integrated Sachs–Wolfe effect

integrated Sachs–Wolfe effect
Name	Integrated Sachs–Wolfe effect
Caption	A timeline of the universe showing the cosmic microwave background and the late-time influence of the integrated Sachs–Wolfe effect.
Field	Physical cosmology
Discovered	Rainer K. Sachs and Arthur M. Wolfe (1967)
Related	Sachs–Wolfe effect, Rees–Sciama effect, Cosmic microwave background

integrated Sachs–Wolfe effect. In physical cosmology, the integrated Sachs–Wolfe effect is a secondary anisotropy in the cosmic microwave background radiation. It arises from the gravitational redshifting or blueshifting of CMB photons as they traverse evolving gravitational potentials in the large-scale structure of the universe. This effect provides a crucial observational link between the CMB and the distribution of matter, offering insights into the composition and dynamics of the cosmos, particularly the influence of dark energy.

Overview

The phenomenon was first described theoretically by Rainer K. Sachs and Arthur M. Wolfe in their seminal 1967 paper. It is distinguished from the primary Sachs–Wolfe effect, which occurs at the surface of last scattering, by being an integrated accumulation of shifts along the photon's path. The effect is most significant when the universe undergoes transitions in its expansion dynamics, such as the onset of matter domination or the recent acceleration driven by dark energy. Detection of the integrated Sachs–Wolfe effect requires cross-correlating CMB maps with tracers of the large-scale structure, such as those from the Sloan Digital Sky Survey or the Dark Energy Survey.

Physical origin

As a CMB photon travels from the surface of last scattering to an observer like those at the South Pole Telescope, it passes through regions of varying gravitational potential caused by the large-scale structure of the universe. If the gravitational potential of a structure is constant, the blueshift gained entering a potential well is canceled by the redshift upon exiting, a consequence of the Einstein field equations. However, if the potential decays due to the expansion of the universe—a process governed by the Friedmann equations—a net shift in the photon's energy occurs. This decay happens during epochs when the universe is not dominated by pressureless matter, such as in the presence of a significant cosmological constant or during the early radiation-dominated era.

Observational evidence

The first statistical detection of the integrated Sachs–Wolfe effect was reported in 2003 by researchers analyzing data from the Wilkinson Microwave Anisotropy Probe cross-correlated with the Hard X-ray Background from HEAO 1. Subsequent confirmations used CMB data from the Planck mission correlated with galaxy surveys like the Sloan Digital Sky Survey and the Two Micron All Sky Survey. Observations of the CMB cold spot in the constellation Eridanus have also been investigated for a possible connection to a supervoid via this effect. These measurements provide a direct probe of dark energy and the growth of structure, independent of other methods like those from Type Ia supernova observations.

Relation to dark energy

The integrated Sachs–Wolfe effect is a powerful probe for dark energy because it is sensitive to the late-time decay of gravitational potentials. In a universe dominated by a cosmological constant or similar form of dark energy, the expansion accelerates, causing potentials to decay and generating a positive correlation between the CMB temperature and the large-scale structure. The absence of this signal in a flat, matter-only Lambda-CDM model universe makes its detection strong evidence for an accelerating cosmos, complementing findings from the Hubble Space Telescope and the Supernova Cosmology Project. Its measurement helps constrain parameters like the equation of state of dark energy.

Impact on cosmic microwave background

The integrated Sachs–Wolfe effect imprints specific secondary anisotropies on the cosmic microwave background, primarily on large angular scales (low multipole moments). It contributes to the temperature power spectrum measured by experiments like WMAP and Planck, though it is subdominant to the primary Sachs–Wolfe effect and other secondary effects like the Sunyaev–Zel'dovich effect. Its signature is also sought in CMB polarization data. Understanding this effect is crucial for accurately separating primordial signals from late-time modifications, which is essential for testing inflationary models and measuring the optical depth to reionization.

Theoretical models and extensions

The standard theoretical framework is based on linear perturbation theory within general relativity, as formulated by Sachs and Wolfe. Extensions include the non-linear Rees–Sciama effect, which becomes important for photons passing through virialized clusters like those in the Virgo Supercluster. Alternative theories of gravity, such as f(R) gravity or models inspired by string theory, predict modified growth of structure and thus alter the expected integrated Sachs–Wolfe signal. Its study also intersects with research on cosmic voids and the Lyman-alpha forest, providing tests for cosmology beyond the standard Lambda-CDM model.

Category:Physical cosmology Category:Cosmic microwave background