As cosmic microwave background (CMB) photons traverse the Universe, anisotropies can be induced via Thomson scattering (proportional to the integrated electron density; optical depth) and inverse Compton scattering (proportional to the integrated electron pressure; thermal Sunyaev-Zel'dovich effect). Measurements of anisotropy in optical depth $τ$ and Compton $y$ parameter are imprinted by the galaxies and galaxy clusters and are thus sensitive to the thermodynamic properties of circumgalactic medium and intergalactic medium. We use an analytic halo model to predict the power spectrum of the optical depth ($ττ$), the cross-correlation between the optical depth and the Compton $y$ parameter ($τy$), as well as the cross-correlation between the optical depth and galaxy clustering ($τg$), and compare this model to cosmological simulations. We constrain the optical depths of halos at $z\lesssim 3$ using a technique originally devised to constrain patchy reionization at a much higher redshift range. The forecasted signal-to-noise ratio is 2.6, 8.5, and 13, respectively, for a CMB-S4-like experiment and a VRO-like optical survey. We show that a joint analysis of these probes can constrain the amplitude of the density profiles of halos to 6.5% and the pressure profile to 13%, marginalizing over the outer slope of the pressure profile. These constraints translate to astrophysical parameters related to the physics of galaxy evolution, such as the gas mass fraction, $f_{\rm g}$, which can be constrained to 5.3% uncertainty at $z\sim 0$, assuming an underlying model for the shape of the density profile. The cross-correlations presented here are complementary to other CMB and galaxy cross-correlations since they do not require spectroscopic galaxy redshifts and are another example of how such correlations are a powerful probe of the astrophysics of galaxy evolution.
We study the Sunyaev-Zel'dovich (SZ) distortion of the cosmic microwave background radiation (CMBR) from extensive circumgalactic gas (CGM) in massive galactic halos. Recent observations have shown that galactic halos contain a large amount of X-ray emitting gas at the virial temperature, as well as a significant amount of warm OVI absorbing gas. We consider the SZ distortion from the hot gas in those galactic halos in which the gas cooling time is longer than the halo destruction time scale. We show that the SZ distortion signal from the hot gas in these galactic halos at redshifts $z\approx …
We propose the use of the kinetic Sunyaev-Zel'dovich (kSZ) effect to probe the circumgalactic medium (CGM), with the aid of a spectroscopic survey covering the same area of a SZ survey. One can design an optimal estimator of the kSZ effect of the CGM with a matched filter, and construct the cross correlation between the estimator and the peculiar velocity recovered from the galaxy survey, which can be measured by stacking a number of galaxies. We investigate two compelling profiles for the CGM, the MB profile (Maller & Bullock 2004) and the $β$ profile, and estimate the detectability against t…
The thermal Sunyaev-Zel'dovich (tSZ) effect is a powerful tool with the potential for constraining directly the properties of the hot gas that dominates dark matter halos because it measures pressure and thus thermal energy density. Studying this hot component of the circumgalactic medium (CGM) is important because it is strongly impacted by star-formation and active galactic nuclei (AGN) activity in galaxies, participating in the feedback loop that regulates star and black hole mass growth in galaxies. We study the tSZ effect across a wide halo mass range using three cosmological hydrodynamic…
Low ionization metal absorption due to OI has been identified as an important probe of the physical state of the inter-/circumgalactic medium at the tail-end of reionization. We use here high-resolution hydrodynamic simulations to interpret the incidence rate of OI absorbers at z~6 as observed by Becker et al. (2011). We infer weak OI absorbers (EW > 0.1 A) to have typical HI column densities in the range of sub-DLAs, densities of 80 times the mean baryonic density and metallicities of about 1/500 th solar. This is similar to the metallicity inferred at similar overdensities at z~3, suggesting…
We present composite spectra constructed from a sample of 242,150 Lyman-alpha (Lya) forest absorbers at redshifts 2.4<z<3.1 identified in quasar spectra from the Baryon Oscillation Spectroscopic Survey (BOSS) as part of Data Release 9 of the Sloan Digital Sky Survey III. We select forest absorbers by their flux in bins 138 km/s wide (approximately the size of the BOSS resolution element). We split these absorbers into five samples spanning the range of flux -0.05 < F<0.45. Tests on a smaller sample of high-resolution spectra show that our three strongest absorption bins would probe circumgalac…
We study the cross-correlation of distribution of galaxies, the Sunyaev-Zel'dovich (SZ) and X-ray power spectra of galaxies from current and upcoming surveys and show these to be excellent probes of the nature, i.e. extent, evolution and energetics, of the circumgalactic medium (CGM). The SZ-galaxy cross-power spectrum, especially at large multipoles, depends on the steepness of the pressure profile of the CGM. This property of the SZ signal can, thus, be used to constrain the pressure profile of the CGM. The X-ray cross power spectrum also has a similar shape. However, it is much more sensiti…
We have constructed a sample of 29 close projected quasar pairs where the background quasar spectrum reveals absorption from optically thick HI gas associated with the foreground quasar. These unique sightlines allow us to study the quasar circumgalactic medium (CGM) in absorption and emission simultaneously, because the background quasar pinpoints large concentrations of gas where Ly-a emission, resulting from quasar-powered fluorescence, resonant Ly-a scattering, and/or cooling radiation, is expected. A sensitive slit-spectroscopic search (1-sigma limits of SB_Lya ~= 3e-18 erg/s/cm^2/arcsec^…
Primordial magnetic fields (PMF) can create polarization $B$-modes in the cosmic microwave background (CMB) through Faraday rotation (FR), leading to non-trivial 2-point and 4-point correlators of the CMB temperature and polarization. We discuss the detectability of primordial magnetic fields using different correlators and evaluate their relative merits. We have fully accounted for the contamination by weak lensing, which contributes to the variance, but whose contribution to the 4-point correlations is orthogonal to that of FR. We show that a Planck-like experiment can detect scale-invariant…
We investigate the degree to which the Cosmic Microwave Background (CMB) can be used to constrain primordial non-Gaussianity coming from the presence of spinning particles coupled to the inflaton. We compute the $\langle TTT \rangle$ and $\langle TTTT \rangle$ correlation functions arising from the exchange of a particle with spin $s$ and generic mass, and the corresponding signal-to-noise ratios for a cosmic-variance-limited CMB experiment. We show that already with \emph{Planck} data one could improve the theoretical bounds on the amplitude of these primordial templates by an order of magnit…
We demonstrate the feasibility to generate surrogates by Fourier-based methods for an incomplete data set. This is performed for the case of a CMB analysis, where astrophysical foreground emission, mainly present in the Galactic plane, is a major challenge. The shuffling of the Fourier phases for generating surrogates is now enabled by transforming the spherical harmonics into a new set of basis functions that are orthonormal on the cut sky. The results show that non-Gaussianities and hemispherical asymmetries in the CMB as identified in several former investigations, can still be detected eve…
Both WMAP and PLANCK missions reported the extremely Cold Spot (CS) centered at Galactic coordinate ($l=209^{\circ}$, $b=-57^{\circ}$) in CMB map. In this paper, we study the local non-Gaussianity of CS by defining the local Minkowski functions. We find that the third Minkowski function $ν_2$ is quite sensitive to the non-Gaussianity caused by CS. Compared with the random Gaussian simulations, WMAP CS deviates from Gaussianity at more than 99% confident level at the scale $R\sim10^{\circ}$. Meanwhile, we find that cosmic texture provides an excellent explanation for these anomalies related to …
CMB photons travel from the last scattering surface, when the primary CMB has been generated, along the surface of the light cone to us. During their travel, they are affected by many secondary effects such as the integrated Sachs-Wolfe effect and CMB lensing. These CMB secondary effects modify the CMB primary power spectrum adding degeneracies and decreasing the sensibility to primordial parameters. The possibility to reconstruct the primary CMB anisotropies will allow us to have a more direct observable to test the physics of the early universe. We propose to study the imprint of features in…
We study the effects of pre-recombination physics on the Stochastic Gravitational Wave Background (SGWB) anisotropies induced by the propagation of gravitons through the large-scale density perturbations and their cross-correlation with Cosmic Microwave Background (CMB) temperature and E-mode polarization ones. As examples of Early Universe extensions to the $Λ$CDM model, we consider popular models featuring extra relativistic degrees of freedom, a massless non-minimally coupled scalar field, and an Early Dark Energy component. Assuming the detection of a SGWB, we perform a Fisher analysis to …
Dark Matter (DM) annihilation and decay during the Dark Ages can affect the cosmic ionization history and leave imprints in the Cosmic Microwave Background (CMB) anisotropy spectra. CMB polarization anisotropy can be sensitive to such energy injection at higher redshifts and help reducing degeneracy with primordial spectral parameters in $Λ$CDM and astrophysical ionization processes during reionization. In light of a number of upcoming CMB polarization experiments, such as AdvACTPol, AliCPT, CLASS, Simons Observatory, Simons Array, SPT-3G, we estimate their prospective sensitivity in probing d…
The detection of the magnetic type $B$-mode polarization is the main goal of future cosmic microwave background (CMB) experiments. In the standard model, the $B$-mode map is a strongly non-gaussian field due to the lensed component. Besides the two-point correlation function, the other statistics are also very important to dig the information of the polarization map. In this paper, we employ the Minkowski functionals to study the morphological properties of the lensed $B$-mode maps. We find that the deviations from Gaussianity are very significant for both full and partial-sky surveys. As an a…
The rotational kinematic Sunyaev-Zeldovich (rkSZ) signal, imprinted on the cosmic microwave background (CMB) by the gaseous halos (spinning "atmospheres") of foreground galaxies, would be a novel probe of galaxy formation. Although the signal is too weak to detect in individual galaxies, we analyze the feasibility of its statistical detection via stacking CMB data on many galaxies for which the spin orientation can be estimated spectroscopically. We use an "optimistic" model, in which fully ionized atmospheres contain the cosmic baryon fraction and spin at the halo's circular velocity $v_{\rm …
In the curvaton scenario, primordial curvature perturbations are produced by a second field that is sub-dominant during inflation. Depending on how the curvaton decays [possibly producing baryon number, lepton number, or cold dark matter (CDM)], mixtures of correlated isocurvature perturbations are produced, allowing the curvaton scenario to be tested using cosmic microwave background (CMB) data. Here, a full range of 27 curvaton-decay scenarios is compared with CMB data, placing limits on the curvaton fraction at decay, $r_D$, and the lepton asymmetry, $ξ_{\rm lep}$. If baryon number is gener…
From measurements of the cosmic microwave background (CMB), the effective number of neutrino is found to be close to the standard model value Neff = 3.046 for the \LambdaCDM cosmology. One can obtain the same CMB angular power spectrum as that of \LambdaCDM for the different value of Neff by using the different dark energy model (i.e. for the different value of w). This degeneracy between Neff and w in CMB can be broken from future galaxy survey using the matter power spectrum.
We perform a comprehensive study of the signatures of Lorentz violation in electrodynamics on the Cosmic Microwave Background (CMB) anisotropies. In the framework of the minimal Standard Model Extension (SME), we consider effects generated by renormalizable operators, both CPT-odd and CPT-even. These operators are responsible for sourcing, respectively, cosmic birefringence and circular polarization. We propagate jointly the effects of all the relevant Lorentz-violating parameters to CMB observables and provide constraints with the most recent CMB datasets. We bound the CPT-even coefficient to…
Global, symmetry-breaking phase transitions in the early universe can generate scaling seed networks which lead to metric perturbations. The acoustic waves in the photon-baryon plasma sourced by these metric perturbations, when Silk damped, generate spectral distortions of the cosmic microwave background (CMB). In this work, the chemical potential distortion ($μ$) due to scaling seed networks is computed and the accompanying Compton $y$-type distortion is estimated. The specific model of choice is the $O(N)$ nonlinear $σ$-model for $N\gg 1$, but the results remain the same order of magnitude f…
We present measurements of $E_G$, a probe of gravity from large-scale structure, using BOSS LOWZ and CMASS spectroscopic samples, with lensing measurements from SDSS (galaxy lensing) and Planck (CMB lensing). Using SDSS lensing and the BOSS LOWZ sample, we measure $\langle{E_G}\rangle=0.40^{+0.05}_{-0.04}$ (stat), $\pm 0.026$ (systematic), consistent with the predicted value from the Planck $Λ$CDM model, $E_G=0.46$. Using CMB lensing, we measure $\langle{E_G}\rangle=0.46^{+0.08}_{-0.09}$ (stat) for LOWZ (statistically consistent with galaxy lensing and Planck predictions) and $\langle{E_G}\ran…
Since the temperature fluctuations in cosmic microwave background (CMB) on large-angular scales probe length scales that were super-horizon sized at photon decoupling and hence insensitive to microphysical processes, the low-multipole CMB data are supposed to be a good probe to the physics of the primordial Universe. In this letter we will constrain the cosmological parameters in the base $Λ$CDM model with tensor perturbations by only using low-multipole CMB data, including Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 (P13) and Wilkinson Microwaves Anis…
We compute the impact of the running of higher order density correlation functions on the two point functions of CMB spectral distortions (SD). We show that having some levels of running enhances all of the SDs by few orders of magnitude which might make them easier to detect. Taking a reasonable range for $ |n_{f_{NL}} |\lesssim 1.1$ and with $f_{NL} = 5$ we show that for PIXIE like experiment, the signal to noise ratio, $(S/N)_{i}$, enhances to $\lesssim 4000$ and $\lesssim 10$ for $μT$ and $yT$ toward the upper limit of $n_{f_{NL}}$. In addition, assuming $ |n_{τ_{NL}}|< 1$ and $τ_{NL} = 10…
Probing the Cosmological Principle with CMB lensing and cosmic shear
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）；Laboratoire Univers et Particules de Montpellier, CNRS & Université de Montpellier（蒙彼利埃宇宙与粒子实验室，法国国家科学研究中心与蒙彼利埃大学）；Queen Mary University of London（伦敦玛丽女王大学）；Université de Genève（日内瓦大学）
Compensated isocurvature perturbations (CIPs) are primordial fluctuations that balance baryon and dark-matter isocurvature to leave the total matter density unperturbed. The effects of CIPs on the cosmic microwave background (CMB) anisotropies are similar to those produced by weak lensing of the CMB: smoothing of the power spectrum, and generation of non-Gaussian features. Previous work considered the CIP effects on the CMB power-spectrum but neglected to include the CIP effects on estimates of the lensing potential power spectrum (though its contribution to the non-Gaussian, connected, part o…
Axion-like particles (ALPs) rotate the linear polarization of photons through the ALP-photon coupling and convert the cosmic microwave background (CMB) $E$-mode to the $B$-mode. We derive the relation between the ALP dynamics and the rotation angle by assuming that the ALP $ϕ$ has a quadratic potential, $V=m^2ϕ^2/2$. We compute the current and future sensitivities of CMB observations to the ALP-photon coupling $g$, which can reach $g=4\times 10^{-21}\,\mathrm{GeV}^{-1}$ for $10^{-32}\,\mathrm{eV}\lesssim m\lesssim 10^{-28}\,\mathrm{eV}$ and extensively exceed the other searches for any mass $m…
Achieving a precise understanding of galaxy formation in a cosmological context is one of the great challenges in theoretical astrophysics, due to the vast range of spatial scales involved in the relevant physical processes. Observations in the millimeter bands, particularly those using the cosmic microwave background (CMB) radiation as a "backlight", provide a unique probe of the thermodynamics of these processes, with the capability to directly measure the density, pressure, and temperature of ionized gas. Moreover, these observations have uniquely high sensitivity into the outskirts of the …
We study the cross-correlation between the Planck CMB lensing convergence map and the eBOSS quasar overdensity obtained from the Sloan Digital Sky Survey (SDSS) IV, in the redshift range $0.9 < z < 2.2$. We detect the CMB lensing convergence-quasar cross power spectrum at $5.4 σ$ significance. The cross power spectrum provides a quasar clustering bias measurement that is expected to be particularly robust against systematic effects. The redshift distribution of the quasar sample has a median redshift $z \approx 1.55$, and an effective redshift about $1.51$. The best fit bias of the quasar samp…
The cosmic history before the BBN is highly determined by the physics that operates beyond the Standard Model (BSM) of particle physics and it is poorly constrained observationally. Ongoing and future precision measurements of the CMB observables can provide us with significant information about the pre-BBN era and hence possibly test the cosmological predictions of different BSM scenarios. Supersymmetry is a particularly motivated BSM theory and it is often the case that different superymmetry breaking schemes require different cosmic histories with specific reheating temperatures or low entr…
The form of the primordial power spectrum (PPS) of cosmological scalar (matter density) perturbations is not yet constrained satisfactorily in spite of the tremendous amount of information from the Cosmic Microwave Background (CMB) data. While a smooth power-law-like form of the PPS is consistent with the CMB data, some PPS with small non-smooth features at large scales can also fit the CMB temperature and polarization data with similar statistical evidence. Future CMB surveys cannot help distinguish all such models due to the cosmic variance at large angular scales. In this paper, we study ho…
The integrated Sachs-Wolfe (ISW) effect provides us the information of the time evolution of gravitational potential. The cross-correlation between the cosmic microwave background (CMB) and the large scale structure (LSS) is known as a promising way to extract the ISW effect. Compared to CMB, the matter fluctuation can grow non-linearly and this is represented in the gravitational potential. Compared to the linear ISW effect, this non-linear ISW effect known as the Rees-Sciama (RS) effect shows the unique behavior by changing the anti-correlated cross correlation between the CMB and the mass t…
We investigate the issue of how accurately we can constrain the lepton number asymmetry xi_nu = mu_nu/T_nu in the Universe by using future observations of 21 cm line fluctuations and cosmic microwave background (CMB). We find that combinations of the 21 cm line and the CMB observations can constrain the lepton asymmetry better than big-bang nucleosynthesis (BBN). Additionally, we also discuss constraints on xi_nu in the presence of some extra radiation, and show that the 21 cm line observations can substantially improve the constraints obtained by CMB alone, and allow us to distinguish the eff…
We consider the prospects of probing features in the primordial power spectrum with future Cosmic Microwave Background (CMB) polarization measurements. In the scope of the inflationary scenario, such features in the spectrum can be produced by local non-smooth pieces in an inflaton potential (smooth and quasi-flat in general) which in turn may originate from fast phase transitions during inflation in other quantum fields interacting with the inflaton. They can fit some outliers in the CMB temperature power spectrum which are unaddressed within the standard inflationary ${\mathrmΛ}$CDM model. W…
Weak gravitational lensing is a powerful statistical tool for probing the growth of cosmic structure and measuring cosmological parameters. However, as shown by studies such as Ménard et al. (2010), dust in the circumgalactic region of haloes dims and reddens background sources. In a weak lensing analysis, this selects against sources behind overdense regions; since there is more structure in overdense regions, we will underestimate the amplitude of density perturbations $σ_8$ if we do not correct for the effects of circumgalactic dust. To model the dust distribution we employ the halo model. …
We describe a methodology to probe gravity with the cosmic microwave background (CMB) lensing convergence $κ$, specifically by measuring $E_G$, the ratio of the Laplacian of the gravitational scalar potential difference with the velocity divergence. Using CMB lensing instead of galaxy-galaxy lensing avoids intrinsic alignments while also lacking a hard limit on the lens redshift and significant uncertainties in the source plane. We model $E_G$ for general relativity and modified gravity, finding that $E_G$ for $f(R)$ gravity should be scale-dependent due to the scale-dependence of the growth r…
Cosmic Reionization imprints its signature on the temperature and polarization anisotropies of the cosmic microwave background (CMB). Advances in CMB telescopes have already placed a significant constraint on the history of reionization. As near-future CMB telescopes target the maximum sensitivity, or observations limited only by the cosmic variance (CV), we hereby forecast the potential of future CMB observations in constraining the history of reionization. In this study, we perform Markov Chain Monte Carlo analysis for CV-limited E-mode polarization observations such as the LiteBIRD (Light s…
We study the capability of future measurements of the galaxy clustering power spectrum to probe departures from a power-law spectrum for primordial fluctuations. On considering the information from the galaxy clustering power spectrum up to quasi-linear scales, i.e. $k<0.1$ h Mpc$^{-1}$, we present forecasts for DESI, Euclid and SPHEREx in combination with CMB measurements. As examples of departures in the primordial power spectrum from a simple power-law, we consider four $Planck$ 2015 best-fits motivated by inflationary models with different breaking of the slow-roll approximation. These fou…
Secondary contributions to the anisotropy of the Cosmic Microwave Background (CMB), such as the integrated Sachs-Wolfe (ISW) effect, the thermal Sunyaev-Zel'dovich effect (tSZ), and the effect of gravitational lensing, have distinctive non-Gaussian signatures, and full descriptions therefore require information beyond that contained in their power spectra. In this paper we use the recently introduced skew-spectra associated with the Minkowski Functionals (MF) to probe the topology of CMB maps to probe the secondary non-Gaussianity as a function of beam-smoothing in order to separate various co…
We constrain the redshift dependence of gas pressure bias $\left\langle b_{y} P_{\mathrm{e}}\right\rangle$ (bias-weighted average electron pressure), which characterises the thermodynamics of intergalactic gas, through a combination of cross-correlations between galaxy positions and the thermal Sunyaev-Zeldovich (tSZ) effect, as well as galaxy positions and the gravitational lensing of the cosmic microwave background (CMB). The galaxy sample is from the fourth data release of the Kilo-Degree Survey (KiDS). The tSZ $y$ map and the CMB lensing map are from the {\textit{Planck}} 2015 and 2018 dat…
We study systematic effects from half-wave plates (HWPs) for cosmic microwave background (CMB) experiments using full-sky time-domain beam convolution simulations. Using an optical model for a fiducial spaceborne two-lens refractor telescope, we investigate how different HWP configurations optimized for dichroic detectors centred at 95 and 150 GHz impact the reconstruction of primordial B-mode polarization. We pay particular attention to possible biases arising from the interaction of frequency dependent HWP non-idealities with polarized Galactic dust emission and the interaction between the H…
Although cosmological observations suggest that the fluctuations of seed fields are almost Gaussian, the possibility of a small deviation of their fields from Gaussianity is widely discussed. Theoretically, there exist numerous inflationary scenarios which predict large and characteristic non-Gaussianities in the primordial perturbations. These model-dependent non-Gaussianities act as sources of the Cosmic Microwave Background (CMB) bispectrum; therefore, the analysis of the CMB bispectrum is very important and attractive in order to clarify the nature of the early Universe. Currently, the imp…
The fine-structure constant, $α$, controls the strength of the electromagnetic interaction. There are extensions of the standard model in which $α$ is dynamical on cosmological length and time-scales. The physics of the cosmic microwave background (CMB) depends on the value of $α$. The effects of spatial variation in $α$ on the CMB are similar to those produced by weak lensing: smoothing of the power spectrum, and generation of non-Gaussian features. These would induce a bias to estimates of the weak-lensing potential power spectrum of the CMB. Using this effect, Planck measurements of the tem…
We analyze relative abundances and ionization conditions in a strong absorption system at z=6.84, seen in the spectrum of the z=7.54 background quasar ULAS J134208.10+092838.61. Singly ionized C, Si, Fe, Mg, and Al measurements are consistent with a warm neutral medium that is metal-poor but not chemically pristine. Firm non-detections of C IV and Si IV imply that any warm ionized phase of the IGM or CGM has not yet been enriched past the ultra-metal-poor regime (<0.001Z_{solar}), unlike lower redshift DLAs where these lines are nearly ubiquitous. Relative abundances of the heavy elements 794 …
We use the cross-correlation power spectrum of the integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB) temperature anisotropy and galaxy fluctuations to probe the physics of late-time cosmic acceleration. For this purpose, we focus on three models of dark energy that belong to a sub-class of Horndeski theories with the speed of gravity equivalent to that of light: Galileon Ghost Condensate (GGC), Generalized Cubic Covariant Galileon (GCCG), and K-mouflage. In the GGC and GCCG models, the existence of cubic-order scalar self-interactions allows a possibility for realizi…
We present new Big Bang Nucleosynthesis (BBN) limits on the cosmic expansion rate or relativistic energy density, quantified via the number $N_ν$ of equivalent neutrino species. We use the latest light element observations, neutron mean lifetime, and update our evaluation for the nuclear rates $d+d \rightarrow He3 + n$ and $d+d \rightarrow H3 + p$. Combining this result with the independent constraints from the cosmic microwave background (CMB) yields tight limits on new physics that perturbs $N_ν$ and $η$ prior to cosmic nucleosynthesis: a joint BBN+CMB analysis gives $N_ν= 2.898 \pm 0.141$, …
We use the optimised skew-spectrum as well as the skew-spectra associated with the Minkowski Functionals (MFs) to test the possibility of using the cross-correlation of the Integrated Sachs-Wolfe effect (ISW) and lensing of the cosmic microwave background (CMB) radiation to detect deviations in the theory of gravity away from General Relativity (GR). We find that the although both statistics can put constraints on modified gravity, the optimised skew-spectra are especially sensitive to the parameter $\rm B_0$ that denotes the the {\em Compton wavelength} of the scalaron at the present epoch. W…
