A flat Universe from high-resolution maps of the cosmic microwave background radiation P.ÊDEÊBERNARDIS, P.ÊA.ÊR.ÊADE, J.ÊJ.ÊBOCK, J.ÊR.ÊBOND, J.ÊBORRILL, A.ÊBOSCALERI, K.ÊCOBLE, B.ÊP.ÊCRILL, G.ÊDEÊGASPERIS, P.ÊC.ÊFARESE, P.ÊG.ÊFERREIRA, K.ÊGANGA, M.ÊGIACOMETTI, E.ÊHIVON, V.ÊV.ÊHRISTOV, A.ÊIACOANGELI, A.ÊH.ÊJAFFE, A.ÊE.ÊLANGE, L.ÊMARTINIS, S.ÊMASI, P.ÊV.ÊMASON, P.ÊD.ÊMAUSKOPF, A.ÊMELCHIORRI, L.ÊMIGLIO, T.ÊMONTROY, C.ÊB.ÊNETTERFIELD, E.ÊPASCALE, F.ÊPIACENTINI, D.ÊPOGOSYAN, S.ÊPRUNET, S.ÊRAO, G.ÊROMEO, J.ÊE.ÊRUHL, F.ÊSCARAMUZZI, D.ÊSFORNA & N.ÊVITTORIO Dipartimento di Fisica, Universita' di Roma "La Sapienza", P.le A. Moro 2, 00185 Roma, Italy. Department of Physics, Queen Mary and Westfield College , Mile End Road, London E1 4NS, UK. Jet Propulsion Laboratory, Pasadena, California 91109, USA. CITA University of Toronto, Toronto M5S 3H8, Canada. NERSC-LBNL, Berkeley, California 94720, USA. IROEÐCNR, Via Panciatichi 64, 50127 Firenze, Italy. Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106 , USA. California Institute of Technology, Mail Code 59-33, Pasadena, California 91125 , USA. Dipartimento di Fisica, Universita' di Roma Tor Vergata , Via della Ricerca Scientifica 1, 00133 Roma, Italy. Astrophysics, University of Oxford, Keble Road, OX1 3RH, UK. PCC, College de France, 11 pl. Marcelin Berthelot, 75231 Paris Cedex 05, France . Center for Particle Astrophysics, University of California at Berkeley, 301 Le Conte Hall, Berkeley, California 94720, USA. ENEA Centro Ricerche di Frascati, Via E. Fermi 45, 00044 Frascati, Italy. Physics and Astronomy Department, Cardiff University , Cardiff CF2 3YB, UK. Department of Physics and Astronomy, University of Massachusetts, Amherst, Massachusetts 01003 , USA. Department of Physics and Astronomy, University of Toronto, Toronto M5S 3H8, Canada. Istituto Nazionale di Geofisica, Via di Vigna Murata 605, 00143, Roma, Italy . Correspondence and requests for materials should be addressed to P. d. B. (e-mail: debernardis@roma1.infn.it). Details of the experiment and numerical data sets are available at the web sites (http://oberon.roma1.infn.it/boomerang) and (http://www.physics.ucsb.edu/~boomerang). The blackbody radiation left over from the Big Bang has been transformed by the expansion of the Universe into the nearly isotropic 2.73ÊK cosmic microwave background. Tiny inhomogeneities in the early Universe left their imprint on the microwave background in the form of small anisotropies in its temperature. These anisotropies contain information about basic cosmological parameters, particularly the total energy density and curvature of the Universe. Here we report the first images of resolved structure in the microwave background anisotropies over a significant part of the sky. Maps at four frequencies clearly distinguish the microwave background from foreground emission. We compute the angular power spectrum of the microwave background, and find a peak at Legendre multipole lpeak = (197 6), with an amplitude T200 = (69 8)ʵK. This is consistent with that expected for cold dark matter models in a flat (euclidean) Universe, as favoured by standard inflationary models. Photons in the early Universe were tightly coupled to ionized matter through Thomson scattering. This coupling ceased about 300,000 years after the Big Bang, when the Universe cooled sufficiently to form neutral hydrogen. Since then, the primordial photons have travelled freely through the Universe, redshifting to microwave frequencies as the Universe expanded. We observe those photons today as the cosmic microwave background (CMB). An image of the early Universe remains imprinted in the temperature anisotropy of the CMB. Anisotropies on angular scales larger than 2¡ are dominated by the gravitational redshift the photons undergo as they leave the density fluctuations present at decoupling1, 2. Anisotropies on smaller angular scales are enhanced by oscillations of the photonÐbaryon fluid before decoupling3. These oscillations are driven by the primordial density fluctuations, and their nature depends on the matter content of the Universe. In a spherical harmonic expansion of the CMB temperature field, the angular power spectrum specifies the contributions to the fluctuations on the sky coming from different multipoles l, each corresponding to the angular scale = /l. Density fluctuations over spatial scales comparable to the acoustic horizon at decoupling produce a peak in the angular power spectrum of the CMB, occurring at multipole lpeak. The exact value of lpeak depends on both the linear size of the acoustic horizon and on the angular diameter distance from the observer to decoupling. Both these quantities are sensitive to a number of cosmological parameters (see, for example, ref. 4), but lpeak primarily depends on the total density of the Universe, 0. In models with a density 0 near 1, lpeak 200/ 1/20. A precise measurement of lpeak can efficiently constrain the density and thus the curvature of the Universe. Observations of CMB anisotropies require extremely sensitive and stable instruments. The DMR5 instrument on the COBE satellite mapped the sky with an angular resolution of 7¡, yielding measurements of the angular power spectrum at multipoles l < 20. Since then, experiments with finer angular resolution6-16 have detected CMB fluctuations on smaller scales and have produced evidence for the presence of a peak in the angular power spectrum at l peak 200. Here we present high-resolution, high signal-to-noise maps of the CMB over a significant fraction of the sky, and derive the angular power spectrum of the CMB from l = 50 to 600. This power spectrum is dominated by a peak at multipole lpeak = (197 6) (1 error). The existence of this peak strongly supports inflationary models for the early Universe, and is consistent with a flat, euclidean Universe. The instrument The Boomerang (balloon observations of millimetric extragalactic radiation and geomagnetics) experiment is a microwave telescope that is carried to an altitude of 38Êkm by a balloon. Boomerang combines the high sensitivity and broad frequency coverage pioneered by an earlier generation of balloon-borne experiments with the long (10 days) integration time available in a long-duration balloon flight over Antarctica. The data described here were obtained with a focal plane array of 16 bolometric detectors cooled to 0.3ÊK. Single-mode feedhorns provide two 18' full-width at half-maximum (FWHM) beams at 90ÊGHz and two 10' FWHM beams at 150ÊGHz. Four multi-band photometers each provide a 10.5', 14' and 13' FWHM beam at 150, 240 and 400ÊGHz respectively. The average in-flight sensitivity to CMB anisotropies was 140, 170, 210 and 2,700ʵKÊs 1/2 at 90, 150, 240 and 400ÊGHz, respectively. The entire optical system is heavily baffled against terrestrial radiation. Large sunshields improve rejection of radiation from >60¡ in azimuth from the telescope boresight. The rejection has been measured to be greater than 80ÊdB at all angles occupied by the Sun during the CMB observations. Further details on the instrument can be found in refsÊ17,18,19, 20,21. Observations Boomerang was launched from McMurdo Station (Antarctica) on 29 December 1998, at 3:30 GMT. Observations began 3 hours later, and continued uninterrupted during the 259-hour flight. The payload approximately followed the 79¡ÊS parallel at an altitude that varied daily between 37 and 38.5Êkm, returning within 50Êkm of the launch site. We concentrated our observations on a target region, centred at roughly right ascension (RA) 5h, declination (dec.) -45¡, that is uniquely free of contamination by thermal emission from interstellar dust22 and that is approximately opposite the Sun during the austral summer. We mapped this region by repeatedly scanning the telescope through 60¡ at fixed elevation and at constant speed. Two scan speeds (1¡Ês-1 and 2¡Ês-1 in azimuth) were used to facilitate tests for systematic effects. As the telescope scanned, degree-scale variations in the CMB generated sub-audio frequency signals in the output of the detector23. The stability of the detector system was sufficient to allow sensitive measurements on angular scales up to tens of degrees on the sky. The scan speed was sufficiently rapid with respect to sky rotation that identical structures were observed by detectors in the same row in each scan. Detectors in different rows observed the same structures delayed in time by a few minutes. At intervals of several hours, the telescope elevation was interchanged between 40¡, 45¡ and 50¡ in order to increase the sky coverage and to provide further systematic tests. Sky rotation caused the scan centre to move and the scan direction to rotate on the celestial sphere. A map from a single day at a single elevation covered roughly 22¡ in declination and contained scans rotated by 11¡ on the sky, providing a cross-linked scan pattern. Over most of the region mapped, each sky pixel was observed many times on different days, both at 1¡Ês-1 and 2¡Ês-1 scan speed, with different topography, solar elongation and atmospheric conditions, allowing strong tests for any contaminating signal not fixed on the celestial sphere. The pointing of the telescope has been reconstructed with an accuracy of 2' r.m.s. using data from a Sun sensor and rate gyros. This precision has been confirmed by analysing the observed positions of bright compact HÊ II regions in the Galactic plane (RCW3824, RCW57, IRAS08576 and IRAS1022) and of radio-bright point sources visible in the target region (the QSO 0483-436, the BL Lac object 0521-365 and the blazar 0537-441). Calibrations The beam pattern for each detector was mapped before flight using a thermal source. The main lobe at 90, 150 and 400ÊGHz is accurately modelled by a gaussian function. The 240ÊGHz beams are well modelled by a combination of two gaussians. The beams have small shoulders (less than 1% of the total solid angle), due to aberrations in the optical system. The beam-widths were confirmed in flight via observations of compact sources. By fitting radial profiles to these sources we determine the effective angular resolution, which includes the physical beamwidth and the effects of the 2' r.m.s. pointing jitter. The effective FWHM angular resolution of the 150ÊGHz data that we use here to calculate the CMB power spectrum is (10 1)' , where the error is dominated by uncertainty in the pointing jitter. We calibrated the 90, 150 and 240ÊGHz channels from their measured response to the CMB dipole. The dipole anisotropy has been accurately (0.7%) measured by COBE-DMR25, fills the beam and has the same spectrum as the CMB anisotropies at smaller angular scales, making it the ideal calibrator for CMB experiments. The dipole signal is typically 3ÊmK peak-to-peak in each 60¡ scan, much larger than the detector noise, and appears in the output of the detectors at f = 0.008ÊHz and f = 0.016ÊHz in the 1¡Ês -1 and 2¡Ês-1 scan speeds, respectively. The accuracy of the calibration is dominated by two systematic effects: uncertainties in the low-frequency transfer function of the electronics, and low-frequency, scan-synchronous signals. Each of these is significantly different at the two scan speeds. We found that the dipole-fitted amplitudes derived from separate analysis of the 1¡Ês-1 and 2¡Ês -1 data agree to within 10% for every channel, and thus we assign a 10% uncertainty in the absolute calibration. From detector signals to CMB maps The time-ordered data comprises 5.4 107 16-bit samples for each channel. These data are flagged for cosmic-ray events, elevation changes, focal-plane temperature instabilities, and electromagnetic interference events. In general, about 5% of the data for each channel are flagged and not used in the subsequent analysis. The gaps resulting from this editing are filled with a constrained realization of noise in order to minimize their effect in the subsequent filtering of the data. The data are deconvolved by the bolometer and electronics transfer functions to recover uniform gain at all frequencies. The noise power spectrum of the data and the maximum-likelihood maps26-28 were calculated using an iterative technique29 that separates the sky signal from the noise in the time-ordered data. In this process, the statistical weights of frequencies corresponding to angular scales larger than 10¡ on the sky are set to zero to filter out the largest-scale modes of the map. The maps were pixelized according to the HEALPix pixelization scheme30. shows the maps obtained in this way at each of the four frequencies. The 400ÊGHz map is dominated by emission from interstellar dust that is well correlated with that observed by the IRAS and COBE/DIRBE satellites. The 90, 150 and 240ÊGHz maps are dominated by degree-scale structures that are resolved with high signal-to-noise ratio. A qualitative but powerful test of the hypothesis that these structures are CMB anisotropy is provided by subtracting one map from another. The structures evident in all three maps disappear in both the 90-150ÊGHz difference and in the 240-150ÊGHz difference, as expected for emission that has the same spectrum as the CMB dipole anisotropy used to calibrate the maps. Figure 1 Boomerang sky maps (equatorial coordinates). ÊÊFullÊlegend Ê High resolution image and legend (226k) To quantify this conclusion, we performed a 'colour index' analysis of our data. We selected the 18,000 14' pixels at Galactic latitude b < - 15¡, and made scatter plots of 90ÊGHz versus 150ÊGHz and 240ÊGHz versus 150ÊGHz. A linear fit to these scatter plots gives slopes of 1.00 0.15 and 1.10 0.16, respectively (including our present 10% calibration error), consistent with a CMB spectrum. For comparison, freeÐfree emission with spectral index -2.35 would produce slopes of 2.3 and 0.85, and was therefore rejected with >99% confidence; emission from interstellar dust with temperature Td = 15ÊK and spectral index of emissivity = 1 would produce slopes of 0.40 and 2.9. For any combination of Td > 7ÊK and 1 < < 2, the dust hypothesis is rejected with >99% confidence. We conclude that the dominant source of structure that we detect at 90, 150 and 240ÊGHz is CMB anisotropy. We further argue that the 150ÊGHz map at b < - 15¡ is free of significant contamination by any known astrophysical foreground. Galactic synchrotron and freeÐfree emission is negligible at this frequency31. Contamination from extragalactic point sources is also small32; extrapolation of fluxes from the PMN survey33 limits the contribution by point sources (including the three above-mentioned radio-bright sources) to the angular power spectrum derived below to <0.7% at l = 200 and <20% at l = 600. The astrophysical foreground that is expected to dominate at 150ÊGHz is thermal emission from interstellar dust. We placed a quantitative limit on this source of contamination as follows. We assumed that dust properties are similar at high ( b < -20¡) and moderate (-20¡ < b < -5¡) Galactic latitudes. We selected the pixels at moderate Galactic latitudes and correlated the structure observed in each of our four bands with the IRAS/DIRBE map, which is dominated by dust in cirrus clouds. The best-fit slope of each of the scatter plots measures the ratios of the dust signal in the Boomerang channels to the dust signal in the IRAS/DIRBE map. We found that the 400ÊGHz map is very well correlated to the IRAS/DIRBE map, and that dust at b < - 20¡ can account for at most 10% of the signal variance at 240ÊGHz, 3% at 150ÊGHz and 0.5% at 90ÊGHz. Angular power spectra We compared the angular power spectrum of the structures evident in Fig. 1 with theoretical predictions. In doing so, we separated and removed the power due to statistical noise and systematic artefacts from the power due to the CMB anisotropies in the maps. The maximum-likelihood angular power spectrum of the maps was computed using the MADCAP34 software package, whose algorithms fully take into account receiver noise and filtering. Full analysis of our entire data set is under way. Because of the computational intensity of this process, we report here the results of a complete analysis of a limited portion of the data chosen as follows. We analysed the most sensitive of the 150ÊGHz detectors. We restricted the sky coverage to an area with RA > 70¡, b < -20¡ and -55¡ < dec. < -35¡, and we used only the 50% of the data from this detector that was obtained at a scan speed of 1¡Ês -1. We used a relatively coarse pixelization of 8,000 14-arcmin pixels as a compromise between computation speed and coverage of high multipoles. Finally, we limited our analysis to l 600 for which the effects of pixel shape and size and our present uncertainty in the beam size (1') are small and can be accurately modelled. The angular power spectrum determined in this way is shown in Fig. 2 and reported in Table 1. The power spectrum is dominated by a peak at lpeak 200, as predicted by inflationary cold dark matter models. These models additionally predict the presence of secondary peaks. The data at high l limit the amplitude, but do not exclude the presence, of a secondary peak. The errors in the angular power spectrum are dominated at low multipoles ( l 350) by the cosmic/sampling variance, and at higher multipoles by detector noise. Figure 2 Angular power spectrum measured by Boomerang at 150ÊGHz. ÊÊFullÊlegend Ê High resolution image and legend (11k) The CMB angular power spectrum shown in Fig. 2 was derived from 4.1 days of observation. As a test of the stability of the result, we made independent maps from the first and second halves of these data. The payload travels several hundred kilometres, and the Sun moves 2¡ on the sky, between these maps. Comparing them provides a stringent test for contamination from sidelobe pickup and thermal effects. The angular power spectrum calculated for the difference map is shown in Fig. 2. The reduced 2 of this power spectrum with respect to zero signal is 1.11 (12 degrees of freedom), indicating that the difference map is consistent with zero contamination. A peak at l 200 implies a flat Universe The location of the first peak in the angular power spectrum of the CMB is well measured by the Boomerang data set. From a parabolic fit to the data at l = 50 to 300 in the angular power spectrum, we find lpeak = (197 6) (1 error). The parabolic fit does not bias the determination of the peak multipole: applying this method to Monte Carlo realizations of theoretical power spectra we recover the correct peak location for a variety of cosmological models. Finally, the peak location is independent of the details of the data calibration, which obviously affect only the height of the peak and not its location. The height of the peak is T200 = (69 4) 7ʵK (1 statistical and calibration errors, respectively). The data are inconsistent with current models based on topological defects (see, for example, ref. 35) but are consistent with a subset of cold dark matter models. We generated a database of cold dark matter models36, 37, varying six cosmological parameters (the range of variation is given in parentheses): the non-relativistic matter density, m (0.05Ð2); the cosmological constant, (0Ð1); the Hubble constant, h (0.5Ð0.8); the baryon density, h2b (0.013Ð0.025), the primordial scalar spectral index, ns (0.8Ð1.3); and the overall normalization A (free parameter) of the primordial density fluctuation power spectrum. We compared these models with the power spectrum we report here to place constraints on allowed regions in this 6-parameter space. In Figure 3 we mark with large black dots the region of the mÐ plane where some combination of the remaining four parameters within the ranges defined by our model space gives a power spectrum consistent with our 95% confidence interval for lpeak. This region is quite narrow, and elongated along the 'flat Universe' line m + = 1. The width of this region is determined by degeneracy in the models, which produce closely similar spectra for different values of the parameters38. We further evaluated the likelihood of the models given the Boomerang measurement and the same priors (constraints on the values of the cosmological parameters) as in ref. 16. Marginalizing over all the other parameters, we found the following 95% confidence interval for 0 = m + : 0.88 < 0 < 1.12. This provides evidence for a euclidean geometry of the Universe. Our data clearly show the presence of power beyond the peak at l = 197, corresponding to smaller-scale structures. The consequences of this fact will be fully analysed elsewhere. Figure 3 Observational constraints on m and . ÊÊFullÊlegend Ê High resolution image and legend (41k) Received 24 March 2000;accepted 3 April 2000 References 1. Sachs,R. K. & Wolfe,A. M. Perturbations of a cosmological model and angular variations of the microwave background. Astrophys. 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