Searching for Integrated Sachs–Wolfe Effect from Fermi-LAT diffuse $\gamma$-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 $\gamma$-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 $1.8\sigma$ confidence level, and the significance would be increased to $2.7\sigma$ 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 ${\mathrm{A}}_{\mathrm{amp}}=0.95\pm 0.53$ (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 $\gamma$-ray data and is consistent with the standard $\Lambda$CDM model prediction essentially. We use a cross-correlation coefficient to show the relation between different energy bins. Furthermore, we vary the cut ranges $\left|b\right|$ of galactic plane on the mask of Fermi map and carefully check the consequent influence on the ISW signal detection.

Introduction

The nature of dark energy is one of the most important question in the modern cosmology. As we know, dark energy is a predominated ingredient of the Universe, which takes 68% of the whole constituents [1]. Measurements of the baryon acoustic oscillation [2], distant Type Ia supernovae [3] and gravitational lensing [4] give a good explanation and evidence that dark energy drives the acceleration of the Universe and the standard $\Lambda$CDM theory can successful explain these observations very well. Furthermore, Cosmic Microwave Background (CMB) as a landmark in Big Bang cosmology theory, is a crucial measurement for many open problems. Besides, the CMB anisotropies which produced at very early times, have several important secondary effects, such as the CMB lensing and the Sunyaev-Zel’dovich effects, which could contribute additional anisotropies on the temperature of CMB photons.

The integrated Sachs-Wolfe effect (ISW; Sachs and Wolfe [5]) is also one of the CMB secondary anisotropies, which is caused by cumulative effect of photons travel from the changing of the gravitational potentials after the recombination epoch. When a CMB photon falls into a gravitational potential well, it gains energy, while it loses energy when it climbs out. These effects would be cancelled if the potential is time independent, such as the matter dominated era in which the gravitational potential stays constant. However, when dark energy or curvature become important at later times, the potential evolves as the photon passes through it. In this case, additional CMB anisotropies will be produced. Therefore, observing the late-time ISW can be a powerful way to probe dark energy and its evolution.

However, the most significant ISW effect contributes to the CMB anisotropies on large scales that are strongly affected by the cosmic variance, which means it is quite challenging to directly extract the ISW information from the CMB observation. Fortunately, this problem can be solved by cross-correlating ISW temperature fluctuation and the density of astrophysical objects like galaxies [6]. Such cross-correlation analysis has been already implemented in the literatures to detect the ISW effect. For the first detection, Crittenden and Turok [6] and Boughn et al. [7] have measured the cross-correlation of High Energy Astronomy Observatory (HEAO) X-ray data and CMB anisotropies from Cosmic Background Explorer (COBE), they claimed it is potential that the ISW effect as an important observation to confront the structures of the Universe. Afterwards, a similar set of analyses have been carried out which relied on CMB data from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite and a variety of large scale structure (LSS) probes, such as the Two-Micron All-Sky Survey galaxy (2MASS) [8], [9], [10], the NRAO VLA Sky Survey (NVSS) radio galaxies [11], galaxies from Sloan Digital Sky Survey (SDSS) [12], [13], [14], [15], the Wide-field Infrared Survey Explorer (WISE) survey [16], [17], and the X-ray background HEAO catalogue [18], [19]. Furthermore, Giannantonio et al. [20], Xia et al. [21] and Khosravi et al. [22] have combined all these measurements together to detect the ISW effect with very high significance. Recently, based on current Planck data release, [23] used the different methods gave the significance of detection ranges from 2 to 4$\sigma$; the detection level achieved at 3$\sigma$ in [24] by combining the cross-correlation signal coming from all the galaxy catalogues; Stölzner et al. [25] also combined various LSS tracer data sets in the radio, optical and infrared wavelength, and obtained more than $2\sigma$ detection of the ISW effect.

In our previous works [26], [27], [28], [29], [30], [31], [32], [33], [34], we have studied that gamma-ray maps of the Unresolved $\gamma$-ray background (UGRB) from Fermi-Large Area Telescope (LAT) data and cross-correlated with different catalogs of galaxies. We observed significant correlation after properly removing various contamination, which means that the UGRB from Fermi data could be a nice LSS tracer and, therefore, has the potential to search for the ISW effect. Therefore, here we use the UGRB from Fermi-LAT 9-year Pass 8 data release and the Planck 2018 temperature anisotropies to detect the ISW effect. This paper is structured as follows: in Section 2, we introduce the data set we use; theoretical formulae are present in Section 3; Sections 4 Numerical results, 5 Systematic tests give numerical results and some systematic checks; final summary is listed in Section 6.