Accepted for Publication in the Astrophysical Journal Supplement Series A Preprint typeset using L TEX style emulateapj v. 08/13/06 FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP1) OBSERVATIONS: COSMOLOGICAL INTERPRETATION E. Komatsu 1, J. Dunkley 2,3,4, M. R. Nolta 5, C. L. Bennett 6, B. Gold 6, G. Hinshaw 7, N. Jarosik 2, D. Larson 6, M. Limon 8 L. Page 2, D. N. Spergel 3,9, M. Halpern 10, R. S. Hill 11, A. Kogut 7, S. S. Meyer 12, G. S. Tucker 13, J. L. Weiland 11, E. Wollack 7, and E. L. Wright 14 Accepted for Publication in the Astrophysical Journal Supplement Series ABSTRACT The WMAP 5-year data provide stringent limits on deviations from the minimal, 6-parameter ΛCDM model. We report these limits and use them to constrain the physics of cosmic inflation via Gaussianity, adiabaticity, the power spectrum of primordial fluctuations, gravitational waves, and spatial curvature. We also constrain models of dark energy via its equation of state, parity- violating interaction, and neutrino properties such as mass and the number of species. We detect no convincing deviations from the minimal model. The 6 parameters and the corresponding 68% uncertainties, derived from the WMAP data combined with the distance measurements from the Type Ia supernovae (SN) and the Baryon Acoustic Oscillations (BAO) in the distribution of galaxies, 2 +0:00058 2 are: Ωbh = 0:02267−0:00059, Ωch = 0:1131 0:0034, ΩΛ = 0:726 0:015, ns = 0:960 0:013, 2 −9 −1 τ = 0:084 0:016, and ∆R = (2:445 0:096) 10 at k = 0:002 Mpc . From these we derive −1 × −1 σ8 = 0:812 0:026, H0 = 70:5 1:3 km s Mpc , Ωb = 0:0456 0:0015, Ωc = 0:228 0:013, 2 +0:0037 WMAP Ωmh = 0:1358−0:0036, zreion = 10:9 1:4, and t0 = 13:72 0:12 Gyr. With the data combined with BAO and SN, we find the limit on the tensor-to-scalar ratio of r < 0:22 (95% CL), and that ns > 1 is disfavored even when gravitational waves are included, which constrains the models of inflation that can produce significant gravitational waves, such as chaotic or power-law inflation models, or a blue spectrum, such as hybrid inflation models. We obtain tight, simultaneous limits on the (constant) equation of state of dark energy and the spatial curvature of the universe: 0:14 < 1 + w < 0:12 (95% CL) and 0:0179 < Ωk < 0:0081 (95% CL). We provide a set of \WMAP distance− priors," to test a variety of−dark energy models with spatial curvature. We test a time- dependent w with a present value constrained as 0:33 < 1 + w0 < 0:21 (95% CL). Temperature and dark matter fluctuations are found to obey −the adiabatic relation to within 8.9% and 2.1% for the axion-type and curvaton-type dark matter, respectively. The power spectra of TB and EB correlations constrain a parity-violating interaction, which rotates the polarization angle and converts E to B. The polarization angle could not be rotated more than 5:9◦ < ∆α < 2:4◦ (95% CL) between the decoupling and the present epoch. We find the limit on the− total mass of massive neutrinos of mν < 0:67 eV (95% CL), which is free from the uncertainty in the normalization of the large- scale structure data. The number of relativistic degrees of freedom, expressed in units of the effective nPumber of neutrino species, is constrained as Neff = 4:4 1:5 (68%), consistent with the standard value of 3.04. Finally, quantitative limits on physically motivated primordial non-Gaussianity parameters local equil are 9 < fNL < 111 (95% CL) and 151 < fNL < 253 (95% CL) for the local and equilateral models,− respectively. − Subject headings: cosmic microwave background, cosmology: observations, early universe, dark matter, space vehicles, space vehicles: instruments, instrumentation: detectors, telescopes 1. INTRODUCTION Electronic address: [email protected] 1 WMAP is the result of a partnership between Princeton Uni- Measurements of microwave background fluctuations versity and NASA's Goddard Space Flight Center. Scientific guid- by the Cosmic Background Explorer (COBE ; Smoot ance is provided by the WMAP Science Team. et al. 1992; Bennett et al. 1994, 1996), the Wilkinson 1 Univ. of Texas, Austin, Dept. of Astronomy, 2511 Speedway, RLM 15.306, Austin, TX 78712 2 Dept. of Physics, Jadwin Hall, Princeton University, Prince- Code 5247, New York, NY 10027-6902 ton, NJ 08544-0708 9 Princeton Center for Theoretical Physics, Princeton Univer- 3 Dept. of Astrophysical Sciences, Peyton Hall, Princeton Uni- sity, Princeton, NJ 08544 versity, Princeton, NJ 08544-1001 10 Dept. of Physics and Astronomy, University of British 4 Astrophysics, University of Oxford, Keble Road, Oxford, OX1 Columbia, Vancouver, BC Canada V6T 1Z1 3RH, UK 11 Adnet Systems, Inc., 7515 Mission Dr., Suite A100, Lanham, 5 Canadian Institute for Theoretical Astrophysics, 60 St. George Maryland 20706 St, University of Toronto, Toronto, ON Canada M5S 3H8 12 Depts. of Astrophysics and Physics, KICP and EFI, Univer- 6 Dept. of Physics & Astronomy, The Johns Hopkins University, sity of Chicago, Chicago, IL 60637 3400 N. Charles St., Baltimore, MD 21218-2686 13 Dept. of Physics, Brown University, 182 Hope St., Providence, 7 Code 665, NASA/Goddard Space Flight Center, Greenbelt, RI 02912-1843 MD 20771 14 UCLA Physics & Astronomy, PO Box 951547, Los Angeles, 8 Columbia Astrophysics Laboratory, 550 W. 120th St., Mail CA 90095-1547 2 Komatsu et al. Microwave Anisotropy Probe (WMAP; Bennett et al. Gaussianity/adiabaticity/scale-invariance of the primor- 2003a,b), and ground and balloon-borne experiments dial fluctuations, and the amplitude of primordial grav- (Miller et al. 1999, 2002; de Bernardis et al. 2000; Hanany itational waves. We discuss their implications for the et al. 2000; Netterfield et al. 2002; Ruhl et al. 2003; Ma- physics of the early, primordial universe. In 4 we son et al. 2003; Sievers et al. 2003, 2007; Pearson et al. demonstrate that the power spectra of TB and EBx cor- 2003; Readhead et al. 2004; Dickinson et al. 2004; Kuo relations16 which are usually ignored in the cosmologi- et al. 2004, 2007; Reichardt et al. 2008; Jones et al. 2006; cal analysis, can be used to constrain a certain parity- Montroy et al. 2006; Piacentini et al. 2006) have ad- violating interaction that couples to photons. In 5 we dressed many of the questions that were the focus of explore the nature of dark energy, and in 6 wexstudy cosmology for the past 50 years: How old is the uni- the properties of neutrinos in cosmology. Wxe conclude in verse? How fast is it expanding? What is the size and 7. shape of the universe? What is the composition of the x universe? What seeded the formation of galaxies and 2. SUMMARY OF 5-YEAR ANALYSIS large-scale structure? 2.1. WMAP 5-year data: temperature and polarization By accurately measuring the statistical properties of the microwave background fluctuations, WMAP has With 5 years of observations of Jupiter and an ex- helped establish a standard cosmology: a flat ΛCDM tensive physical optics modeling of beams (Hill et al. model composed of atoms, dark matter and dark energy, 2008), our understanding of the beam transfer function, with nearly scale-invariant adiabatic Gaussian fluctua- bl, has improved significantly: the fractional beam errors, ∆b =b , have been nearly halved in most Differencing As- tions. With our most recent measurements, WMAP has l l measured the basic parameters of this cosmology to high semblies (DAs). In some cases, e.g., W4, the errors have been reduced by as much as a factor of 4. precision: with the WMAP 5-year data alone, we find Many of the small-scale CMB experiments have been the density of dark matter (21.4%), the density of atoms WMAP (4.4%), the expansion rate of the universe, the ampli- calibrated to the 3-year data at high multi- tude of density fluctuations, and their scale dependence, poles. Since the new beam model raises the 5-year as well as the optical depth due to reionization (Dunkley power spectrum almost uniformly by 2:5% relative to the 3-year power spectrum over l &∼200 (Hill et al. et al. 2008). Cosmologists are now focused on a new set of ques- 2008), those small-scale CMB experiments have been under-calibrated by the same amount, i.e., 2:5% in tions: What is the nature of the dark energy? What ∼ is the dark matter? Did inflation seed the primordial power, and 1:2% in temperature. For example, the fluctuations? If so, what is the class of the inflationary latest ACBAR data (Reichardt et al. 2008) report on model? How did the first stars form? Microwave back- the calibration error of 2.23% in temperature (4.5% in ground observations from WMAP, Planck, and from the power), which is twice as large as the magnitude of mis- calibration; thus, we expect the effect of mis-calibration upcoming generation of CMB ground and balloon-borne experiments will play an important role in addressing to be sub-dominant in the error budget. Note that the change in the beam is fully consistent with the 1-σ er- these questions. WMAP This paper will discuss how the WMAP results, partic- ror of the previous beam reported in Page et al. (2003). Since the ACBAR calibration error includes the ularly when combined with other astronomical observa- WMAP tions (mainly the distance measurements), are now pro- previous beam error, the change in the beam viding new insights into these questions through con- should have a minimal impact on the current ACBAR calibration.