Inflationary models

Wilkinson Microwave Anisotropy Probe

The Wilkinson Microwave Anisotropy Probe (WMAP) — also known as the Microwave Anisotropy Probe (MAP), and Explorer 80 — measures the temperature of the Big Bang's remnant radiant heat. Headed by Professor Charles L. Bennett, Johns Hopkins University, the mission is a joint project between the NASA Goddard Space Flight Center and Princeton University. The WMAP satellite was launched on 30 June 2001, at 19:46:46 GDT, from Florida. The WMAP succeeds the COBE and medium-class (MIDEX) satellites of the Explorer program. The WMAP honours Dr. David Wilkinson, who died in September of 2002.

The WMAP's measurements are more accurate than previous measurements; per the Lambda-CDM model of the universe, the data indicate the age of the universe is 13.73 ± 0.12 billion years old, with a Hubble constant of 70.1 ± 1.3 km·s-1·Mpc-1, and is composed of 4.6% ordinary baryonic matter; 23% unknown dark matter that neither emits nor absorbs light; 72% dark energy that accelerates expansion; and less than 1% neutrinos — all consistent with a flat geometry, and the ratio of energy density to the critical density Ω = 1.02 ± 0.02. These results support the Lambda-CDM model and the cosmologic scenarios of cosmic inflation, and evidence of cosmic neutrino background radiation.

The data contain unexplained features; an anomaly at the greatest angular measurements of the quadrupole moment and a large cold spot. Per Science magazine, the WMAP was the Breakthrough of the Year for 2003. This mission's results papers were first and second in the "Super Hot Papers in Science Since 2003" list. As of 2008, the WMAP continues working, slated to end in September of 2009.


The WMAP is to measure the temperature differences in the Cosmic Microwave Background (CMB) radiation. The anisotropies then are used to measure the universe's geometry, content, and evolution; and to test the Big Bang model, and the cosmic inflation theory. For that, the mission is creating a full-sky map of the CMB, with a 13 arcminute resolution via multi-frequency observation. The map requires the fewest systematic errors, no correlated pixel noise, and accurate calibration, to ensure angular-scale accuracy greater than its resolution. The map contains 3,145,728 pixels, and uses the HEALPix scheme to pixelize the sphere. The telescope also measures the CMB's E-mode polarization, and foreground polarization; its life is 27 months; 3 to reach the L2 position, 2 years of observation.


The MAP mission was proposed to NASA in 1995, selected for definition study in 1996, and approved for development in 1997.

The WMAP was preceded by two missions to observe the CMB; (i) the Soviet RELIKT-1 that reported the upper-limit measurements of CMB anisotropies, and (ii) the U.S. COBE satellite that reported large-scale CMB fluctuations, and the ground-based and balloon experiments measuring the small-scale fluctuations in patches of sky: the Boomerang, the Cosmic Background Imager, and the Very Small Array. The WMAP is 45 times more sensitive, with 33 times the angular resolution of its COBE satellite predecessor.

The spacecraft

The telescope's primary reflecting mirrors are a pair of Gregorian 1.4m x 1.6m dishes (facing opposite directions), that focus the signal onto a pair of 0.9m x 1.0m secondary reflecting mirrors. They are shaped for optimal performance: a carbon fibre shell upon a Korex core, thinly-coated with aluminium and silicon oxide. The secondary reflectors transmit the signals to the corrugated feedhorns that sit on a focal plane array box beneath the primary reflectors.

The receivers are differential radiometers (sensitive to polarization) measuring the difference between a two telescope beams. The signal is amplified with HEMT low-noise amplifiers. There are 20 feeds, 10 in each direction, from which a radiometer collects a signal; the measure is the difference in the sky signal from opposite directions. The directional separation azimuth is 180 degrees; the total angle is 141 degrees. To avoid collecting Milky Way galaxy foreground signals, the WMAP uses five discrete radio frequency bands, from 23GHz to 94GHz.

Properties of WMAP at different frequencies
Property K-band Ka-band Q-band V-band W-band
Central wavelength (mm) 13 9.1 7.3 4.9 3.2
Central frequency (GHz) 23 33 41 61 94
Bandwidth (GHz) 5.5 7.0 8.3 14.0 20.5
Beam size (arcminutes) 52.8 39.6 30.6 21 13.2
Number of radiometers 2 2 4 4 8
System temperature (K) 29 39 59 92 145
Sensitivity (mK s^{1/2}) 0.8 0.8 1.0 1.2 1.6

The WMAP's base is a 5.0m-diameter solar panel array that keeps the instruments in shadow during CMB observations, (by keeping the craft constantly angled at 22 degrees, relative to the sun). Upon the array sit a bottom deck (supporting the warm components) and a top deck. The telescope's cold components: the focal-plane array and the mirrors, are separated from the warm components with a cylindrical, 33cm-long thermal isolation shell atop the deck.

Passive thermal radiators cool the WMAP to ca. 90 degrees K; they are connected to the low-noise amplifiers. The telescope consumes 419 W of power. The available telescope heaters are emergency-survival heaters, and there is a transmitter heater, used to warm them when off. The WMAP spacecraft's temperature is monitored with platinum resistance thermometers.

The WMAP's calibration is effected with the CMB dipole and measurements of Jupiter; the beam patterns are measured against Jupiter. The telescope's data are relayed daily via a 2GHz transponder providing a 667kbs downlink to a 70m Deep Space Network telescope. The spacecraft has two transponders, one a redundant back-up; they are minimally active — ca. 40 minutes daily — to minimize radio frequency interference. The telescope's position is maintained, in its three axes, with three reaction wheels, gyroscopes, two star trackers and sun sensors, and is steered with eight hydrazine thrusters.

Launch, trajectory, and orbit

The WMAP satellite arrived at the Kennedy Space Center on 20 April 2001, was tested for two months, mounted atop a Delta II 7425 rocket, and fired to outer space on 30 June 2001. It began operating on its internal power five minutes before its launching, and so continued operating until the solar panel array deployed. The WMAP was activated and monitored while it cooled. On 2 July, it began working, first with in-flight testing (from launching 'til 17 August), then began constant, formal work. Afterwards, it effected three Earth-Moon phase loops, measuring its sidelobes, then flew by the Moon on 30 July, enroute to the the L2 Sun-Earth Lagrangian point, arriving there on 1 October 2001, becoming, thereby, the first CMB observation mission permanently posted there.

The satellite's orbit at Lagrange 2, (1.5 million kilometers from Earth) minimizes the amount of contaminating solar, terrestrial, and lunar emissions registered, and to thermally stabilize it. To view the entire sky, without looking to the sun, the WMAP orbits around L2 in a Lissajous orbit ca. 1.0 degree to 10 degrees, with a 6-month period. The telescope rotates once every 2 minutes, 9 seconds" (0.464 rpm) and precesses at the rate of 1 revolution per hour. WMAP measures the entire sky every six months, and completed its first, full-sky observation in April of 2002.

Foreground radiation subtraction

The WMAP observes in five frequencies, permitting the measurement and subtraction of foreground contamination (from the Milky Way and extra-galactic sources) of the CMB. The main emission mechanisms are synchrotron radiation and free-free emission (dominating the lower frequencies), and astrophysical dust emissions (dominating the higher frequencies). The spectral properties of these emissions contribute different amounts to the five frequencies, thus permitting their identification and subtraction.

Foreground contamination is removed in several ways. First, subtract extant emission maps from the WMAP's measurements; second, use the components' known, spectral values to identify them; third, simultaneously fit the position and spectra data of the foreground emission, using extra data sets. Foreground contamination also is reduced by using only the the full-sky map portions with the least foreground contamination, whilst masking the remaining map portions.

The five-year models of foreground emission, at different frequencies. Red = Synchrotron; Green = free-free; Blue = thermal dust.
23 GHz 33 GHz 41 GHz 61 GHz 94 GHz

Measurements and discoveries

One-year data release

On 11 February 2003, based upon one year's worth of WMAP data, NASA published the latest calculated age, composition, and image of the universe to date, that \"contains such stunning detail, that it may be one of the most important scientific results of recent years\"; the data surpass previous CMB measurements.

Based upon the Lambda-CDM model, the WMAP team produced cosmological parameters from the WMAP's first-year results. Three sets are given below; the first and second sets are WMAP data; the difference is the addition of spectral indices, predictions of some inflationary models. The third data set combines the WMAP constraints with those from other CMB experiments (ACBAR and CBI), and constraints from the 2dF Galaxy Redshift Survey and Lyman alpha forest measurements. Note that there are degenerations among the parametres, the most significant is between n_s and tau; the errors given are at 68% confidence.

Best-fit cosmological parameters from WMAP one-year results
Parameter Symbol Best fit (WMAP only) Best fit (WMAP, extra parameter) Best fit (all data)
Hubble's constant ( ) H_0 0.72 ± 0.05 0.70 ± 0.05 0.71^{+0.04}_{-0.03}
Baryonic content Omega_b h^2 0.024 ± 0.001 0.023 ± 0.002 0.0224 ± 0.0009
Matter content Omega_m h^2 0.14 ± 0.02 0.14 ± 0.02 0.135^{+0.008}_{-0.009}
Optical depth to reionization tau 0.166^{+0.076}_{-0.071} 0.20 ± 0.07 0.17 ± 0.06
Amplitude A 0.9 ± 0.1 0.92 ± 0.12 0.83^{+0.09}_{-0.08}
Scalar spectral index n_s 0.99 ± 0.04 0.93^{+0.07}_{-0.07} 0.93 ± 0.03
Running of spectral index dn_s / dk -0.047 ± 0.04 -0.031^{+0.016}_{-0.017}
Fluctuation amplitude at 8h−1 Mpc sigma_8 0.9 ± 0.1 0.84 ± 0.04
Age of the universe (Ga) t_0 13.4 ± 0.3 13.7 ± 0.2
Total density of the universe Omega_{tot} 1.02 ± 0.02
Using the best-fit data and theoretical models, the WMAP team determined the times of important universal events, including the redshift of reionization, 17 ± 4; the redshift of decoupling, 1089 ± 1 (and the universe's age at decoupling, 379^{+8}_{-7} kyr); and the redshift of matter/radiation equality, 3233^{+194}_{-210}. They determined the thickness of the surface of last scattering to be 195 ± 2 in redshift, or 118^{+3}_{-2} kyr. They determined the current density of baryons, (2.5 pm 0.1) times 10^{-7} cm^{-1}, and the ratio of baryons to photons, (6.1^{+0.3}_{-0.2}) times 10^{-10}. The WMAP's detection of an early reionization excluded warm dark matter.

The team also examined Milky Way emissions at the WMAP frequencies, producing a 208-point source catalogue. Also, they observed the Sunyaev-Zel'dovich effect at 2.5 sigma the strongest source is the Coma cluster.

Three-year data release

The three-year WMAP data were released on March 17, 2006. The data included temperature and polarization measurements of the CMB, which provided further confirmation of the standard flat Lambda-CDM model and new evidence in support of inflation.

The 3-year WMAP data alone shows that the universe must have dark matter. Results were computed both only using WMAP data, and also with a mix of parameter constraints from other instruments, including other CMB experiments (ACBAR, CBI and BOOMERANG), SDSS, the 2dF Galaxy Redshift Survey, the Supernova Legacy Survey and constraints on the Hubble constant from the Hubble Space Telescope.

Best-fit cosmological parameters from WMAP three-year results
Parameter Symbol Best fit (WMAP only)
Hubble's constant ( ) H_0 0.732^{+0.031}_{-0.032}
Baryonic content Omega_b h^2 0.0229 ± 0.00073
Matter content Omega_m h^2 0.1277^{+0.0080}_{-0.0079}
Optical depth to reionization tau 0.089 ± 0.030
Scalar spectral index n_s 0.958 ± 0.016
Fluctuation amplitude at 8h−1 Mpc sigma_8 0.761^{+0.049}_{-0.048}
Age of the universe (Ga) t_0 13.73^{+0.16}_{-0.15}
Tensor-to-scalar ratio r <0.65
[a] Optical depth to reionization improved due to polarization measurements.
[b] < 0.30 when combined with SDSS data. No indication of non-gaussianity.

Five-year data release

The five-year WMAP data were released on February 28, 2008. The data included new evidence for the cosmic neutrino background, evidence that it took over half a billion years for the first stars to reionize the universe, and new constraints on cosmic inflation.

The improvement in the results came from both having an extra 2 years of measurements (the data set runs between midnight on 10 August 2001 to midnight of 9 August 2006), as well as using improved data processing techniques and a better characterization of the instrument, most notably of the beam shapes. They also make use of the 33GHz observations for estimating cosmological parameters; previously only the 41 and 61GHz channels had been used. Finally, improved masks were used to remove foregrounds.

Improvements to the spectra were in the 3rd acoustic peak, and the polarization spectra.

The measurements put constraints on the content of the universe at the time that the CMB was emitted; at the time 10% of the universe was made up of neutrinos, 12% of atoms, 15% of photons and 63% dark matter. The contribution of dark energy at the time was negligible.

The WMAP five-year data was combined with measurements from Type Ia supernova (SNe) and Baryon acoustic oscillations (BAO).

Best-fit cosmological parameters from WMAP five-year results
Parameter Symbol Best fit (WMAP only) Best fit (WMAP + SNe + BAO)
Hubble's constant ( ) H_0 0.719^{+0.026}_{-0.027} 0.701 ± 0.013
Baryonic content Omega_b h^2 0.02273 ± 0.00062 0.02265 ± 0.00059
Cold dark matter content Omega_c h^2 0.1099 ± 0.0062 0.1143 ± 0.0034
Dark energy content Omega_Lambda 0.742 ± 0.030 0.721 ± 0.015
Optical depth to reionization tau 0.087 ± 0.017 0.084 ± 0.016
Scalar spectral index n_s 0.963^{+0.014}_{-0.015} 0.960^{+0.014}_{-0.013}
Running of spectral index dn_s / dk −0.037 ± 0.028 -0.032^{+0.021}_{-0.020}
Fluctuation amplitude at 8h−1 Mpc sigma_8 0.796 ± 0.036 0.817 ± 0.026
Age of the universe (Ga) t_0 13.69 ± 0.13 13.73 ± 0.12
Total density of the universe Omega_{tot} 1.099^{+0.100}_{-0.085} 1.0052 ± 0.0064
Tensor-to-scalar ration r <0.20
The data puts a limits on the value of the tensor-to-scalar ratio, r < 0.20 (95% certainty), which determines the level at which gravitational waves affect the polarization of the CMB, and also puts limits on the amount of primordial non-gaussianity. Improved constraints were put on the redshift of reionization, which is 10.8 ± 1.4, the redshift of decoupling, 1091.00^{+0.72}_{-0.73} (as well as age of universe at decoupling, 375,938^{+3148}_{-3115} years) and the redshift of matter/radiation equality, 3280^{+88}_{-89}.

The extragalactic source catalogue was expanded to include 390 sources, and variability was detected in the emission from Mars and Saturn.

The five-year maps at different frequencies from WMAP with foregrounds (the red band)
23 GHz 33 GHz 41 GHz 61 GHz 94 GHz

Future measurements

The original timeline for WMAP gave it two years of observations; these were completed by September 2003. Mission extensions were granted in both 2002 and 2004, giving the spacecraft a total of 8 observing years (the originally proposed duration), which end in September 2009.

WMAP's results will be built upon by several other instruments that are currently under construction. These will either be focusing on higher sensitivity total intensity measurements or measuring the polarization more accurately in the search of B-mode polarization indicative of primordial gravitational waves.

The next space-based instrument will be the Planck satellite, which is currently being built and will launch towards the end of 2008. This instrument aims to measure the CMB more accurately than WMAP at all angular scales, both in total intensity and polarization. Various ground- and balloon-based instruments are being constructed to look for B-mode polarization, including Clover and EBEX.


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