First year results from the

Wilkinson Microwave Anisotropy Probe (WMAP)

Rachel Bean, Princeton Collaboration rbean@astro.princeton.edu

The cosmic microwave background (CMB), along with the distribution of large scale structure, has become one of the principal tools for deciphering the cosmological content and history of the universe. The WMAP satellite, launched on June 30, 2001, completed its first full year of measurements of the CMB in August 2002, with the data analyzed and published earlier this year. This article presents a brief summary of the approach and key findings from the mission's first results. For further details see [1] and the 12 companion papers referred to within it, in particular this article focuses on the cosmological parameters extracted from the data discussed in [2].

For those not familiar with the CMB, it is comprised of photons that interacted strongly with the plasma of free electrons and baryonic ions in the early universe. At this time the photon mean free path was short and the universe was effectively opaque. As the universe expanded and subsequently cooled below 3000K, 380,000 years after the Big Bang, electrons recombined with nuclei and fewer charged particles were present to interact with the CMB photons, the photons `decoupled' from the rest of the matter and the universe became transparent. The distribution of temperature and polarization fluctuations that we measure today in the CMB are therefore effectively those imprinted at the epoch of recombination,``the decoupling surface".

Within the last decade, starting with the results from COBE [3], a plethora of experiments have measured the anisotropy in the fluctuations in the CMB temperature. Together they have incontrovertibly detected the first acoustic peak of oscillations in the CMB power spectrum. This peak arises from oscillations in the coupled photon- baryon fluid just prior to when photons decoupled and is direct experimental support for the CMB being decoupled photons and for the standard recombination model. In addition, last year, there was the first detection of anisotropy in the polarization of the CMB [4].

WMAP was created with the aim of extending on previous observations in two main ways: to make a map of the full sky, and to measure the CMB with much improved precision by minimizing systematic errors. The precision is obtained through measuring the CMB over five frequency bands, which allow external contaminants such as dust and point sources to be removed more efficiently. WMAP observes the sky convolved with the beam pattern (the ``window function") of the detectors. Imperfect knowledge of the window function is one of the main internal systematics and therefore minimizing this uncertainty by accurate in-flight determination of the beam patterns has also been a key factor in achieving WMAP's precision. Figure 1 shows the improved resolution of the WMAP results in comparison to the only previous full sky map, that of COBE. Also shown is the power spectrum of fluctuations measured by WMAP for temperature-temperature ``TT" and temperature-polarization ``TE" correlations , in multipoles, $l$, from spherical harmonic decomposition of the sky,.

Figure 1: Left panel: An all-sky image of the Universe 380,000 years after the Big Bang. In 1992, NASA's COBE mission first detected tiny temperature fluctuations (shown as color variations) in the infant universe. The WMAP's improved resolution brings the COBE picture into sharper focus. Right panel: The ``angular spectrum" of the fluctuations in the WMAP full-sky map. The top curve shows the power spectrum for the temperature fluctuations, while the lower curve shows the cross correlation of temperature with polarization. In each figure the best fit cosmological model is shown in red for the `standard' scenario discussed in the text. The grey region shows the `cosmic variance', the inherent statistical uncertainty in the measurements arising from the simple fact that we can only ever measure one sky.
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One of the key applications of the WMAP data is to constrain cosmological models. A `standard' model has established itself over the last few decades, consistent with observations from galactic scales to the largest scales observable, in which the universe is spatially flat, and homogeneous and isotropic on large scales, and comprises radiation, normal matter (electrons, baryons, neutrinos), non-baryonic cold, dark matter, and dark energy.

In addition to the matter constituents, WMAP also tests several important predictions of the inflationary scenario. Inflation predicts that the universe is spatially flat and that fluctuations in radiation and matter energy density are Gaussian with a nearly scale invariant spectrum, $n_{s}\approx 1$.

WMAP is a critical test of these models, and finds them in good agreement with the data. Under the assumption of flatness the CMB can constrain a range of parameters on its own: the Hubble constant, $H_{0}=100 \ h$ km/s/Mpc, is found to be $h=0.72\pm0.05$ (all error bars are at the 68% level), the universe is found to have an age of 13.4 $\pm$ 0.03 Gyr. For a measure of the dark matter density today, as a fraction of the critical density (to give flat spatial curvature) $\Omega_{m}$, WMAP finds $\Omega_{m}h^{2}=0.14\pm0.02$, and similarly for the fractional baryon density $\Omega_{b}h^{2}=0.024\pm0.001$, this latter one in good agreement with constraints from nucleosynthesis. The optical depth to the decoupling surface, $\tau$, determined by the history of recombination and re-ionization, is also constrained although it is highly degenerate with the spectral tilt, $n_{s}$. WMAP has made the first measurements of CMB polarization that can be used as an independent measurement of $\tau$ and seems to give the strongest evidence yet for an epoch of re-ionization. With TT and TE data combined WMAP finds, $\tau=0.166^{+0.076}_{-0.071}$ and $n_{s}=0.99\pm0.04$. The value of $\tau$ signals that re-ionization occurred earlier than previously expected, at around a redshift of 17$\pm 5$. Early re-ionization implies that structure was forming at these redshifts providing evidence against the presence of significant warm dark matter which would suppress structure formation until much later times.

A spectral index close to unity is one finding that is consistent with inflation. In addition to this WMAP also finds that the fluctuations are entirely consistent with Gaussianity, and have placed the tightest constraints yet on the level of non-Gaussianity within the primordial spectrum. Testing the inflationary prediction of flatness is made difficult by the presence of a geometrical degeneracy between the fractional energy densities of spatial curvature and dark energy. A determination of the spatial curvature and dark energy contributions can only be obtained by breaking this degeneracy through the inclusion of independent data sets such as the HST Key Project measurement of $h=0.72\pm0.05$ [5]. The data then shows a strong preference for flatness ( $\Omega_{tot}=1$) finding $\Omega_{tot}=1.02\pm0.02$. In combination with complementary data sets, the WMAP data implies that the universe today is made up of 73% dark energy, 22% dark matter and 4.4% baryons.

The standard models described above employ the smallest number of parameters to fit the data, however the CMB in combination with external data sets can be used to probe beyond these to more exotic models. One good example of this is the placing of constraints on the equation of state of dark energy, $w$; the additional inclusion of supernovae observations indicates $w<-0.78$, and is entirely consistent with the presence of a cosmological constant $\Lambda$ which has $w=-1$. WMAP, in combination with the 2dF galaxy [6] and Lyman $\alpha$ [7] power spectra, tends to favor a varying spectral tilt i.e. d$n_{s}$/d$\ln k \neq 0$. This variation is a prediction of inflation but further analysis and data will help to ascertain if the effect really is arising from subtleties of the primordial spectrum.

WMAP continues to collect data and its planned operation is for at least 4 years. It is hoped that this will lead to even better understanding of systematics, better resolution at smaller scales and improved measurement of the polarization. We are looking forward to an exciting era in cosmology promising the elucidation of the matter content and ionization history of the universe as well as a clearer understanding of the inflationary epoch.

References:

[1] Bennett, C. et al., accepted by ApJ, astro-ph/0302208.

[2] Spergel, D. et al., accepted by ApJ, astro-ph/0302209.

[3] Bennett, C. et al., ApJ, 396, (1992) L7.

[4] Kovac, J. et al., Nature 420 (2002) 772.

[5] Freedman, W. L. et al., ApJ 553 (2001) 47.

[6] Percival, W. J. et al., MNRAS 327 (2001) 1297.

[7] Croft, R. A. C. et al., ApJ 581 (2002) 20; Gnedin N. Y. et al., MNRAS 334 (2002) 107.


Jorge Pullin 2003-09-15