Three‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Implications for Cosmology

Abstract

A simple cosmological model with only six parameters (matter density, m h 2 , baryon density, b h 2 , Hubble constant, H 0 , amplitude of fluctuations, 8 , optical depth, , and a slope for the scalar perturbation spectrum, n s ) fits not only the 3 year WMAP temperature and polarization data, but also small-scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the bestfit values for cosmological parameters for the power-law flat à cold dark matter (ÃCDM) model are ( m h 2 ; b h 2 ; h; n s ; ; 8 ) ¼ (0:1277 þ0:0080 À0:0079 ;0:02229 AE 0:00073;0:732 þ0:031 À0:032 ;0:958 AE 0:016;0:089 AE 0:030; 0:761 þ0:049 À0:048 ). The 3 year data dramatically shrink the allowed volume in this six-dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power-law spectrum, the WMAP data alone require dark matter and favor a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n s ¼ 1; r ¼ 0). Adding additional data sets improves the constraints on these components and the spectral slope. For power-law models, WMAP data alone puts an improved upper limit on the tensor-to-scalar ratio, r 0:002 < 0:65 (95% CL) and the combination of WMAP and the lensing-normalized SDSS galaxy survey implies r 0:002 < 0:30 (95% CL). Models that suppress largescale power through a running spectral index or a large-scale cutoff in the power spectrum are a better fit to the WMAP and small-scale CMB data than the power-law ÃCDM model; however, the improvement in the fit to the WMAP data is only Á 2 ¼ 3 for 1 extra degree of freedom. Models with a running-spectral index are consistent with a higher amplitude of gravity waves. In a flat universe, the combination of WMAP and the Supernova Legacy Survey (SNLS) data yields a significant constraint on the equation of state of the dark energy, w ¼ À0:967 þ0:073 À0:072 . If we assume w ¼ À1, then the deviations from the critical density, K , are small: the combination of WMAP and the SNLS data implies k ¼ À0:011 AE 0:012. The combination of WMAP 3 year data plus the HST Key Project constraint on H 0 implies k ¼ À0:014 AE 0:017 and à ¼ 0:716 AE 0:055. Even if we do not include the prior that the universe is flat, by combining WMAP, large-scale structure, and supernova data, we can still put a strong constraint on the dark energy equation of state, w ¼ À1:08 AE 0:12. For a flat universe, the combination of WMAP and other astronomical data yield a constraint on the sum of the neutrino masses, P m < 0:66 eV (95%CL). Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps using Minkowski functionals, the bispectrum, trispectrum, and a new statistic designed to detect large-scale anisotropies in the fluctuations. Subject headingg s: cosmic microwave background -cosmology: observations

Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

“…Following [52], we used a modified version of the CAMB code [10] to compute the CMB temperature and polarisation anisotropies seeded by the slow-roll scalar and tensor primordial power spectra of equation (45). The parameter space has been sampled by using Markov Chain Monte Carlo (MCMC) methods implemented in the COSMOMC code [11] and using the likelihood estimator provided by the WMAP team [2,4,3,1]. The likelihood code settings have been kept to their default values which include the pixel based analysis at large scales, a Gaussian likelihood for the beam, with diagonal covariance matrix, and point source corrections [3,53,6].…”

“…Let us notice that, even if ǫ 1 ≪ 1 while inflation is proceeding, one could have ǫ 2 1 at some point [80]. In such a case, inflation would not stop but the slow-roll approximation would break down when ǫ 2 = 1.…”

“…In particular, it is important to known whether it is necessary to go beyond a simple Harrison-Zeldovitch (scale-invariant) power spectrum to correctly fit the data. If so, as indicated by the results of reference [2] and from a model building point of view, this means that the inflaton potential is not completely flat and/or that inflation is not driven by a pure cosmological constant. Equivalently, this also means that the observations start feeling the non-trivial shape of the potential.…”

“…The recent release of the three years WMAP data [1,2,3,4] constitutes an important step for the theory of inflation. One now has at our disposal high accuracy data that can be used to probe the details of the inflationary scenario and to learn about the physical conditions that prevailed in the very early universe, at very high energies comparable to the Grand Unified Theory (GUT) scale.…”

“…These exact power spectra are computed mode by mode and fed into a modified Cosmic Background Microwave (CMB) code, here a modified CAMB code [10], which allows us to determine the temperature and polarisation multipole moments. Finally, we explore the corresponding parameters space by using MonteCarlo techniques as implemented in the COSMOMC code [11] together with the likelihood code developed by the WMAP team [2]. This allows us to put constraints on the free parameters characterising the models during the inflationary phase but also, in principle, during the reheating phase although, most of the time, the accuracy of the data is not sufficient to obtain relevant limits on the reheating temperature.…”