The Sachs–Wolfe effect, named after
Rainer K. Sachs and
Arthur M. Wolfe, is a property of the
cosmic microwave background radiation
The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dar ...
(CMB), in which photons from the CMB are
gravitationally redshifted, causing the CMB spectrum to appear uneven. This effect is the predominant source of fluctuations in the CMB for angular scales larger than about ten degrees.
Non-integrated Sachs–Wolfe effect
The non-integrated Sachs–Wolfe effect is caused by gravitational redshift occurring at the
surface of last scattering. The effect is not constant across the sky due to differences in the matter/energy density at the time of last scattering.
Integrated Sachs–Wolfe effect
The integrated Sachs–Wolfe (ISW) effect is also caused by gravitational redshift, but it occurs between the surface of last scattering and the
Earth
Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...
, so it is not part of the primordial
CMB. It occurs when the
Universe
The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...
is dominated in its energy density by something other than matter. If the Universe is dominated by matter, then large-scale
gravitational potential energy
Gravitational energy or gravitational potential energy is the potential energy an object with mass has due to the gravitational potential of its position in a gravitational field. Mathematically, it is the minimum Work (physics), mechanical work t ...
wells and hills do not evolve significantly. If the Universe is dominated by
radiation
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes:
* ''electromagnetic radiation'' consisting of photons, such as radio waves, microwaves, infr ...
, or by
dark energy
In physical cosmology and astronomy, dark energy is a proposed form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. It also slows the rate of structure format ...
, though, those potentials do evolve, subtly changing the energy of
photons
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that ...
passing through them.
There are two contributions to the ISW effect. The "early-time" ISW occurs immediately after the (non-integrated) Sachs–Wolfe effect produces the primordial CMB, as photons course through density fluctuations while there is still enough
radiation
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes:
* ''electromagnetic radiation'' consisting of photons, such as radio waves, microwaves, infr ...
around to affect the Universe's expansion. Although it is physically the same as the late-time ISW, for observational purposes it is usually lumped in with the primordial CMB, since the matter fluctuations that cause it are in practice undetectable.
Late-time integrated Sachs–Wolfe effect
The "late-time" ISW effect arises quite recently in cosmic history, as
dark energy
In physical cosmology and astronomy, dark energy is a proposed form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. It also slows the rate of structure format ...
, or the
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is a coefficient that Albert Einstein initially added to his field equations of general rel ...
, starts to govern the Universe's expansion. Unfortunately, the nomenclature is a bit confusing. Often, "late-time ISW" implicitly refers to the late-time ISW effect to
linear/first order in density perturbations. This linear part of the effect entirely vanishes in a
flat universe with only matter, but dominates over the higher-order part of the effect in a universe with dark energy. The full
nonlinear
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...
(linear + higher-order) late-time ISW effect, especially in the case of individual voids and clusters, is sometimes known as the
Rees–Sciama effect, since