $\sim200\;h^{-1}$Mpc and average density contrast of $\sim-0.1$ aligned with the Cold Spot direction has been recently reported. It has been argued that, although the first-order integrated Sachs-Wolfe (ISW) effect of such a void on the CMB is small, the second-order Rees-Sciama (RS) contribution exceeds this by an order of magnitude and can entirely explain the observed Cold Spot temperature profile. In this paper we examine this surprising claim using both an exact calculation with the spherically symmetric Lema\^itre-Tolman-Bondi metric, and perturbation theory about a background Friedmann-Robertson-Walker (FRW) metric. We show that both approaches agree well with each other, and both show that the dominant temperature contribution of the postulated void is an unobservable dipole anisotropy. If this dipole is subtracted, we find that the remaining temperature anisotropy is dominated by the linear ISW signal, which is orders of magnitude larger than the second-order RS effect, and that the total magnitude is too small to explain the observed Cold Spot profile. We calculate the density and size of a void that would be required to explain the Cold Spot, and show that the probability of existence of such a void is essentially zero in $\Lambda$CDM. We identify the importance of \emph{a posteriori} selection effects in the identification of the Cold Spot, but argue that even after accounting for them, a supervoid explanation of the Cold Spot is always disfavoured relative to a random statistical fluctuation on the last scattering surface.

A POSSIBLE COLD IMPRINT OF VOIDS ON THE MICROWAVE BACKGROUND RADIATION

We measure the average temperature decrement on the cosmic microwave background (CMB) produced by voids selected in the SDSS DR7 spectroscopic redshift galaxy catalog, spanning redshifts $0<z<0.44$. We find an imprint of amplitude between 2.6 and 2.9$\mu K$ as viewed through a compensated top-hat filter scaled to the radius of each void; we assess the statistical significance of the imprint at ~2$\sigma$. We make crucial use of $N$-body simulations to calibrate our analysis. As expected, we find that large voids produce cold spots on the CMB through the Integrated Sachs-Wolfe (ISW) effect. However, we also find that small voids in the halo density field produce hot spots, because they reside in contracting, larger-scale overdense regions. This is an important effect to consider when stacking CMB imprints from voids of different radius. We have found that the same filter radius that gives the largest ISW signal in simulations also yields close to the largest detected signal in the observations. However, although it is low in significance, our measured signal is much higher-amplitude than expected from ISW in the concordance $\Lambda$CDM universe. The discrepancy is also at the ~2$\sigma$ level. We have demonstrated that our result is robust against the varying of thresholds over a wide range.

The integrated Sachs-Wolfe effect in f(R) gravity

We study the late-time Integrated Sachs-Wolfe (ISW) effect in $f(R)$ gravity using N-body simulations. In the $f(R)$ model under study, the linear growth rate is larger than that in general relativity (GR). This slows down the decay of the cosmic potential and induces a smaller ISW effect on large scales. Therefore, the $\dot\Phi$ (time derivative of the potential) power spectrum at $k<0.1h$/Mpc is suppressed relative to that in GR. In the non-linear regime, relatively rapid structure formation in $f(R)$ gravity boosts the non-linear ISW effect relative to GR, and the $\dot\Phi$ power spectrum at $k>0.1h$/Mpc is increased (100$\%$ greater on small scales at $z=0$). We explore the detectability of the ISW signal via stacking supercluster and supervoids. The differences in the corresponding ISW cold or hot spots are $\sim 20\%$ for structures of $\sim 100$Mpc/$h$. Such differences are greater for smaller structures, but the amplitude of the signal is lower. The high amplitude of ISW signal detected by Granett et al. can not explained in the $f(R)$ model. We find relatively big differences between $f(R)$ and GR in the transverse bulk motion of matter, and discuss its detectability via the relative frequency shifts of photons from multiple lensed images.