Image Earle th f yso Universe from the BOOMERanG experiment Bernardise Pd . 1, P.A.R.Ade2, JJ.Bock3, J.R.Bond4, J.Borrill5'6, A.Boscaleri7, K.Coble8, B.P.Crill9, G.De Gasperis10, G.De Troia1, P.C.Farese8, P.G.Ferreira11, K.Ganga9'12, M.Giacometti1, E.Hivon9, V.V.Hristov9, AJacoangeli1, A.HJaffe6, A.E.Lange9, L.Martinis13, S.Masi1, P.Mason9, P.D.Mauskopf14'15, A.Melchiorri1, L.Miglio16, T.Montroy8, C.B.Netterfield16, E.Pascale7, F.Piacentini1, G.Polenta1, D.Pogosyan4, S.Prunet4, S.Rao17, G.Romeo17, J.E.Ruhl8, F.Scaramuzzi13, D.Sforna1, N.Vittorio10 Dipartimento1 Fisica,di Universitd Romadi Sapienza,La 001852, P.leRoma,Mow A. Italy, 2 Department of Physics, Queen Mary and Westfield College, Mile End Road, London, El 4NS, UK, 3 Jet Propulsion Laboratory, Pasadena, CA, USA, 4 CITA University of Toronto, Canada, NERSC-LBNL,5 Berkeley, USA,CA, 6 Center for Particle Astrophysics, University of California at Berkeley, 301 Le Conte Hall, Berkeley CA 94720, USA, 1IROE CNR,- PanciatichiVia 64,50127 Firenze, Italy, 8 Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA, 9 California Institute of Technology, Mail Code: 59-33, Pasadena, CA 91125, USA, 10 Dipartimento di Fisica, Universitd di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy, 1 ] Astrophysics, University of Oxford, Keble Road, 3RH,OX1 UK, 12 PCC, College de France, 11 pi. Marcelin Berthelot, 75231 Paris Cedex 05, France, 13 ENEA Centra Ricerche Frascati,i d . FermiE a , 00044Vi 45 Frascati, Italy, 4 Physics1 Astronomyd an Dept, Cardiff University,, UK 5 Dept1 of Physics Astronomy,d an UMass. Amherst, , USA,MA 16 Departments of Physics and Astronomy, University of Toronto, Canada, 17 Istituto Nazionale di Geofisica, Via di Vigna Murata 605, 00143, Roma, Italy,. THE CMB AND THE CURVATURE OF THE UNIVERSE The CMB is the fundamental tool to study the properties of the early universe and of the universe at large scales. In the framework of the Hot Big Bang model, when we look to plasme th f looo e a w d redshif keraa t B en bac a ,e timn th kCM i t o e et ~ th 1000, when the univers ^s 5000ewa 0 times younger, ~ 1000 times time9 hotte ~10 d san rdense r than today. The image of the CMB can be used to study the physical processes there, to infer what happened before alsd studo an ,t backgroune yth d geometr Universer ou f yo . traveB spacn photone CM i billiol 5 r ~e 1 Th efo th f nso years before reachinr gou CP586, Relativistic Astrophysics: 20th Texas Symposium, edited by J. C. Wheeler and H. Mattel © 2001 American Institut Physicf eo s 0-73 54-0026-1/017$ 18.00 157 Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp microwave telescopes. Originally visible and near infrared light, they are converted in a faint glow of microwaves by the expansion of the Universe. Since CMB photons travel so long in the Universe, their trajectories are affected significantly by any large-scale curvature of space. The image of the CMB can thus be used to study the large scale geometry of space. The scale of the acoustic horizon at recombination is the "standard ruler" neede thesr dfo e studies: density fluctuations larger tha horizoe nth frozene nar , while fluctuations smaller than the horizon can oscillate, arriving at recombination in a compressed or rarefied state, and thus producing a characteristic pattern of hot and cold spots in the CMB (see e.g. [1] [2] [3] [4] [5]). In fact temperature th , relatee densite ar e th fluctuation B do t yCM fluctuatione th f so s at recombination through three physical processes: the photon density fluctuations 8Y accompanying the fluctuation of density; the gravitational redshift/blueshift of photons coming from overdense/underdense regions with gravitational potential <|); the Doppler shift produced by scatter of photons by electrons moving with velocity v with the perturbation. In formulas (see e.g.[6]): where n is the line of sight vector and the subscript r labels quantities at recombination. In the CMB temperature distribution we see a snapshot of the status of the density perturbation t recombinationa s characteristie th : horizoe c e densitth siz th f eo n ni y fluctuations is thus directly translated in a characteristic size in the spots of the CMB. Recombinatio f hydrogeno n happens whe temperature nth e drops below ~ 300(MT, i.e. about 300000 year Bangg scausae Bi afte e Th . th rl horizo abous ni t 300000 light years there. Since the distance travelled by CMB photons is ^ 15 billion light years, and lenghts in the Universe increase by a factor 1000 meanwhile, the angle subtended now by the horizons at recombination is expected to be close to one degree, in a Euclidean Universe typicae Th . l observe dcold angulaan d t spotho re s sizth strongl f eo y depends on the average mass-energy density parameter Q. The presence of mass and energy acts as a magnifying (Q > 1) or demagnifying (Q < 1) lens, producing horizon-sized spots larger or smaller than ~ \° in the two cases, respectively. The image of the CMB is described in statistical terms: the temperature field is expane multipolen di s The aim are random variables with zero average and ensemble variance < atma*£,m, >= $U'&mm'- represenS Q' e angulae Th th t r power spectru CMBe compute th w f mf o I . e thc e power spectru imagCMBe e peaa th th expec e m f f e multipolet eko o ,w a se o tt \ s^i 200 corresponding to these degree-size spots. The location of the peak will be mainly drive, thuQ sy nb allowin gmeasuremena thif o t s elusive cosmological parametere Th . dependanc t simplpresentle no th \ i fros i n ef i emo Q y favoured cosmological model with significant vacuum energy OA [7] [8], Full spectral data must be compared to spectral models compute f cosmologicao d t frose ma l parameters degeneracied an , s mus takee tb n into account [9], [10] remaint .I s confirmed, however, tha maie tth n driver 158 Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp locatioe fo th firsre th t f nacoustio c . valuThie peathun O th retrievef e sca s kesi o b d with good accuracy from the power specturm of an image of the CMB with sub-degree resolution. After recombination, the same density fluctuations driving the acoustic oscillations grow, and form the jerarchy of structures we see in the Universe today. Thus, the image of CMB anisotropies represents also a fundamental tool in the study of the formation of structure Universee th n si . The detailed shape of the CMB power spectrum Q has been computed in a num- ber of scenarios with very high detail. A wide literature is available on the subject as wel publicalls a l y available software ([11], [12] accuratelo )t y comput powee eth r spec- trum cosmologicaf o give t se na l parameter framewore th n si adiabatif ko c inflationary models. More work remains to be done for the general case (for example including isocurvature modes, see e.g. [13]). maie Th n feature, i.e harmonia . c serie f peakso s followin describefirse e gth on t d above, can be understood as follows. The acoustic horizon increases with time, and at some point becomes larger tha givena n perturbation size t thiA . s perture pointth l al ,- bations present in the Universe with that size will start to oscillate. This can be seen as a cosmic synchronization process, which initiates the oscillation of small perturbations befor oscillatioe eth largf no e ones perturbationphase e :th th f eo recombinatioe th t sa n depends on their intrinsic size. Perturbations with size close to the horizon at recom- bination start lasthavd an ,e just enough tim maximuarrive o et th o et m compression, producing the degree-size spots in the CMB, i.e. the first "acoustic" peak in the angular powe anisotropyB r spectruCM e th f m. o Perturbation s with smaller intrinsic size have entere acoustie dth c horizon before arrivd an , recombinatiot ea n afte fula r l compression and a return to the average density. They will produce a CMB temperature fluctuation smaller tha previoue nth s ones, because amon three gth e physical processes producing temperature fluctuations from density ones, onl Dopplee yth r effec effectives i t . This angulae th correspond n i rp powe di t multipole a a B o srt spectruCM e s th large f mo r tha firse nth t acoustic peak. Even smaller perturbations have enough tim compresso et , return to the average density, and then arrive to the maximum rarefaction at recombina- tion, producing a second peak in power spectrum, at multipoles about twice of those of firse th t one. Repeating this reasoning expece ,w harmonita c serie acoustif so c peaksp ,u vero t y small sizes, smaller tha thicknese nth lase th t f scatterinso g surface. Photons dif- fusion, and the fact that many small-size positive and negative perturbations are aligned on the same line of sight, damps the temperature fluctuations measurable in the CMB at very high multipoles. poweshape e th Th f eo r spectru CMBe th , f dependmo Q , severan so l cosmological parameter addition si .