Editing Cosmic microwave background (section)

====Primary anisotropy====
[[File:PowerSpectrumExt.svg|thumb|right|300px|The power spectrum of the cosmic microwave background radiation temperature anisotropy in terms of the angular scale (or [[multipole moment]]). The data shown comes from the [[WMAP]] (2006), [[Arcminute Cosmology Bolometer Array Receiver|Acbar]] (2004) [[BOOMERanG experiment|Boomerang]] (2005), [[Cosmic Background Imager|CBI]] (2004), and [[Very Small Array|VSA]] (2004) instruments. Also shown is a theoretical model (solid line).]]
The [[anisotropy]], or directional dependency, of the cosmic microwave background is divided into two types: primary anisotropy, due to effects that occur at the surface of last scattering and before; and secondary anisotropy, due to effects such as interactions of the background radiation with intervening hot gas or gravitational potentials, which occur between the last scattering surface and the observer.

The structure of the cosmic microwave background anisotropies is principally determined by two effects: acoustic oscillations and [[diffusion damping]] (also called collisionless damping or [[Joseph Silk|Silk]] damping). The acoustic oscillations arise because of a conflict in the [[photon]]–[[baryon]] plasma in the early universe. The pressure of the photons tends to erase anisotropies, whereas the gravitational attraction of the baryons, moving at speeds much slower than light, makes them tend to collapse to form overdensities. These two effects compete to create acoustic oscillations, which give the microwave background its characteristic peak structure. The peaks correspond, roughly, to resonances in which the photons decouple when a particular mode is at its peak amplitude.

The peaks contain interesting physical signatures. The angular scale of the first peak determines the [[shape of the universe|curvature of the universe]] (but not the [[topology]] of the universe). The next peak—ratio of the odd peaks to the even peaks—determines the reduced baryon density.<ref>{{cite web |url=http://background.uchicago.edu/~whu/intermediate/baryons.html |title=Baryons and Inertia |author=Wayne Hu}}</ref> The third peak can be used to get information about the dark-matter density.<ref>{{cite web |url=http://background.uchicago.edu/~whu/intermediate/driving.html |title=Radiation Driving Force |author=Wayne Hu}}</ref>

The locations of the peaks give important information about the nature of the primordial density perturbations. There are two fundamental types of density perturbations called ''adiabatic'' and ''isocurvature''. A general density perturbation is a mixture of both, and different theories that purport to explain the primordial density perturbation spectrum predict different mixtures.
; Adiabatic density perturbations:In an adiabatic density perturbation, the fractional additional number density of each type of particle (baryons, [[photon]]s, etc.) is the same. That is, if at one place there is a 1% higher number density of baryons than average, then at that place there is a 1% higher number density of photons (and a 1% higher number density in neutrinos) than average. [[Cosmic inflation]] predicts that the primordial perturbations are adiabatic.
; Isocurvature density perturbations:In an isocurvature density perturbation, the sum (over different types of particle) of the fractional additional densities is zero. That is, a perturbation where at some spot there is 1% more energy in baryons than average, 1% more energy in photons than average, and 2% {{em|less}} energy in neutrinos than average, would be a pure isocurvature perturbation. Hypothetical [[cosmic string]]s would produce mostly isocurvature primordial perturbations.

The CMB spectrum can distinguish between these two because these two types of perturbations produce different peak locations. Isocurvature density perturbations produce a series of peaks whose angular scales (''ℓ'' values of the peaks) are roughly in the ratio 1&nbsp;:&nbsp;3&nbsp;:&nbsp;5&nbsp;:&nbsp;..., while adiabatic density perturbations produce peaks whose locations are in the ratio 1&nbsp;:&nbsp;2&nbsp;:&nbsp;3&nbsp;:&nbsp;...<ref name="hu_white_1996">{{cite journal|last1=Hu |first1=W.|last2=White|first2=M.|year=1996|title=Acoustic Signatures in the Cosmic Microwave Background|journal=[[Astrophysical Journal]]|volume=471|pages=30–51|doi=10.1086/177951|bibcode=1996ApJ...471...30H|arxiv = astro-ph/9602019 |s2cid=8791666}}</ref> Observations are consistent with the primordial density perturbations being entirely adiabatic, providing key support for inflation, and ruling out many models of structure formation involving, for example, cosmic strings.

Collisionless damping is caused by two effects, when the treatment of the primordial plasma as [[fluid]] begins to break down:
* the increasing [[mean free path]] of the photons as the primordial plasma becomes increasingly rarefied in an expanding universe,
* the finite depth of the last scattering surface (LSS), which causes the mean free path to increase rapidly during decoupling, even while some Compton scattering is still occurring.
These effects contribute about equally to the suppression of anisotropies at small scales and give rise to the characteristic exponential damping tail seen in the very small angular scale anisotropies.

The depth of the LSS refers to the fact that the decoupling of the photons and baryons does not happen instantaneously, but instead requires an appreciable fraction of the age of the universe up to that era. One method of quantifying how long this process took uses the ''photon visibility function'' (PVF). This function is defined so that, denoting the PVF by ''P''(''t''), the probability that a CMB photon last scattered between time ''t'' and {{nowrap|''t'' + ''dt''}} is given by ''P''(''t''){{thin space}}''dt''.

The maximum of the PVF (the time when it is most likely that a given CMB photon last scattered) is known quite precisely. The first-year [[Wilkinson Microwave Anisotropy Probe|WMAP]] results put the time at which ''P''(''t'') has a maximum as 372,000 years.<ref name="WMAP_1_cosmo_params">{{cite journal|author=WMAP Collaboration|year=2003|title=First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters|journal=[[Astrophysical Journal Supplement Series]]|volume=148|last2=Verde|issue=1|pages=175–194|first2=L.|doi=10.1086/377226|last3=Peiris|first3=H. V.|last4=Komatsu|first4=E.|last5=Nolta|first5=M. R.|last6=Bennett|first6=C. L.|last7=Halpern|first7=M.|last8=Hinshaw|first8=G.|last9=Jarosik|first9=N.|arxiv=astro-ph/0302209|bibcode=2003ApJS..148..175S|s2cid=10794058| display-authors = 8}}</ref> This is often taken as the "time" at which the CMB formed. However, to figure out how {{em|long}} it took the photons and baryons to decouple, we need a measure of the width of the PVF. The WMAP team finds that the PVF is greater than half of its maximal value (the "full width at half maximum", or FWHM) over an interval of 115,000 years.<ref name="WMAP_1_cosmo_params"/>{{rp|179}} By this measure, decoupling took place over roughly 115,000 years, and thus when it was complete, the universe was roughly 487,000 years old.