The subject of this paper is the derivation of the integrated Sachs-Wolfe (iSW) effect in cosmologies with coupled dark matter and dark energy fluids. These couplings influence the iSW-effect in three ways: The Hubble function assumes a different scaling, the structure growth rate shows a different time evolution, and in addition, the Poisson equation, which relates the density perturbations to fluctuations in the gravitational potential, is changed, due to the violation of the scaling rho ~ a^{-3} of the matter density rho with scale factor a. Exemplarily, I derive the iSW-spectra for a model in which dark matter decays into dark energy, investigate the influence of the dark matter decay rate and the dark energy equation of state on the iSW-signal, and discuss the analogies for gravitational lensing. Quite generally iSW-measurements should reach similar accuracy in determining the dark energy equation of state parameter and the coupling constant.
We present a pedagogical derivation of the Sachs-Wolfe effect, specifically the factor 1/3 relating the temperature fluctuations to gravitational potentials. The result arises from a cancellation between gravitational redshifts and intrinsic temperature fluctuations which can be derived from a coordinate transformation of the background.
Cartan torsion contribution to Sachs-Wolfe effect in the inflationary phase of the Universe is discussed.From the COBE data of the microwave anisotropy is possible to compute the spin-density in the Universe as $10^{16}$ mks units.The spin-density fluctuations at the hadron era is shown to coincide with the anisotropy temperature fluctuations.
We study a braneworld model in which a phantom-like behaviour occurs with only cold dark matter and a cosmological constant, due to a large distance modification of gravity. With the addition of curvature, the geometrical tests are not strict enough to rule out models in which gravity is modified significantly on large scales. We show that this degeneracy in the parameter space is broken by the structure formation tests, such as the integrated Sachs-Wolfe effect, which can probe general relativity on large scales.
The integrated Sachs-Wolfe effect (ISW) can be an important factor in the generation of Cosmic Microwave Background anisotropies on all scales, especially in a reionized curvature or lambda dominated universe. We present an analytic treatment of the ISW effect, which is analogous to thick last scattering surface techniques for the Doppler effect, that compares quite well with the full numerical calculations. The power spectrum of temperature fluctuations due to the small scale ISW effect has wave number dependence k^{-5} times that of the matter power spectrum.
The Integrated Sachs-Wolfe effect is studied in non-standard cosmologies. By considering flat universes with a non-fluctuating dark energy component, it is shown how the quadrupole power can be suppressed by atypical evolution of the scale factor. For example, a brief period of non-standard evolution at a high redshift can suppress the quadrupole significantly. The effect on the overall normalization of the CMB power spectrum is also discussed. Non-standard cosmologies can affect the overall normalization significantly and enhance the primordial fluctuations. The possibility of constraining su…
In some scenarios, the peculiar gravitational potential of linear and mildly nonlinear structures depends on time and, as a result of this dependence, a late integrated Sachs-Wolfe effect appears. Here, an appropriate formalism is used which allows us to improve on the analysis of the spatial scales and locations of the main cosmological inhomogeneities producing this effect. The study is performed in the framework of the currently preferred flat model with cosmological constant, and it is also developed in an open model for comparisons. Results from this analysis are used to discuss the contr…
We have detected statistically significant correlations between the cosmic microwave background and two tracers of large-scale structure, the HEAO1 A2 full sky hard X-ray map and the NVSS 1.4 GHz, nearly full sky radio galaxy survey. The level of correlations in these maps is consistent with that predicted for the integrated Sachs-Wolfe (ISW) effect in the context of a Lambda CDM cosmological model and, therefore, provides independent evidence for a cosmological constant. A maximum likelihood fit to the amplitude of the ISW effect relative to the predicted value is 1.13 +- 0.35 (statistical er…
The Sachs-Wolfe temperature fluctuations produced by primordial density perturbations are proportional to the potential field ϕ, which is a weighted integral over the density field δ. Because of the central limit theorem, ϕcan be approximately Gaussian even when δis non-Gaussian. Using the Wold representation for non-Gaussian density fields, δ(\rvec) = \int f(|\rvec - \rvec^\prime|) Δ(\rvec^\prime) d^3 \rvec^\prime, we find conditions on Δand f for which ϕmust have a Gaussian one-point distribution, while δcan be non-Gaussian. Sufficient (but not necessary) conditions are that the density fiel…
A consequence of non-Gaussian perturbations on the Sachs-Wolfe effect is studied. For a particular power spectrum, predicted Sachs-Wolfe effects are calculated for two cases: Gaussian (random phase) configuration, and a specific kind of non-Gaussian configuration. We obtain a result that the Sachs-Wolfe effect for the latter case is smaller when each temperature fluctuation is properly normalized with respect to the corresponding mass fluctuation ${δM\over M}(R)$. The physical explanation and the generality of the result are discussed.
Recent detections of the Integrated Sachs-Wolfe effect through the correlation of the cosmic microwave background temperature anisotropy with traces of large scale structure provided independent evidence for the expansion of the universe being dominated by something other than matter. Even with perfect data, statistical errors will limit the accuracy of such measurements to worse than 10%. On the other hand, the extraordinary sensitivity of the ISW effect to the details of structure formation should help to make up for the lack of precision. In these conference proceedings I discuss the extent…
I present to this conference our latest measurements of the integrated Sachs-Wolfe (ISW) effect. After a brief review of the reasons for which this effect arises and of the technique to detect it by cross-correlating the cosmic microwave background (CMB) with the large scale structure of the Universe (LSS), I describe the current state of the art measurement. This is obtained from a combined analysis of six different galaxy datasets, and has a significance level of ~ 4.5 sigma. I then describe the cosmological implications, which show agreement with a flat LCDM model with Omega_m = 0.20 +0.19 …
Deviations from the Friedmann-Robertson-Walker (FRW) cosmological model in the form of density inhomogeneities induce observational effects on the light propagating through these fluctuations. Using a rigorously parametrized metric whose pseudo-Newtonian potential is related to (possibly nonlinear) density inhomogeneities through a relativistic Green function, the behavior of radiation propagating through this approximation to our universe is investigated, without relying on any spatial averaging or late time, short perturbation wavelength Newtonian limit. In certain regimes the energy shift o…
We present evidence of a large angle correlation between the cosmic microwave background measured by WMAP and a catalog of photometrically detected quasars from the SDSS. The observed cross correlation is (0.30 +- 0.14) microK at zero lag, with a shape consistent with that expected for correlations arising from the integrated Sachs-Wolfe effect. The photometric redshifts of the quasars are centered at z ~ 1.5, making this the deepest survey in which such a correlation has been observed. Assuming this correlation is due to the ISW effect, this constitutes the earliest evidence yet for dark ener…
The scattering of temperature anisotropy quadrupole by free electrons in galaxy clusters leads to a now well-known polarization signal in the cosmic microwave background (CMB) fluctuations. Using multi-frequency polarization data, one can extract the temperature quadrupole and separate it from the contaminant polarization associated with the kinematic quadrupole due to transverse motion of clusters. At low redshifts, the temperature quadrupole contains a significant contribution from the integrated Sachs-Wolfe effect (ISW) associated with the growth of density fluctuations. Using polarization …
We construct a map of the time derivative of the gravitational potential traced by SDSS Luminous Red Galaxies. The potential decays on large scales due to cosmic acceleration, leaving an imprint on cosmic microwave background (CMB) radiation through the integrated Sachs-Wolfe (ISW) effect. With a template fit, we directly measure this signature on the CMB at a 2-sigma confidence level. The measurement is consistent with the cross-correlation statistic, strengthening the claim that dark energy is indeed the cause of the correlation. This new approach potentially simplifies the cosmological inte…
In this paper we address two points concerning the Sachs-Wolfe effect: (i) the gauge independence of the observable temperature anisotropy, and (ii) a gauge-invariant expression of the effect considering the most general situation of hydrodynamic perturbations. The first result follows because the gauge transformation of the temperature fluctuation at the observation event only contributes to the isotropic temperature change which, in practice, is absorbed into the definition of the background temperature. Thus, we proceed without fixing the gauge condition, and express the Sachs-Wolfe effect …
A generic prediction of general relativity is that the cosmological linear density growth factor $D$ is scale independent. But in general, modified gravities do not preserve this signature. A scale dependent $D$ can cause time variation in gravitational potential at high redshifts and provides a new cosmological test of gravity, through early time integrated Sachs-Wolfe (ISW) effect-large scale structure (LSS) cross correlation. We demonstrate the power of this test for a class of $f(R)$ gravity, with the form $f(R)=-λ_1 H_0^2\exp(-R/λ_2H_0^2)$. Such $f(R)$ gravity, even with degenerate expans…
We present a global measurement of the integrated Sachs-Wolfe (ISW) effect obtained by cross-correlating all relevant large scale galaxy data sets with the cosmic microwave background radiation map provided by the Wilkinson Microwave Anisotropy Probe. With these measurements, the overall ISW signal is detected at the ~ 4.5 sigma level. We also examine the cosmological implications of these measurements, particularly the dark energy equation of state w, its sound speed, and the overall curvature of the Universe. The flat LCDM model is a good fit to the data and, assuming this model, we find tha…
Dark matter currents in the large-scale structure give rise to gravitomagnetic terms in the metric, which affect the light propagation. Corrections to the weak lensing power spectrum due to these gravitomagnetic potentials are evaluated by perturbation theory. A connection between gravitomagnetic lensing and the integrated Sachs-Wolfe (iSW) effect is drawn, which can be described by a line-of-sight integration over the divergence of the gravitomagnetic vector potential. This allows the power spectrum of the iSW-effect to be derived within the framework of the same formalism as derived for grav…
We present a new approach to the Sachs-Wolfe effect, which is based on the dynamics of photons in a space and time varying gravitational field. We consider the influence of plasma dispersion effects on photon propagation, and establish the limits of validity of the usual results of the standard cosmological approach, for the large scale temperature anisotropies of the cosmic microwave background. New dynamical contributions to the integrated Sachs-Wolfe effect are also discussed.
We discuss the correlation between late-time integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB) temperature anisotropies and the large scale structure of the local universe. This correlation has been proposed and studied in the literature as a probe of the dark energy and its physical properties. We consider a variety of large scale structure tracers suitable for a detection of the ISW effect via a cross-correlation. In addition to luminous sources, we suggest the use of tracers such as dark matter halos or galaxy clusters. A suitable catalog of mass selected halos fo…
In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies in large angular scales (larger than $\vartheta \gtrsim 2^\circ$) which do not differ from the ones produced in Friedmann-Lemaître-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by th…
We discuss the non-linear extension to the integrated Sachs-Wolfe effect (ISW) resulting from the divergence of the large scale structure momentum density field. The non-linear ISW effect leads to an increase in the total ISW contribution by roughly two orders of magnitude at l ~ 1000. This increase, however, is still below the cosmic variance limit of the primary anisotropies; at further small angular scales, secondary effects such as gravitational lensing and the kinetic Sunyaev-Zel'dovich (SZ) effect dominates the non-linear ISW power spectrum. We show this second-order non-linear ISW contr…
In this paper I investigate the family of mixed three-point correlation functions <tau^q gamma^{3-q}>, q=0,1,2, between the integrated Sachs-Wolfe (iSW) temperature perturbation tau and the galaxy overdensity gamma as a tool for detecting the gravitational interaction of cosmic microwave background (CMB) photons with the potentials of nonlinearly evolving cosmological structures. Both the iSW-effect as well as the galaxy overdensity are derived in hyper-extended perturbation theory to second order and I emphasise the different parameter sensitivities of the linear and non-linear iSW-effect. I …
We perform a cross-correlation of the Cosmic Microwave Background (CMB) using the third year Wilkinson Microwave Anisotropy Probe (WMAP) data with the 2 Micron All Sky Survey (2MASS) galaxy map (about 828 000 galaxies with median redshift z ~ 0.07). One motivation is to detect the Integrated Sachs-Wolfe (ISW) effect, expected if the cosmic gravitational potential is time dependent; for example, as it is in a flat universe with a Dark Energy component. The measured spherical harmonic cross-correlation signal favours the ISW signal expected in the concordance LambdaCDM model over that of zero co…
The cross-correlation between cosmic microwave background (CMB) temperature anisotropies and the large scale structure (LSS) traced by the galaxy distribution, or sources at different wavelengths, is now well known. This correlation results from the integrated Sachs-Wolfe (ISW) effect in CMB anisotropies generated at late times due to the dark energy component of the Universe. In a reionized universe, the ISW quadrupole rescatters and contributes to the large-scale polarization signal. Thus, in principle, the large-scale polarization bump in the E-mode should also be correlated with the galaxy…
We present a coherent theoretical framework for computing gravitational lensing effects and redshift-space distortions in an inhomogeneous universe and investigate their impacts on galaxy two-point statistics. Adopting the linearized FRW metric, we derive the gravitational lensing and the generalized Sachs-Wolfe effects that include the weak lensing distortion, magnification, and time delay effects, and the redshift-space distortion, Sachs-Wolfe, and integrated Sachs-Wolfe effects, respectively. Based on this framework, we first compute their effects on observed source fluctuations, separating…
We point out that a pseudo-Newtonian interpretations of the $(1/3)$ factor in the Sachs-Wolfe effect, which relates the fluctuations in temperature and potential, $(δT/ T) = (1/ 3) δΦ$, is not supported by the General Relativistic analysis. Dividing the full gravitational effect into separate parts depends on the choice of time slicing (gauge) and there exist infinitely many different choices. More importantly, interpreting the parts as being due to the gravitational redshift and the time dilation is not justified in the rigorous relativistic perturbation theory. We suggest to regard the $(1/3…
We measure hot and cold spots on the microwave background associated with supercluster and supervoid structures identified in the Sloan Digital Sky Survey Luminous Red Galaxy catalog. The structures give a compelling visual imprint, with a mean temperature deviation of 9.6 +/- 2.2 microK, i.e. above 4 sigma. We interpret this as a detection of the late-time Integrated Sachs-Wolfe (ISW) effect, in which cosmic acceleration from dark energy causes gravitational potentials to decay, heating or cooling photons passing through density crests or troughs. In a flat universe, the linear ISW effect is …
We present a 2.5 sigma detection of the Integrated Sachs-Wolfe (ISW) effect and discuss the constraints it places on cosmological parameters. We cross-correlate microwave temperature maps from the WMAP satellite with a 4000 deg^2 luminous red galaxy (LRG) overdensity map measured by the Sloan Digital Sky Survey. Accurate photometric redshifts allow us to perform a reliable auto-correlation analysis of the LRGs, eliminating the uncertainty in the galaxy bias, and combined with cross correlation signal, constrains cosmological parameters -- in particular, the matter density. We find a 2.5 sigma …
The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to the temperature variations $δT/T$ in the cosmic microwave background radiation; $δT/T$ can be observed in all directions around us. A standard but idealised model of this effect leads to an infinite set of moment-like equations: the integral of $P(k) j_\ell^2(ky)$ with respect to k ($0<k<\infty$) is equal to a given constant, $C_\ell$, for $\ell=0,1,2,...$. Here, P is the power spectrum of the primordial density variations, $j_\ell$ is a spherical Bessel function and y is a positive constant. It is shown how to solve …
We reassess the estimate of the cross-correlation of the spatial distribution of the NRAO VLA Sky Survey (NVSS) radio sources with that of Cosmic Microwave Background (CMB) anisotropies from the Wilkinson Microwave Anisotropy Probe (WMAP). This re-analysis is motivated by the fact that most previous studies adopted a redshift distribution of NVSS sources inconsistent with recent data. We find that the constraints on the bias-weighted redshift distribution, b(z)xN(z), of NVSS sources, set by the observed angular correlation function, w(theta), strongly mitigate the effect of the choice of N(z).…
The cosmic neutrino background (CNB) consists of low-energy relic neutrinos which decoupled from the cosmological fluid at a redshift z ~ 10^{10}. Despite being the second-most abundant particles in the universe, direct observation remains a distant challenge. Based on the measured neutrino mass differences, one species of neutrinos may still be relativistic with a thermal distribution characterized by the temperature T ~ 1.9K. We show that the temperature distribution on the sky is anisotropic, much like the photon background, experiencing Sachs-Wolfe and integrated Sachs-Wolfe effects.
Models with dark energy decaying into dark matter have been proposed in Cosmology to solve the coincidence problem. We study the effect of such coupling on the cosmic microwave background temperature anisotropies. The interaction changes the rate of evolution of the metric potentials, the growth rate of matter density perturbations and modifies the Integrated Sachs-Wolfe component of cosmic microwave background temperature anisotropies, enhancing the effect. Cross-correlation of galaxy catalogs with CMB maps provides a model independent test to constrain the interaction. We particularize our a…
We cross-correlate the new 3 year Wilkinson Microwave Anistropy Probe (WMAP) cosmic microwave background (CMB) data with the NRAO VLA Sky Survey (NVSS) radio galaxy data, and find further evidence of late integrated Sachs-Wolfe (ISW) effect taking place at late times in cosmic history. Our detection makes use of a novel statistical method \cite{Baldi et al. 2006a, Baldi et al. 2006b} based on a new construction of spherical wavelets, called needlets. The null hypothesis (no ISW) is excluded at more than 99.7% confidence. When we compare the measured cross-correlation with the theoretical predi…
The Integrated Sachs-Wolfe (ISW) effect is a direct signature of the presence of dark energy in the universe, in the absence of spatial curvature. A powerful method for observing the ISW effect is through cross-correlation of the Cosmic Microwave Background (CMB) with a tracer of the matter in the low redshift universe. In this paper, we describe the dependence of the obtained cross-correlation signal on the geometry and other properties of a survey of the low redshift universe. We show that an all-sky survey with about 10 million galaxies, almost uniformly distributed within 0<z<1 should yiel…
Any hint of non-gaussianity in the cosmological initial conditions will provide us with a unique window into the physics of early universe. We show that the impact of a small local primordial non-gaussianity (generated on super-horizon scales) on the statistics of collapsed objects (such as galaxies or clusters) can be approximated by using slightly modified, but gaussian, initial conditions, which we describe through simple analytic expressions. Given that numerical simulations with gaussian initial conditions are relatively well-studied, this equivalence provides us with a simple tool to pre…
We report the first detection of the ISW effect in wavelet space, at scales in the sky around 7 degrees with a significance of around 3.3 sigma, by cross-correlating the WMAP first-year data and the NRAO VLA Sky Survey (NVSS). In addition, we present a detailed comparison among the capabilities of three different techniques for two different objectives: to detect the ISW and to put constraints in the nature of the dark energy. The three studied techniques are: the cross-angular power spectrum (CAPS, harmonic space), the correlation function (CCF, real space) and the covariance of the Spherical…
The pattern of anisotropies in the Cosmic Microwave Background depends upon the masses and lifetimes of the three neutrino species. A neutrino species of mass greater than 10 eV with lifetime between 10^{13} sec and 10^{17} sec leaves a very distinct signature (due to the integrated Sachs-Wolfe effect): the anisotropies at large angles are predicted to be comparable to those on degree scales. Present data exclude such a possibility and hence this region of parameter space. For $m_ν\simeq 30$ eV, $τ\simeq 10^{13}$ sec, we find an interesting possibility: the Integrated Sachs Wolfe peak produced…
We examine, from both a qualitative and a numerical point of view, the evolution of Kantowski--Sachs cosmological models whose source is a mixture of a gas of weakly interacting massive particles (WIMP's) and a radiative gas made up of a ``tightly coupled'' mixture of electrons, baryons and photons from the end of nucleosynthesis up to the duration of radiative interactions. In this cosmic era annihilation processes are negligible, while the WIMP's only interact gravitationally with the radiative gas and the latter behaves as a single dissipative fluid that can be studied within a hydrodynamic…
We calculate the full second-order radiation transfer function for Cosmic Microwave Background anisotropies on large angular scales in a flat universe filled with matter and cosmological constant. It includes (i) the second-order generalization of the Sachs-Wolfe effect, and of (ii) both the early and late Integrated Sachs-Wolfe effects, (iii) the contribution of the second-order tensor modes, and is valid for a generic set of initial conditions specifying the level of primordial non-Gaussianity.
We study the behavior of light rays in perturbed Robertson-Walker cosmologies, calculating the redshift between an observer and the surface of last scattering to second order in the metric perturbation. At first order we recover the classic results of Sachs and Wolfe, and at second order we delineate the various new effects which appear; there is no {\it a priori} guarantee that these effects are significantly smaller than those at first order, since there are large length scales in the problem which could lead to sizable prefactors. We find that second order terms of potential observational i…
We cross-correlate the third-year WMAP data with galaxy samples extracted from the SDSS DR5 (SDSS5) covering 16% of the sky. These measurements confirm a positive cross-correlation, which is well fitted by the integrated Sachs-Wolfe (ISW) effect for flat LCDM models with a cosmological constant.
Gravitational interaction of cosmic microwave background (CMB) photons with matter perturbations present along the line-of-sight to the surface of last scattering modifies the shape of the CMB anisotropy power spectrum. Here I focus on (linear) integrated Sachs-Wolfe and (non-linear) gravitational lensing effects and discuss the detectability of the resulting distortions and their possible consequences for the CMB-based estimation of cosmological parameters. Specifically, I discuss if any of those effects may allow us to use CMB experiments to put independent constraints on the curvature of th…
We consider the CMB bispectrum signal induced by structure formation through the correlation between the Integrated Sachs-Wolfe and the weak lensing effect. We investigate how the bispectrum knowledge can improve our knowledge of the most important cosmological parameters, focusing on the dark energy ones. Preliminary results suggest a consistent improvement on the estimation of dark energy abundance and on dynamical properties of the equation of state.
We present a generalization and refinement of the Sachs-Wolfe technique which unifies many of the approaches taken to date and clarifies both the physical and the mathematical character of the method. We illustrate the formalism with a calculation of the behavior of light passing a moving lens on a Minkowski background.
We consider directly the equations by which matter imposes anisotropies on freely propagating background radiation, leading to a new way of using anisotropy measurements to limit the deviations of the Universe from a Friedmann-Robertson-Walker (FRW) geometry. This approach is complementary to the usual Sachs-Wolfe approach: the limits obtained are not as detailed, but they are more model-independent. We also give new results about combined matter-radiation perturbations in an almost-FRW universe, and a new exact solution of the linearised equations.
We perform an analytical study of the Integrated Sachs-Wolfe (ISW) effect within the framework of Unified Dark Matter models based on a scalar field which aim at a unified description of dark energy and dark matter. Computing the temperature power spectrum of the Cosmic Microwave Background anisotropies we are able to isolate those contributions that can potentially lead to strong deviations from the usual ISW effect occurring in a $Λ$CDM universe. This helps to highlight the crucial role played by the sound speed in the Unified Dark Matter models. Our treatment is completely general in that a…
