| Physical cosmology |
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| Universe · Big Bang Age of the universe Timeline of the Big Bang Ultimate fate of the universe |
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In cosmology, cosmic microwave background (CMB) radiation (also CMBR, CBR, MBR, and relic radiation) is thermal radiation filling the observable universe almost uniformly.[1]
With a traditional optical telescope, the space between stars and galaxies (the background) is completely dark. But a sufficiently sensitive radio telescope shows a faint background glow, almost exactly the same in all directions, that is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The CMB's serendipitous discovery in 1964 by American radio astronomers Arno Penzias and Robert Wilson[2] was the culmination of work initiated in the 1940s, and earned them the 1978 Nobel Prize.
Cosmic background radiation is well explained as radiation left over from an early stage in the development of the universe, and its discovery is considered a landmark test of the Big Bang model of the universe. When the universe was young, before the formation of stars and planets, it was smaller, much hotter, and filled with a uniform glow from its white-hot fog of hydrogen plasma. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons could form neutral atoms. These atoms could no longer absorb the thermal radiation, and the universe became transparent instead of being an opaque fog. The photons that existed at that time have been propagating ever since, though growing fainter and less energetic, since exactly the same photons fill a larger and larger universe. This is the source for the alternate term relic radiation.
Precise measurements of cosmic background radiation are critical to cosmology, since any proposed model of the universe must explain this radiation. The CMBR has a thermal black body spectrum at a temperature of 2.725 K, thus the spectrum peaks in the microwave range frequency of 160.2 GHz, corresponding to a 1.9 mm wavelength. This holds if measured per unit frequency, as in Planck's law. If measured instead per unit wavelength, using Wien's law, the peak will be at 1.06 mm corresponding to a frequency of 283 GHz.
The glow is very nearly uniform in all directions, but the tiny remaining variations show a very specific pattern equal to that expected if a fairly uniformly distributed hot gas is expanded to the current size of the universe. In particular, the spatial power spectrum (how much difference is observed versus how far apart the regions are on the sky) contains small anisotropies, or irregularities, which vary with the size of the region examined. They have been measured in detail, and match what would be expected if small thermal variations, generated by quantum fluctuations of matter in a very tiny space, had expanded to the size of the observable universe we see today. This is still a very active field of study, with scientists seeking both better data (for example, the Planck spacecraft) and better interpretations of the initial conditions of expansion.
Although many different processes might produce the general form of a black body spectrum, no model other than the Big Bang has yet explained the fluctuations. As a result, most cosmologists consider the Big Bang model of the universe to be the best explanation for the CMBR.
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The cosmic microwave background (CMB) radiation is an emission of uniform, black body thermal energy coming from all parts of the sky. The radiation is isotropic to roughly one part in 100,000: the root mean square variations are only 18 µK,[4] after subtracting out a dipole anisotropy from the Doppler shift of the background radiation. The latter is caused by the peculiar velocity of the Earth relative to the comoving cosmic rest frame as the planet moves at some 627 km/s towards the constellation Virgo.
In the Big Bang model for the formation of the universe, Inflationary Cosmology predicts that after about 10−37 seconds[5] the nascent universe underwent exponential growth that smoothed out nearly all inhomogeneities. The remaining inhomogeneities were caused by quantum fluctuations in the inflaton field that caused the inflation event.[6] After 10−6 seconds, the early universe was made up of a hot, interacting plasma of photons, electrons, and baryons. As the universe expanded, adiabatic cooling caused the plasma to lose energy until it became favorable for electrons to combine with protons, forming hydrogen atoms. This recombination event happened when the temperature was around 3000 K or when the universe was approximately 379,000 years old.[7] At this point, the photons no longer interacted with the now electrically neutral atoms and began to travel freely through space, resulting in the decoupling of matter and radiation.[8]
The color temperature of the decoupled photons has continued to diminish ever since; now down to 2.725 K, their temperature will continue to drop as the universe expands. According to the Big Bang model, the radiation from the sky we measure today comes from a spherical surface called the surface of last scattering. This represents the set of locations in space at which the decoupling event is believed to have occurred[9] and at a point in time such that the photons from that distance have just reached observers. Most of the radiation energy in the universe is in the cosmic microwave background,[10] making up a fraction of roughly 6×10−5 of the total density of the universe.[11]
Two of the greatest successes of the Big Bang theory are its prediction of the almost perfect black body spectrum and its detailed prediction of the anisotropies in the cosmic microwave background. The CMB spectrum has become the most precisely measured black body spectrum in nature.[3]
| Timeline of Observations of the CMB | |
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| Important people and dates | |
| 1941 | Andrew McKellar was attempting to measure the average temperature of the interstellar medium, and reported the observation of an average bolometric temperature of 2.3 K based on the study of interstellar absorption lines.[12][13] |
| 1946 | Robert Dicke predicts ".. radiation from cosmic matter" at <20 K but did not refer to background radiation[14] |
| 1948 | George Gamow calculates a temperature of 50 K (assuming a 3-billion-year old Universe),[15] commenting it ".. is in reasonable agreement with the actual temperature of interstellar space", but does not mention background radiation. |
| 1948 | Ralph Alpher and Robert Herman estimate "the temperature in the Universe" at 5 K. Although they do not specifically mention microwave background radiation, it may be inferred.[16] |
| 1950 | Ralph Alpher and Robert Herman re-estimate the temperature at 28 K. |
| 1953 | George Gamow estimates 7 K.[14] |
| 1955 | Émile Le Roux of the Nançay Radio Observatory, in a sky survey at λ=33 cm, reported a near-isotropic background radiation of 3 kelvins, plus or minus 2.[14] |
| 1956 | George Gamow estimates 6 K.[14] |
| 1957 | Tigran Shmaonov reports that "the absolute effective temperature of the radioemission background ... is 4±3K".[17] It is noted that the "measurements showed that radiation intensity was independent of either time or direction of observation... it is now clear that Shmaonov did observe the cosmic microwave background at a wavelength of 3.2 cm"[18] |
| 1960s | Robert Dicke re-estimates a MBR (microwave background radiation) temperature of 40 K[14] |
| 1964 | A. G. Doroshkevich and Igor Novikov publish a brief paper, where they name the CMB radiation phenomenon as detectable.[19] |
| 1964–65 | Arno Penzias and Robert Woodrow Wilson measure the temperature to be approximately 3 K. Robert Dicke, P. J. E. Peebles, P. G. Roll, and D. T. Wilkinson interpret this radiation as a signature of the big bang. |
| 1983 | RELIKT-1 Soviet CMB anisotropy experiment was launched. |
| 1990 | FIRAS on COBE measures the black body form of the CMB spectrum with exquisite precision. |
| Apr 1992 | Scientists who analyzed data from COBE DMR announce the discovery of the primary temperature anisotropy.[20] |
| 1999 | First measurements of acoustic oscillations in the CMB anisotropy angular power spectrum from the TOCO, BOOMERANG, and Maxima Experiments. |
| 2002 | Polarization discovered by DASI.[21] |
| 2004 | E-mode polarization spectrum obtained by the CBI.[22] |
| 2005 | Ralph A. Alpher is awarded the National Medal of Science for his groundbreaking work in nucleosynthesis and prediction that the universe expansion leaves behind background radiation, thus providing a model for the Big Bang theory. |
| 2006 | Two of COBE's principal investigators, George Smoot and John Mather, received the Nobel Prize in Physics in 2006 for their work on precision measurement of the CMBR. |
The cosmic microwave background was predicted in 1948 by George Gamow, Ralph Alpher, and Robert Herman.[23][24][25] Alpher and Herman were able to estimate the temperature of the cosmic microwave background to be 5 K, though two years later they re-estimated it at 28 K. This high estimate was due to an mis-estimate of the Hubble constant by Alfred Behr, which could not be replicated and was later abandoned for the earlier estimate. Although there were several previous estimates of the temperature of space, these suffered from two flaws. First, they were measurements of the effective temperature of space and did not suggest that space was filled with a thermal Planck spectrum. Next, they depend on our being at a special spot at the edge of the Milky Way galaxy and they did not suggest the radiation is isotropic. The estimates would yield very different predictions if Earth happened to be located elsewhere in the Universe.[26]
The 1948 results of Alpher and Herman were discussed in many physics settings through about 1955, when each left the Applied Physics Laboratory at Johns Hopkins University. The mainstream astronomical community, however, was not intrigued at the time by cosmology. Alpher and Herman's prediction was rediscovered by Yakov Zel'dovich in the early 1960s, and independently predicted by Robert Dicke at the same time. The first published recognition of the CMB radiation as a detectable phenomenon appeared in a brief paper by Soviet astrophysicists A. G. Doroshkevich and Igor Novikov, in the spring of 1964.[27] In 1964, David Todd Wilkinson and Peter Roll, Dicke's colleagues at Princeton University, began constructing a Dicke radiometer to measure the cosmic microwave background.[28] In 1965, Arno Penzias and Robert Woodrow Wilson at the Crawford Hill location of Bell Telephone Laboratories in nearby Holmdel Township, New Jersey had built a Dicke radiometer that they intended to use for radio astronomy and satellite communication experiments. Their instrument had an excess 3.5 K antenna temperature which they could not account for. After receiving a telephone call from Crawford Hill, Dicke famously quipped: "Boys, we've been scooped."[1][29][30] A meeting between the Princeton and Crawford Hill groups determined that the antenna temperature was indeed due to the microwave background. Penzias and Wilson received the 1978 Nobel Prize in Physics for their discovery.[31]
The interpretation of the cosmic microwave background was a controversial issue in the 1960s with some proponents of the steady state theory arguing that the microwave background was the result of scattered starlight from distant galaxies.[32] Using this model, and based on the study of narrow absorption line features in the spectra of stars, the astronomer Andrew McKellar wrote in 1941: "It can be calculated that the 'rotational temperature' of interstellar space is 2 K."[12] However, during the 1970s the consensus was established that the cosmic microwave background is a remnant of the big bang. This was largely because new measurements at a range of frequencies showed that the spectrum was a thermal, black body spectrum, a result that the steady state model was unable to reproduce.[33]
Harrison, Peebles, Yu and Zel'dovich realized that the early universe would have to have inhomogeneities at the level of 10−4 or 10−5.[34][35][36] Rashid Sunyaev later calculated the observable imprint that these inhomogeneities would have on the cosmic microwave background.[37] Increasingly stringent limits on the anisotropy of the cosmic microwave background were set by ground based experiments during the 1980s. RELIKT-1, a Soviet cosmic microwave background anisotropy experiment on board the Prognoz 9 satellite (launched 1 July 1983) gave upper limits on the large-scale anisotropy. The NASA COBE mission clearly confirmed the primary anisotropy with the Differential Microwave Radiometer instrument, publishing their findings in 1992.[38][39] The team received the Nobel Prize in physics for 2006 for this discovery.
Inspired by the COBE results, a series of ground and balloon-based experiments measured cosmic microwave background anisotropies on smaller angular scales over the next decade. The primary goal of these experiments was to measure the scale of the first acoustic peak, which COBE did not have sufficient resolution to resolve. This peak corresponds to large scale density variations in the early universe that are created by gravitational instabilities, resulting in acoustical oscillations in the plasma.[40] The first peak in the anisotropy was tentatively detected by the Toco experiment and the result was confirmed by the BOOMERanG and MAXIMA experiments.[41][42][43] These measurements demonstrated that the geometry of the Universe is approximately flat, rather than curved.[44] They ruled out cosmic strings as a major component of cosmic structure formation and suggested cosmic inflation was the right theory of structure formation.[45]
The second peak was tentatively detected by several experiments before being definitively detected by WMAP, which has also tentatively detected the third peak.[46] As of 2010, several experiments to improve measurements of the polarization and the microwave background on small angular scales are ongoing. These include DASI, WMAP, BOOMERanG, QUaD, Planck spacecraft, Atacama Cosmology Telescope, South Pole Telescope and the QUIET telescope.
The cosmic microwave background radiation and the cosmological redshift are together regarded as the best available evidence for the Big Bang theory. Measurements of the CMB have made the inflationary Big Bang theory the standard model of the earliest eras of the universe.[47] The discovery of the CMB in the mid-1960s curtailed interest in alternatives such as the steady state theory.[48]
The Big Bang theory predicts that the initial conditions for the universe are originally random in nature, and inhomogeneities follow a roughly Gaussian probability distribution, which, when graphed in cross-section, form bell-shaped curves. By analyzing this distribution at different frequencies, a spectral density or power spectrum is generated. The power spectrum of these fluctuations has been calculated, and agrees with the observations. The resulting standard model of the Big Bang uses a Gaussian random field with a nearly scale invariant or Harrison-Zel'dovich spectrum to represent the primeval inhomogeneities.[49][50]
Certain observables, for example the overall amplitude of the fluctuations, are more or less free parameters of the cosmic inflation model.[51] Therefore, meaningful statements about the inhomogeneities in the universe need to be statistical in nature. This leads to cosmic variance in which the uncertainties in the variance of fluctuations at the largest scale observed are difficult to accurately compare to theory.
The CMB gives a snapshot of the universe when, according to standard cosmology, the temperature dropped enough to allow electrons and protons to form hydrogen atoms, thus making the universe transparent to radiation. When it originated some 380,000 years after the Big Bang—this time is generally known as the "time of last scattering" or the period of recombination or decoupling—the temperature of the universe was about 3000 K. This corresponds to an energy of about 0.25 eV, which is much less than the 13.6 eV ionization energy of hydrogen.[52]
Since decoupling, the temperature of the background radiation has dropped by a factor of roughly 1,100[53] due to the expansion of the universe. As the universe expands, the CMB photons are redshifted, making the radiation's temperature inversely proportional to a parameter called the universe's scale length. The temperature Tr of the CMB as a function of redshift, z, can be shown to be proportional to the temperature of the CMB as observed in the present day (2.725 K or 0.235 meV):[54]
For details about the reasoning that the radiation is evidence for the Big Bang, see Cosmic background radiation of the Big Bang.
The anisotropy of the cosmic microwave background is divided into two sorts: primary anisotropy, due to effects which occur at the last scattering surface and before; and secondary anisotropy, due to effects such as interactions of the background radiation with 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 Silk damping). The acoustic oscillations arise because of a competition 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 dense haloes. 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 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.[55] The third peak can be used to pull information about the dark matter density.[56]
The locations of the peaks also give important information about the nature of the primordial density perturbations. There are two fundamental brands 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.
The CMB spectrum is able to distinguish these two because these two brands 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 1:3:5:..., while adiabatic density perturbations produce peaks whose locations are in the ratio 1:2:3:...[57] 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:
These effects contribute about equally to the suppression of anisotropies on 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 to quantify exactly 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 t+dt is given by P(t)dt.
The maximum of the PVF (the time where it is most likely that a given CMB photon last scattered) is known quite precisely. The first-year WMAP results put the time at which P(t) is maximum as 372±14 ka.[58] This is often taken as the "time" at which the CMB formed. However, to figure out how 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 maximum value (the "full width at half maximum", or FWHM) over an interval of 115±5 ka. By this measure, decoupling took place over roughly 115,000 years, and when it was complete, the universe was roughly 487,000 years old.
Since the CMB came into existence, it has apparently been modified by several subsequent physical processes, which are collectively referred to as late-time anisotropy, or secondary anisotropy. When the CMB photons became free to travel unimpeded, ordinary matter in the universe was mostly in the form of neutral hydrogen and helium atoms. However, observations of galaxies today seem to indicate that most of the volume of the intergalactic medium (IGM) consists of ionized material (since there are few absorption lines due to hydrogen atoms). This implies a period of reionization during which some of the material of the universe was broken into hydrogen ions.
The CMB photons scatter off free charges such as electrons that are not bound in atoms. In an ionized universe, such charged particles have been liberated from neutral atoms by ionizing (ultraviolet) radiation. Today these free charges are at sufficiently low density in most of the volume of the Universe that they do not measurably affect the CMB. However, if the IGM was ionized at very early times when the universe was still denser, then there are two main effects on the CMB:
Both of these effects have been observed by the WMAP spacecraft, providing evidence that the universe was ionized at very early times, at a redshift more than 17. The detailed provenance of this early ionizing radiation is still a matter of scientific debate. It may have included starlight from the very first population of stars (population III stars), supernovae when these first stars reached the end of their lives, or the ionizing radiation produced by the accretion disks of massive black holes.
The time following the emission of the cosmic microwave background—and before the observation of the first stars—is semi-humorously referred to by cosmologists as the dark age, and is a period which is under intense study by astronomers (See 21 centimeter radiation).
Two other effects which occurred between reionization and our observations of the cosmic microwave background, and which appear to cause anisotropies, include the Sunyaev–Zel'dovich effect, where a cloud of high-energy electrons scatters the radiation, transferring some of its energy to the CMB photons, and the Sachs–Wolfe effect, which causes photons from the Cosmic Microwave Background to be gravitationally redshifted or blueshifted due to changing gravitational fields.
The cosmic microwave background is polarized at the level of a few microkelvins. There are two types of polarization, called E-modes and B-modes. This is in analogy to electrostatics, in which the electric field (E-field) has a vanishing curl and the magnetic field (B-field) has a vanishing divergence. The E-modes arise naturally from Thomson scattering in a heterogeneous plasma. The B-modes, which have not been measured and are thought to have an amplitude of at most a 0.1 µK, are not produced from the plasma physics alone. They are a signal from cosmic inflation and are determined by the density of primordial gravitational waves. Detecting the B-modes will be extremely difficult, particularly given that the degree of foreground contamination is unknown, and the weak gravitational lensing signal mixes the relatively strong E-mode signal with the B-mode signal.[59]
Subsequent to the discovery of the CMB, hundreds of cosmic microwave background experiments have been conducted to measure and characterize the signatures of the radiation. The most famous experiment is probably the NASA Cosmic Background Explorer (COBE) satellite that orbited in 1989–1996 and which detected and quantified the large scale anisotropies at the limit of its detection capabilities. Inspired by the initial COBE results of an extremely isotropic and homogeneous background, a series of ground- and balloon-based experiments quantified CMB anisotropies on smaller angular scales over the next decade. The primary goal of these experiments was to measure the angular scale of the first acoustic peak, for which COBE did not have sufficient resolution. These measurements were able to rule out cosmic strings as the leading theory of cosmic structure formation, and suggested cosmic inflation was the right theory. During the 1990s, the first peak was measured with increasing sensitivity and by 2000 the BOOMERanG experiment reported that the highest power fluctuations occur at scales of approximately one degree. Together with other cosmological data, these results implied that the geometry of the Universe is flat. A number of ground-based interferometers provided measurements of the fluctuations with higher accuracy over the next three years, including the Very Small Array, Degree Angular Scale Interferometer (DASI), and the Cosmic Background Imager (CBI). DASI made the first detection of the polarization of the CMB and the CBI provided the first E-mode polarization spectrum with compelling evidence that it is out of phase with the T-mode spectrum.
In June 2001, NASA launched a second CMB space mission, WMAP, to make much more precise measurements of the great scale anisotropies over the full sky. WMAP used symmetric, rapid-multi-modulated scanning, rapid switching radiometers to minimize non-sky signal noise.[53] The first results from this mission, disclosed in 2003, were detailed measurements of the angular power spectrum to below degree scales, tightly constraining various cosmological parameters. The results are broadly consistent with those expected from cosmic inflation as well as various other competing theories, and are available in detail at NASA's data bank for Cosmic Microwave Background (CMB) (see links below). Although WMAP provided very accurate measurements of the great angular-scale fluctuations in the CMB (structures about as broad in the sky as the moon), it did not have the angular resolution to measure the smaller scale fluctuations which had been observed by former ground-based interferometers.
A third space mission, the ESA (European Space Agency) Planck Surveyor, launched in May, 2009 and is currently performing an even more detailed investigation. Planck employs both HEMT radiometers as well as bolometer technology and will measure the CMB on smaller scales than WMAP. Its detectors got a trial run at the Antarctic Viper telescope as ACBAR (Arcminute Cosmology Bolometer Array Receiver) experiment—which has produced the most precise measurements at small angular scales to date—and at the Archeops balloon telescope.
Additional ground-based instruments such as the South Pole Telescope in Antarctica and the proposed Clover Project, Atacama Cosmology Telescope and the QUIET telescope in Chile will provide additional data not available from satellite observations, possibly including the B-mode polarization.
Raw CMBR data coming down from the space vehicle (i.e., WMAP) contain foreground effects that completely obscure the fine-scale structure of the Cosmic Microwave background. The fine-scale structure is superimposed on the raw CMBR data but is too small to be seen at the scale of the raw data. The most prominent of the foreground effects is the dipole anisotropy caused by the Sun's motion relative to the CMBR background. The dipole anisotropy and others due to Earth's annual motion relative to the Sun and numerous microwave sources in the galactic plane and elsewhere must be subtracted out to reveal the extremely tiny variations characterizing the fine-scale structure of the CMBR background.
The detail analysis of CMBR data to produce maps, an angular power spectrum, and ultimately cosmological parameters is a complicated, computationally difficult problem. Although computing a power spectrum from a map is in principle a simple Fourier transform, decomposing the map of the sky into spherical harmonics, in practice it is hard to take the effects of noise and foreground sources into account. In particular, these foregrounds are dominated by galactic emissions such free-free, synchrotron, and dust that emit in the microwave band; in practice, the galaxy has to be removed resulting in a CMB map that is not a full-sky map. In addition, point sources like galaxies and clusters represent another source of foreground which must be removed lest they distort the short scale structure of the CMB power spectrum.
Constraints on many cosmological parameters can be obtained from their effects on the power spectrum, and results are often calculated using Markov Chain Monte Carlo sampling techniques.
From the CMB data it is seen that our local group of galaxies (the galactic cluster that includes the Solar System's Milky Way Galaxy) appears to be moving at 627±22 km/s relative to the reference frame of the CMB (also called the CMB rest frame, or the frame of reference in which there is no motion through the CMB) in the direction of galactic longitude l = 276±3°, b = 30±3°.[60] This motion results in an anisotropy of the data (CMB appearing slightly warmer in the direction of movement than in the opposite direction).[61] The standard interpretation of this temperature variation is a simple velocity redshift and blueshift due to motion relative to the CMB, but alternative cosmological models can explain some fraction of the observed dipole temperature distribution in the CMB.[62]
With the increasingly precise data provided by WMAP, there have been a number of claims that the CMB suffers from anomalies, such as very great-scale anisotropies, anomalous alignments, and non-Gaussian distributions.[63][64][65][66] The most longstanding of these is the low-l multipole controversy. Even in the COBE map, it was observed that the quadrupole (l=2 spherical harmonic) has a low amplitude compared to the predictions of the big bang. Some observers have pointed out that the anisotropies in the WMAP data did not appear to be consistent with the big bang picture. In particular, the quadrupole and octupole (l=3) modes appear to have an unexplained alignment with each other and with the ecliptic plane,[67][68][69] an alignment sometimes referred to as the axis of evil.[64] A number of groups have suggested that this could be the signature of new physics at the greatest observable scales; other groups suspect systematic errors in the data.[70][71][72] Ultimately, due to the foregrounds and the cosmic variance problem, the greatest modes will never be as well measured as the small angular scale modes. The analyses were performed on two maps that have had the foregrounds removed as best as is possible: the "internal linear combination" map of the WMAP collaboration and a similar map prepared by Max Tegmark and others.[46][53][73] Later analyses have pointed out that these are the modes most susceptible to foreground contamination from synchrotron, dust, and free-free emission, and from experimental uncertainty in the monopole and dipole. A full Bayesian analysis of the WMAP power spectrum demonstrates that the quadrupole prediction of Lambda-CDM cosmology is consistent with the data at the 10% level and that the observed octupole is not remarkable.[74] Carefully accounting for the procedure used to remove the foregrounds from the full sky map further reduces the significance of the alignment by ~5%.[75][76][77][78]
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