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Register a new userThe Integrated Sachs-Wolfe effect in $f(R)$ gravity
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Yan-Chuan Cai
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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 $dotPhi$ (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 $dotPhi$ 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.
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Based on CMB maps from the 2013 Planck Mission data release, this paper presents the detection of the ISW effect, i.e., the correlation between the CMB and large-scale evolving gravitational potentials. The significance of detection ranges from 2 to 4 sigma, depending on which method is used. We investigate three separate approaches, which cover essentially all previous studies, as well as breaking new ground. (i) Correlation of the CMB with the Planck reconstructed gravitational lensing potential (for the first time). This detection is made using the lensing-induced bispectrum; the correlation between lensing and the ISW effect has a significance close to 2.5 sigma. (ii) Cross-correlation with tracers of LSS, yielding around 3 sigma significance, based on a combination of radio (NVSS) and optical (SDSS) data. (iii) Aperture photometry on stacked CMB fields at the locations of known large-scale structures, which yields a 4 sigma signal when using a previously explored catalogue, but shows strong discrepancies in amplitude and scale compared to expectations. More recent catalogues give more moderate results, ranging from negligible to 2.5 sigma at most, but with a more consistent scale and amplitude, the latter being still slightly above what is expected from numerical simulations within LCMD. Where they can be compared, these measurements are compatible with previous work using data from WMAP, which had already mapped these scales to the limits of cosmic variance. Plancks broader frequency coverage confirms that the signal is achromatic, bolstering the case for ISW detection. As a final step we use tracers of large-scale structure to filter the CMB data, presenting maps of the ISW temperature perturbation. These results provide complementary and independent evidence for the existence of a dark energy component that governs the current accelerated expansion of the Universe.
This paper presents a study of the ISW effect from the Planck 2015 temperature and polarization data release. The CMB is cross-correlated with different LSS tracers: the NVSS, SDSS and WISE catalogues, and the Planck 2015 lensing map. This cross-correlation yields a detection at $4,sigma$, where most of the signal-to-noise is due to the Planck lensing and NVSS. In fact, the ISW effect is detected only from the Planck data (through the ISW-lensing bispectrum) at $approx 3,sigma$, which is similar to the detection level achieved by combining the cross-correlation signal coming from all the catalogues. The ISW signal allow us to detect $Omega_Lambda$ at more than $3,sigma$. This cross-correlation analysis is performed only with the Planck temperature data, since the polarization scales available in the 2015 release do not permit significant improvement of the CMB-LSS cross-correlation detectability. Nevertheless, polarization data is used to study the anomalously large ISW signal previously reported through the stacking of CMB features at the locations of known superstructures. We find that the current Planck polarization data do not exclude that this signal could be caused by the ISW effect. In addition, the stacking of the Planck lensing map on the locations of superstructures exhibits a positive cross-correlation with these large-scale structures. Finally, we have improved our previous reconstruction of the ISW temperature fluctuations by combining the information encoded in all the previously mentioned LSS tracers. In particular, we construct a map of the ISW secondary anisotropies and the corresponding uncertainties map, obtained from simulations. We also explore the reconstruction of the ISW anisotropies caused by the LSS traced by the 2MPZ survey by directly inverting the density field into the gravitational potential field.
We show that linear redshift distortions in the galaxy distribution can affect the ISW galaxy-temperature signal, when the galaxy selection function is derived from a redshift survey. We find this effect adds power to the ISW signal at all redshifts and is larger at higher redshifts. Omission of this effect leads to an overestimation of the dark energy density $Omega_Lambda$ as well as an underestimation of statistical errors. We find a new expression for the ISW Limber equation which includes redshift distortions, though we find that Limber equations for the ISW calculation are ill-suited for tomographic calculations when the redshift bin width is small. The inclusion of redshift distortions provides a new cosmological handle in the ISW spectrum, which can help constrain dark energy parameters, curvature and alternative cosmologies. Code is available on request and will soon be added as a module to the iCosmo platform (http://www.icosmo.org)
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 integrated Sachs-Wolfe (ISW) effect is caused by the decay of cosmological gravitational potential, and is therefore a unique probe of dark energy. However, its robust detection is still problematic. Various tensions between different data sets, different large scale structure (LSS) tracers, and between data and the $Lambda$CDM theory prediction, exist. We propose a novel method of ISW measurement by cross correlating CMB and the LSS traced by low-density-position (LDP, citet{2019ApJ...874....7D}). It isolates the ISW effect generated by low-density regions of the universe, but insensitive to selection effects associated with voids. We apply it to the DR8 galaxy catalogue of the DESI Legacy imaging surveys, and obtain the LDPs at $zleq 0.6$ over $sim$ 20000 $deg^2$ sky coverage. We then cross correlate with the Planck temperature map, and detect the ISW effect at $3.2sigma$. We further compare the measurement with numerical simulations of the concordance $Lambda$CDM cosmology, and find the ISW amplitude parameter $A_{ISW}=1.14pm0.38$ when we adopt a LDP definition radius $R_s=3^{}$, fully consistent with the prediction of the standard $Lambda$CDM cosmology ($A_{ISW}=1$). This agreement with $Lambda$CDM cosmology holds for all the galaxy samples and $R_s$ that we have investigated. Furthermore, the S/N is comparable to that of galaxy ISW measurement. These results demonstrate the LDP method as a competitive alternative to existing ISW measurement methods, and provide independent checks to existing tensions.
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