Article Cosmic microwave background anisotropies from scaling seeds : global defect models DURRER, Ruth, KUNZ, Martin, MELCHIORRI, Alessandro Abstract We investigate the global texture model of structure formation in cosmogonies with a nonzero cosmological constant for different values of the Hubble parameter. We find that the absence of significant acoustic peaks and little power on large scales are robust predictions of these models. However, from a careful comparison with data we conclude that at present we cannot safely reject the model on the grounds of present CMB data. Exclusion by means of galaxy correlation data requires assumptions on biasing and statistics. New, very stringent constraints come from peculiar velocities. Investigating the large-N limit, we argue that our main conclusions apply to all global O(N) models of structure formation. Reference DURRER, Ruth, KUNZ, Martin, MELCHIORRI, Alessandro. Cosmic microwave background anisotropies from scaling seeds : global defect models. Physical Review. D, 1999, vol. 59, no. 123005, p. 26 DOI : 10.1103/PhysRevD.59.123005 arxiv : astro-ph/9811174 Available at: http://archive-ouverte.unige.ch/unige:976 Disclaimer: layout of this document may differ from the published version. 1 / 1 Cosmic Microwave Background Anisotropies from Scaling Seeds Global Defect Mo dels R Durrer M Kunz and A Melchiorri Departement de Physique Theorique Universite de Geneve quai Ernest Ansermet CH Geneve Switzerland cosmic uid only gravitationally and which represents al ways a small fraction of the total energy of the universe They induce geometrical p erturbations but their inu Abstract ence on the evolution of the background universe can b e We investigate the global texture mo del of structure forma neglected Furthermore in rst order p erturbation the tion in cosmogonies with nonzero cosmological constant for ory seeds evolve according to the unp erturb ed spacetime dierent values of the Hubble parameter We nd that the geometry absence of signicant acoustic p eaks and little p ower on large Here we mainly investigate the mo dels of structure for scales are robust predictions of these mo dels However from a mation with global texture This mo dels for matter careful comparison with data we conclude that at present we show discrepancies with the observed intermediate cannot safely reject the mo del on the grounds of present CMB scale CMB anisotropies and with the galaxy p ower sp ec data Exclusion by means of galaxy correlation data requires trum on large scales Recently it has b een argued assumptions on biasing and statistics New very stringent that the addition of a cosmological constant leads to b et constraints come from p eculiar velo cities ter agreement with data for the cosmic string mo del of Investigating the largeN limit we argue that our main structure formation We analyze this question for the conclusions apply to all global O N mo dels of structure for texture mo del by using ab initio simulation of cosmic mation texture as describ ed in Ref We determine the CMB anisotropies the dark matter p ower sp ectrum and the bulk velo cities for these mo dels We also compare our results with the largeN limit of global O N mo dels and we discuss briey which typ e of parameter changes I INTRODUCTION in the p oint functions of the seeds may lead to b etter agreement with data Recently a lot of eort has gone into the determina We nd that the absence of signicant acoustic p eaks tion of cosmological parameters from measurements of in the CMB anisotropy sp ectrum is a robust result for cosmic microwave background CMB anisotropies es global texture as well as for the largeN limit for all p ecially in view of the two planned satellite exp eriments choices of cosmological parameters investigated Further MAP and PLANCK However we b elieve it is im more the dark matter p ower sp ectrum on large scales p ortant to b e aware of the heavy mo deling which enters h Mp c is substantially lower than the measured these results In general simple p ower law initial sp ectra galaxy p ower sp ectrum for scalar and tensor p erturbations and vanishing vector However comparing our CMB anisotropy sp ectra with p erturbations are assumed as predicted from ination present data we cannot safely reject the mo del On large To repro duce observational data the comp osition of the angular scales the CMB sp ectrum is in quite go o d agree dark matter and the cosmological parameters as well as ment with the COBE data set while on smaller scales we the input sp ectrum and the scalar to tensor ratio are nd a signicant disagreement only with the Saskato on varied exp eriment Furthermore for nonsatellite exp eriments We want to take a dierent approach We mo dify the foreground contamination remains a serious problem due mo del for structure formation We assume that cosmic to the limited sky and frequency coverage structure was induced by scaling seeds Using a simplied The dark matter p ower sp ectra are clearly to o low on and not very accurate treatment for the photon prop large scales but in view of the unresolved biasing prob agation we have already shown that some key observa lem we feel reluctant to rule out the mo dels on these tions can b e repro duced within a very restricted family of grounds A much clearer rejection may come from the scaling seed mo dels Here we want to outline in detail bulk velo city on large scales Our prediction is by a fac a more accurate computation with a fully gaugeinvariant tor to lower than the POTENT result on large scales Boltzmann co de esp ecially adapted to treat mo dels with Since global texture and the largeN limit lead to very sources In this pap er we follow the philosophy of a gen similar results we conclude that all global O N mo dels eral analysis of scaling seed mo dels motivated in Ref of structure formation for the cosmogonies investigated Seeds are an inhomogeneously distributed form of mat in this work are ruled out if the bulk velo city on scales of ter like eg top ological defects which interacts with the h Mp c is around kms or if the CMB primordial In the next subsection we parameterize in a completely anisotropies p ower sp ectrum really shows a structure of general way the degrees of freedom of the seed energy mo p eaks on subdegree angular scales mentum tensor Subsection B is devoted to the p ertur This pap er is the rst of a series of analyses of mo d bation of Einsteins equations and the uid equations of els with scaling seeds We therefore fully present the motion Next we treat the Boltzmann p erturbation equa formalism used for our calculations in the next section tion In Subsection D we explain how we determine the There we also explain in detail the eigenvector expan p ower sp ectra of CMB anisotropies density uctuation sion which allows to calculate the CMB anisotropies and and p eculiar velo cities by means of the derived p ertur matter p ower sp ectra in mo dels with seeds from the two bation equations and the unequal time correlators of the p oint functions of the seeds alone This section can b e seed energy momentum tensor which are obtained by skipp ed if the reader is mainly interested in the results numerical simulations In Subsection E we give the ini Section is devoted to a brief description of the numeri tial conditions and a brief description of our Boltzmann cal simulations In Section we analyze our results and co de in Section we draw some conclusions Two app endices are devoted to detailed denitions of the p erturbation variables and to some technical derivations A The seed energy momentum tensor Notation We always work in a spatially at Fried mann universe The metric is given by Since the energy momentum tensor of the seeds i j ds at dt dx dx ij has no homogeneous background contribution it is gauge invariant by itself according to the StewartWalker where t denotes conformal time Lemma Greek indices denote spacetime co ordinates to can b e calculated by solving the matter equa whereas Latin ones run from to Three dimensional tions for the seeds in the Friedmann background geometry vectors are denoted by b old face characters Since has no background comp onent it satises the unp erturb ed conservation equations We decomp ose into scalar vector and tensor contributions They I I THE FORMALISM decouple within linear p erturbation theory and it is thus p ossible to write the equations for each of these contribu Anisotropies in the CMB are small and can thus b e tions separately As always unless noted otherwise we describ ed by rst order cosmological p erturbation theory work in Fourier space We parameterize the scalar S which we apply throughout We neglect the nonlinear vector V and tensor T contributions to in the evolution of density uctuations on smaller scales Since form mo dels with seeds are genuinely nonGaussian the usual numerical Nb o dy simulations which start from Gaussian S M f initial conditions cannot b e used to describ e the evolution S on smaller scales iM k f j v j Gaugeinvariant p erturbation equations for cosmolog S ical mo dels with seeds have b een derived in Refs f M k f k k f p j l j l j l Here we follow the notation and use the results presented v V in Ref Denitions of all the gaugeinvariant p ertur M w j j bation variables used here in terms of p erturbations of V iM k w k w the metric the energy momentum tensor and the bright j l j j l l ness are given in App endix A for completeness T M ij We consider a background