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The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

We study how Abelian-gauge-field production during inflation affects scalar perturbations in the case when the gauge field interacts with the inflaton directly (by means of generic kinetic and axial couplings) and via gravity. The homogeneous background solution is defined by self-consistently taking into account the backreaction of the gauge field on the evolution of the inflaton and the scale factor. For the perturbations on top of this background, all possible scalar contributions coming from the inflaton, the metric, and the gauge field are considered. We derive a second-order differential equation for the curvature perturbation, $\zeta$, capturing the impact of the gauge field, both on the background dynamics and on the evolution of scalar perturbations. The latter is described by a source term in the $\zeta$ equation, which is quadratic in the gauge-field operators and leads to non-Gaussianities in the curvature perturbations. We derive general expressions for the induced scalar power spectrum and bispectrum. Finally, we apply our formalism to the well-known case of axion inflation without backreaction. Numerical results show that, in this example, the effect of including metric perturbations is small for values of the gauge-field production parameter $\xi> 3$. This is in agreement with the previous results in the literature. However, in the region of smaller values, $\xi\lesssim 2$, our new results exhibit order-of-unity deviations when compared to previous results., Comment: 40 pages, 6 figures, 1 table, 146 references

In this paper we investigate the impact of lensing magnification on the analysis of Euclid's spectroscopic survey, using the multipoles of the 2-point correlation function for galaxy clustering. We determine the impact of lensing magnification on cosmological constraints, and the expected shift in the best-fit parameters if magnification is ignored. We consider two cosmological analyses: i) a full-shape analysis based on the $\Lambda$CDM model and its extension $w_0w_a$CDM and ii) a model-independent analysis that measures the growth rate of structure in each redshift bin. We adopt two complementary approaches in our forecast: the Fisher matrix formalism and the Markov chain Monte Carlo method. The fiducial values of the local count slope (or magnification bias), which regulates the amplitude of the lensing magnification, have been estimated from the Euclid Flagship simulations. We use linear perturbation theory and model the 2-point correlation function with the public code coffe. For a $\Lambda$CDM model, we find that the estimation of cosmological parameters is biased at the level of 0.4-0.7 standard deviations, while for a $w_0w_a$CDM dynamical dark energy model, lensing magnification has a somewhat smaller impact, with shifts below 0.5 standard deviations. In a model-independent analysis aiming to measure the growth rate of structure, we find that the estimation of the growth rate is biased by up to $1.2$ standard deviations in the highest redshift bin. As a result, lensing magnification cannot be neglected in the spectroscopic survey, especially if we want to determine the growth factor, one of the most promising ways to test general relativity with Euclid. We also find that, by including lensing magnification with a simple template, this shift can be almost entirely eliminated with minimal computational overhead., Comment: 23 pages, 14 figures

In this work, we study general features of a regime where gauge fields produced during inflation cause a strong backreaction on the background evolution and its impact on the spectrum and the correlation length of gauge fields. With this aim, the gradient-expansion formalism previously proposed for the description of inflationary magnetogenesis in purely kinetic or purely axial coupling models, is extended to the case when both types of coupling are present. As it is formulated in position space, this method allows us to self-consistently take into account the backreaction of generated gauge fields on the inflationary background because it captures the nonlinear evolution of all physically relevant gauge-field modes at once. Using this extended gradient-expansion formalism, suitable for a wide range of inflationary magnetogenesis models, we study the gauge-field production in a specific generalization of the Starobinsky $R^2$-model with a nonminimal coupling of gauge fields to gravity. In the Einstein frame, this model implies, in addition to an asymptotically flat inflaton potential, also a nontrivial form of kinetic and axial coupling functions which decrease in time and, thus, are potentially suitable for the generation of gauge fields with a scale-invariant or even red-tilted power spectrum. The numerical analysis shows, however, that backreaction, which unavoidably occurs in this model for the interesting range of parameters, strongly alters the behavior of the spectrum and does not allow us to obtain a sufficiently large correlation length for the magnetic field. The oscillatory behavior of the generated field, caused by the retarded response of the gauge field to changes of the inflaton velocity, was revealed., Comment: 25 pages, 9 figures

In the framework of mixed Higgs-Starobinsky inflation, we consider the generation of Abelian gauge fields due to their nonminimal coupling to gravity (in two different formulations of gravity -- metric and Palatini). We couple the gauge-field invariants $F_{\mu\nu}F^{\mu\nu}$ and $F_{\mu\nu}\tilde{F}^{\mu\nu}$ to an integer power of the scalar curvature $R^n$ in Jordan frame and, treating these interactions perturbatively, switch to the Einstein frame where they lead to effective kinetic and axial couplings between gauge fields and inflaton. We determine the power spectra, energy densities, correlation length, and helicality of the generated gauge fields for different values of the nonminimal coupling constants and parameter $n$. We analytically estimate the spectral index $n_{B}$ of the magnetic power spectrum and show that for $n>1$ it is possible to get the scale-invariant or even red-tilted spectrum for a wide range of modes that implies larger correlation length of the generated fields. On the other hand, the magnitude of these fields typically decreases in time becoming very small in the end of inflation. Thus, it is difficult to obtain both large magnitude and correlation length of the gauge field in the frame of this model., Comment: 20 pages, 7 figures

We investigate the importance of lensing magnification for estimates of galaxy clustering and its cross-correlation with shear for the photometric sample of Euclid. Using updated specifications, we study the impact of lensing magnification on the constraints and the shift in the estimation of the best fitting cosmological parameters that we expect if this effect is neglected. We follow the prescriptions of the official Euclid Fisher matrix forecast for the photometric galaxy clustering analysis and the combination of photometric clustering and cosmic shear. The slope of the luminosity function (local count slope), which regulates the amplitude of the lensing magnification, and the galaxy bias have been estimated from the Euclid Flagship simulation.We find that magnification significantly affects both the best-fit estimation of cosmological parameters and the constraints in the galaxy clustering analysis of the photometric sample. In particular, including magnification in the analysis reduces the 1$\sigma$ errors on $\Omega_{\text{m},0}, w_{0}, w_a$ at the level of 20-35%, depending on how well we will be able to independently measure the local count slope. In addition, we find that neglecting magnification in the clustering analysis leads to shifts of up to 1.6$\sigma$ in the best-fit parameters. In the joint analysis of galaxy clustering, cosmic shear, and galaxy-galaxy lensing, magnification does not improve precision, but it leads to an up to 6$\sigma$ bias if neglected. Therefore, for all models considered in this work, magnification has to be included in the analysis of galaxy clustering and its cross-correlation with the shear signal ($3\times2$pt analysis) for an accurate parameter estimation., Comment: 26 pages, 11 figures. Version accepted for publication in A&A

In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA scientific community in the area of fundamental physics. We organize these directions through a "science-first" approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics., Comment: 22 pages, 1 figure, to appear in General Relativity and Gravitation

Following the pioneering observations with COBE in the early 1990s, studies of the cosmic microwave background (CMB) have focused on temperature and polarization anisotropies. CMB spectral distortions - tiny departures of the CMB energy spectrum from that of a perfect blackbody - provide a second, independent probe of fundamental physics, with a reach deep into the primordial Universe. The theoretical foundation of spectral distortions has seen major advances in recent years, which highlight the immense potential of this emerging field. Spectral distortions probe a fundamental property of the Universe - its thermal history - thereby providing additional insight into processes within the cosmological standard model (CSM) as well as new physics beyond. Spectral distortions are an important tool for understanding inflation and the nature of dark matter. They shed new light on the physics of recombination and reionization, both prominent stages in the evolution of our Universe, and furnish critical information on baryonic feedback processes, in addition to probing primordial correlation functions at scales inaccessible to other tracers. In principle the range of signals is vast: many orders of magnitude of discovery space could be explored by detailed observations of the CMB energy spectrum. Several CSM signals are predicted and provide clear experimental targets, some of which are already observable with present-day technology. Confirmation of these signals would extend the reach of the CSM by orders of magnitude in physical scale as the Universe evolves from the initial stages to its present form. The absence of these signals would pose a huge theoretical challenge, immediately pointing to new physics., Comment: Astro2020 Science White Paper, 5 pages text, 13 pages in total, 3 Figures, minor update to references

Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology. In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the CORE space mission proposed to ESA in answer to the "M5" call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. CORE is designed as a near-ultimate CMB polarisation mission which, for optimal complementarity with ground-based observations, will perform the observations that are known to be essential to CMB polarisation scienceand cannot be obtained by any other means than a dedicated space mission., Comment: 79 pages, 14 figures

High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for relativistic corrections to the clustering statistics is particularly important for the upcoming galaxy surveys covering progressively larger fraction of the sky. We focus on relativistic projection effects due to the fact that we observe the galaxies through the light that reaches the telescope on perturbed geodesics. These projection effects can give rise to an effective $f_{\rm NL}$ that can be misinterpreted as the primordial non-Gaussianity signal and hence is a systematic to be carefully computed and accounted for in modelling of the bispectrum. We develop the technique to properly account for relativistic effects in terms of purely observable quantities, namely angles and redshifts. We give some examples by applying this approach to a subset of the contributions to the tree-level bispectrum of the observed galaxy number counts calculated within perturbation theory and estimate the corresponding non-Gaussianity parameter, $f_{\rm NL}$, for the local, equilateral and orthogonal shapes. For the local shape, we also compute the local non-Gaussianity resulting from terms obtained using the consistency relation for observed number counts. Our goal here is not to give a precise estimate of $f_{\rm NL}$ for each shape but rather we aim to provide a scheme to compute the non-Gaussian contamination due to relativistic projection effects. For the terms considered in this work, we obtain contamination of $f_{\rm NL}^{\rm loc} \sim {\mathcal O}(1)$., Comment: 31 pages, 6 figures, Typos corrected to match the published version in JCAP

We determine the best-fit values and confidence limits for dynamical dark energy parameters together with other cosmological parameters on the basis of different datasets which include WMAP9 or Planck-2013 results on CMB anisotropy, BAO distance ratios from recent galaxy surveys, magnitude-redshift relations for distant SNe Ia from SNLS3 and Union2.1 samples and the HST determination of the Hubble constant. We use a Markov Chain Monte Carlo routine to map out the likelihood in the multi-dimensional parameter space. We show that the most precise determination of cosmological parameters with the narrowest confidence limits is obtained for the Planck{+}HST{+}BAO{+}SNLS3 dataset. The best-fit values and 2$\sigma$ confidence limits for cosmological parameters in this case are $\Omega_{de}=0.718\pm0.022$, $w_0=-1.15^{+0.14}_{-0.16}$, $c_a^2=-1.15^{+0.02}_{-0.46}$, $\Omega_bh^2=0.0220\pm0.0005$, $\Omega_{cdm}h^2=0.121\pm0.004$, $h=0.713\pm0.027$, $n_s=0.958^{+0.014}_{-0.010}$, $A_s=(2.215^{+0.093}_{-0.101})\cdot10^{-9}$, $\tau_{rei}=0.093^{+0.022}_{-0.028}$. For this dataset, the $\Lambda$CDM model is just outside the 2$\sigma$ confidence region, while for the dataset WMAP9{+}HST{+}BAO{+}SNLS3 the $\Lambda$CDM model is only 1$\sigma$ away from the best fit. The tension in the determination of some cosmological parameters on the basis of two CMB datasets WMAP9 and Planck-2013 is highlighted., Comment: 16 pages, 5 figures, 2 tables; accepted for publication in JCAP

We review the possible mechanisms for the generation of cosmological magnetic fields, discuss their evolution in an expanding Universe filled with the cosmic plasma and provide a critical review of the literature on the subject. We put special emphasis on the prospects for observational tests of the proposed cosmological magnetogenesis scenarios using radio and gamma-ray astronomy and ultra high energy cosmic rays. We argue that primordial magnetic fields are observationally testable. They lead to magnetic fields in the intergalactic medium with magnetic field strength and correlation length in a well defined range. We also state the unsolved questions in this fascinating open problem of cosmology and propose future observations to address them., Comment: to appear in Astronomy & Astrophysics Review

We analyze the possibility to distinguish between quintessence and phantom scalar field models of dark energy using observations of luminosity distance moduli of SNe Ia, CMB anisotropies and polarization, matter density perturbations and baryon acoustic oscillations. Among the present observations only Planck data on CMB anisotropy and SDSS DR9 data on baryon acoustic oscillations may be able to decide between quintessence or phantom scalar field models, however for each model a set of best-fit parameters exists, which matches all data with similar goodness of fit. We compare the relative differences of best-fit model predictions with observational uncertainties for each type of data and we show that the accuracy of SNe Ia luminosity distance data is far from the one necessary to distinguish these types of dark energy models, while the CMB data (WMAP, ACT, SPT and especially Planck) are close to being able to reliably distinguish them. Also an improvement of the large-scale structure data (future releses of SDSS BOSS and e.g. Euclid or BigBOSS) will enable us to surely decide between quintessence and phantom dark energy., Comment: 16 pages, 8 figures, 2 tables, accepted for publication in JCAP

We introduce the concepts of adiabatic (curvature) and isocurvature (entropy) cosmological perturbations and present their relevance for parameter estimation from cosmic microwave background anisotropies data. We emphasize that, while present-day data are in excellent agreement with pure adiabaticity, subdominant isocurvature contributions cannot be ruled out. We discuss model independent constraints on the isocurvature contribution. Finally, we argue that the Planck satellite will be able to do precision cosmology even if the assumption of adiabaticity is relaxed., Comment: Proceedings of the 10th Marcel Grossmann Meeting, Rio de Janeiro, July 2003, 5 pages, 2 figures

We investigate both analytically and numerically the evolution of scalar perturbations generated in models which exhibit a smooth transition from a contracting to an expanding Friedmann universe. We find that the resulting spectral index in the late radiation dominated universe depends on which of the $\Psi$ or \$zeta$ variables passes regularly through the transition. The results can be parameterized through the exponent $q$ defining the rate of contraction of the universe. For $q \geq -1/2$ we find that there are no stable cases where both variables are regular during the transition. In particular, for $0

We investigate in detail the question whether a non-vanishing cosmological constant is required by present-day cosmic microwave background and large scale structure data when general isocurvature initial conditions are allowed for. We also discuss differences between the usual Bayesian and the frequentist approaches in data analysis. We show that the COBE-normalized matter power spectrum is dominated by the adiabatic mode and therefore breaks the degeneracy between initial conditions which is present in the cosmic microwave background anisotropies. We find that in a flat universe the Bayesian analysis requires \Omega_\Lambda \neq 0 to more than 3 \sigma, while in the frequentist approach \Omega_\Lambda = 0 is still within 3 \sigma for a value of h < 0.48. Both conclusions hold regardless of initial conditions., Comment: 10 pages, 9 figures and 1 table; references added, minor typos fixed to match version accepted by PRD, results unchanged

At low energy, the four-dimensional effective action of the ekpyrotic model of the universe is equivalent to a slightly modified version of the pre big bang model. We discuss cosmological perturbations in these models. In particular we address the issue of matching the perturbations from a collapsing to an expanding phase in full generality. We show that, generically, one obtains $n=0$ for the spectrum of scalar perturbations in the original pre big model (with vanishing potential). When an exponential potential for the dilaton is included, a scale invariant spectrum ($n=1$) of adiabatic scalar perturbations is produced under very generic matching conditions, both in a modified pre big bang and ekpyrotic scenario. We also derive general results valid for power law scale factors matched to a radiation dominated era., Comment: 11 pages, 1 figure, revised version with small corrections to match version in print. Results and conclusions unchanged

The locations and amplitudes of three acoustic peaks and two dips in the last releases of the Boomerang, MAXIMA and DASI measurements of the cosmic microwave background (CMB) anisotropy power spectra as well as their statistical confidence levels are determined in a model-independent way. It is shown that the Boomerang-2001 data (Netterfield et al. 2001) fixes the location and amplitude of the first acoustic peak at more than 3\sigma confidence level. The next two peaks and dips are determined at a confidence level above 1\sigma but below 2\sigma. The locations and amplitudes of the first three peaks and two dips are 212+/-17, 5426+/-1218\mu K^2, 544+/-56, 2266+/-607\mu K^2, 843+/-35, 2077+/-876\mu K^2, 413+/-50, 1960+/-503\mu K^2, 746+/-89, 1605+/-650\mu K^2 respectively (1\sigma errors include statistical and systematic errors). The MAXIMA and DASI experiments give similar values for the extrema which they determine. The determined cosmological parameters from the CMB acoustic extrema data show good agreement with other determinations, especially with the baryon content as deduced from standard nucleosynthesis constraints. These data supplemented by the constraints from direct measurements of some cosmological parameters and data on large scale structure lead to a best-fit model which agrees with practically all the used experimental data within 1\sigma. The best-fit parameters are: \Omega_{\Lambda}=0.64^{+0.14}_{-0.27}, \Omega_{m}= 0.36^{+0.21}_{-0.11}, \Omega_b=0.047^{+0.093}_{-0.024}, n_s=1.0^{+0.59}_{-0.17}, h=0.65^{+0.35}_{-0.27} and \tau_c=0.15^{+0.95}_{-0.15} (plus/minus values show 1\sigma upper/lower limits obtained by marginalization over all other model parameters). The best-fit values of \Omega_{\nu} and T/S are close to zero, their 1\sigma upper limits are 0.17 and 1.7 respectively., Comment: 34 pages, 10 figures; accepted by ApJ; some corrections in the text are made and a few references are added

Topological defects are ubiquitous in physics. Whenever a symmetry breaking phase transition occurs, topological defects may form. The best known examples are vortex lines in type II super conductors or in liquid Helium, and declination lines in liquid crystals. In an adiabatically expanding universe which cools down from a very hot initial state, it is quite natural to postulate that topological defects may have emerged during a phase transition in the early universe and that they may have played the role of initial inhomogeneities seeding the formation of cosmic structure. This basic idea goes back to Kibble (1976). In this report we summarize the progress made in the investigation of Kibble's idea during the last 25 years. Our understanding of the formation and evolution of topological defects is reported almost completely in the beautiful book by Vilenkin & Shellard or the excellent Review by Hindmarsh & Kibble, and we shall hence be rather short on that topic. Nevertheless, in order to be self contained, we have included a short chapter on spontaneous symmetry breaking and defect formation. Our main topic is however the calculation of structure formation with defects, results which are not included in the above references., Comment: Review for Physics Reports, 133 pages 29 figures. Updated to match published version. Better quality and color figures are available at http://mpej.unige.ch/~durrer

Recently high quality data of the cosmic microwave background anisotropies have been published. In this work we study to which extent the cosmological parameters determined by using this data depend on assumptions about the initial conditions. We show that for generic initial conditions, not only the best fit values are very different but, and this is our main result, the allowed parameter range enlarges dramatically., Comment: 4 pages, 5 figures, submitted to PRL; Major changes following referees suggestions; the allowed cosmological parameter range enlarges dramatically

Observational data on the large scale structure (LSS) of the Universe are used to establish an upper limit for the amplitude of the tensor mode marginalized over all other cosmological parameters within the class of adiabatic inflationary models. It is shown that the upper 1$\sigma$ limit for the contribution of a tensor mode to the COBE DMR data is T/S$<1$., Comment: 3 pages, to appear in the proceedings of the IAU Symposium 201, Manchester, 7-11 August 2000

The observational data on the large scale structure (LSS) of the Universe are used to establish the upper limit on the neutrino content marginalized over all other cosmological parameters within the class of adiabatic inflationary models. It is shown that the upper 2$\sigma$ limit on the neutrino content can be expressed in the form $\Omega_{\nu}h^2/N_{\nu}^{0.64}\le0.042$ or, via the neutrino mass, $m_{\nu}\le4.0$eV., Comment: 5 pages, to appear in the proceedings of the CAPP2000 Conference, Verbier, Switzerland, July, 2000

During the last years it has become clear that global O(N) defects and U(1) cosmic strings do not lead to the pronounced first acoustic peak in the power spectrum of anisotropies of the cosmic microwave background which has recently been observed to high accuracy. Inflationary models cannot easily accommodate the low second peak indicated by the data. Here we construct causal scaling seed models which reproduce the first and second peak. Future, more precise CMB anisotropy and polarization experiments will however be able to distinguish them from the ordinary adiabatic models., Comment: 6 pages 2 figures, revtex; minor corrections and references added

We present some phenomenological aspects of the pre-big-bang cosmological model inspired by the duality properties of string theory. In particular, assuming the spatial sections of the homogeneous background geometry to be isotropic, we discuss the quantum production of perturbations of the background fields (gravitons, dilatons, moduli fields), as well as the production of particles which do not contribute to the background, which we call ``seeds''. As such we consider the cases of electromagnetic and axionic seeds. We also discuss their possible observational consequences, for example, we study whether they can provide the origin of primordial galactic magnetic fields, and whether they can generate the initial fluctuations leading to the formation of large-scale structure and the measured cosmic microwave background anisotropies. We finally analyze axion and photon production in four dimensional anisotropic pre-big-bang cosmological models., Comment: Review article for the memorial volume of Dennis Sciama to be published in New Astronomy Review. In this revised version new results, especially for the dilaton and moduli spectra have been included and several typos have been corrected. Version to match the one presently in print

The observational data on the large scale structure (LSS) of the Universe are used to determine cosmological parameters within the class of adiabatic inflationary models. We show that a mixed dark matter model with cosmological constant ($\Lambda$MDM model) and parameters $\Omega_m=0.37^{+0.25}_{-0.15}$, $\Omega_{\Lambda}=0.69^{+0.15}_{-0.20}$, $\Omega_{\nu}=0.03^{+0.07}_{-0.03}$, $N_{\nu}=1$, $\Omega_b=0.037^{+0.033}_{-0.018}$, $n_s=1.02^{+0.09}_{-0.10}$, $h=0.71^{+0.22}_{-0.19}$, $b_{cl}=2.4^{+0.7}_{-0.7}$ (1$\sigma$ confidence limits) matches observational data on LSS, the nucleosynthesis constraint, direct measurements of the Hubble constant, the high redshift supernova type Ia results and the recent measurements of the location and amplitude of the first acoustic peak in the CMB anisotropy power spectrum. The best model is $\Lambda$ dominated (65% of the total energy density) and has slightly positive curvature, $\Omega=1.06$. The clustered matter consists in 8% massive neutrinos, 10% baryons and 82% cold dark matter (CDM). It is shown that the LSS observations together with the Boomerang (+MAXIMA-1) data on the first acoustic peak rule out zero-$\Lambda$ models at more than $2\sigma$ confidence level., Comment: 5 pages (Proceedings of International Conference "Astronomy In Ukraine - 2000 And Beyond", Kyiv, Ukraine, 5-8 June 2000; to be published in Supplement Series of the "Kinematics and Physics of Celestial Bodies")

We use observational data on the large scale structure (LSS) of the Universe measured over a wide range of scales from sub-galactic up to horizon scale and on the cosmic microwave background anisotropies to determine cosmological parameters within the class of adiabatic inflationary models. We show that a mixed dark matter model with cosmological constant ($\Lambda$MDM model) and parameters $\Omega_m=0.37^{+0.25}_{-0.15}$, $\Omega_{\Lambda}=0.69^{+0.15}_{-0.20}$, $\Omega_{\nu}=0.03^{+0.07}_{-0.03}$, $N_{\nu}=1$, $\Omega_b=0.037^{+0.033}_{-0.018}$, $n_s=1.02^{+0.09}_{-0.10}$, $h=0.71^{+0.22}_{-0.19}$, $b_{cl}=2.4^{+0.7}_{-0.7}$ (1$\sigma$ confidence limits) matches observational data on LSS, the nucleosynthesis constraint, direct measurements of Hubble constant, the high redshift supernova type Ia results and the recent measurements of the location and amplitude of the first acoustic peak in the CMB anisotropy power spectrum. The best model is $\Lambda$ dominated (65% of the total energy density) and has slightly positive curvature, $\Omega=1.06$. The clustered matter consists in 8% massive neutrinos, 10% baryons and 82% cold dark matter (CDM). The upper 2$\sigma$ limit on the neutrino content can be expressed in the form $\Omega_{\nu}h^2/N_{\nu}^{0.64}\le0.042$ or, via the neutrino mass, $m_{\nu}\le4.0$eV. The upper 1(2)$\sigma$ limit for the contribution of a tensor mode to the COBE DMR data is T/S$<1(1.5)$. Furthermore, it is shown that the LSS observations together with the Boomerang (+MAXIMA-1) data on the first acoustic peak rule out zero-$\Lambda$ models at more than $2\sigma$ confidence limit., Comment: 13 pages, 3 figures; accepted by MNRAS; minor corrections in the text, a few references are added

We present an alternative scenario for cosmic structure formation where initial fluctuations are due to Kalb-Ramond axions produced during a pre-big bang phase of inflation. We investigate whether this scenario, where the fluctuations are induced by seeds and therefore are of isocurvature nature, can be brought in agreement with present observations by a suitable choice of cosmological parameters. We also discuss several observational signatures which can distinguish axion seeds from standard inflationary models. We finally discuss the gravitational wave background induced in this model and we show that it may be well within the range of future observations., Comment: 33 pages, 18 figures, corrected some typos

The possibility of determining cosmological parameters on the basis of a wide set of observational data including the Abell-ACO cluster power spectrum and mass function, peculiar velocities of galaxies, the distribution of Ly-$\alpha$ clouds and CMB temperature fluctuations is analyzed. Using a $\chi^2$ minimization method, assuming $\Omega_{\Lambda}+\Omega_m =1$ and no contribution from gravity waves, we found that a tilted $\Lambda$MDM model with one sort of massive neutrinos and the parameters $n\approx 1.12$, $\Omega_m\approx 0.4$ ($\Omega_{\Lambda}\approx 0.6$), $\Omega_{cdm}\approx 0.3$, $\Omega_{\nu}\approx 0.06$, $\Omega_b\approx 0.04$ and $h\approx 0.7$ matches observational data best. $\Omega_{\nu}$ is higher for more species of massive neutrinos, $\sim 0.1$ for two and $\sim 0.13$ for three species. $\Omega_m$ raises by $\sim 0.08$ and $\sim 0.15$ respectively. Varying only a subset of parameters and fixing the others shows also that the observational data set used here rules out pure CDM models with $h\ge 0.5$, scale invariant primordial power spectrum, zero cosmological constant and spatial curvature at a very high confidence level, $>99.99%$. The corresponding class of MDM models are ruled out at $\sim 95%$ C.L. It is notable also that this data set determines the amplitude of scalar fluctuations approximately at the same level as COBE four-year data. It indicates that a possible tensor component in the COBE data cannot be very substantial., Comment: 9 pages, 1 figures (Proceedings of IV International Conference "Cosmology. Relativistic Astrophysics. Cosmoparticle Physics", Moscow, 17-24 October 1999; to be published in "Gravitation & Cosmology, Vol. 5 (1999), Supplement)

The possibility of determining cosmological parameters on the basis of a wide set of observational data including the Abell-ACO cluster power spectrum and mass function, peculiar velocities of galaxies, the distribution of Ly-$\alpha$ clouds and CMB temperature fluctuations is analyzed. Using a $\chi^2$ minimization method, assuming $\Omega_{\Lambda}+\Omega_{\rm{matter}} =1 $ and no contribution from gravity waves, we found that a tilted $\Lambda$MDM model with one sort of massive neutrinos and the parameters $n=1.12\pm 0.10$, $\Omega_m=0.41\pm 0.11$ ($\Omega_{\Lambda}=0.59\pm0.11$), $\Omega_{cdm}=0.31\pm 0.15$, $\Omega_{\nu}=0.059\pm 0.028$, $\Omega_b=0.039\pm 0.014$ and $h=0.70\pm 0.12$ matches observational data best. The 1$\sigma$ (68.3%) confidence limits on each cosmological parameter, which are obtained by marginalizing over the other parameters, are $0.82\le n\le1.39$, $0.19\le\Omega_m\le 1$ ($0\le\Omega_{\Lambda}\le 0.81$), $0\le\Omega_{\nu}\le 0.17$, $0.021\le \Omega_b\le 0.13$ and $0.38\le h\le 0.85$ $1.5\le b_{cl}\le 3.5$. Here $b_{cl}$ is the cluster bias parameter. The best-fit parameters for 31 models which are inside of $1\sigma$ range of the best model are presented. It is shown also that observational data set used here rules out the class of CDM models with $h\ge 0.5$, scale invariant primordial power spectrum, zero cosmological constant and spatial curvature at very high confidence level, $>99.99%$. The corresponding class of MDM models are ruled out at $\sim 95%$ C.L., Comment: 19 pages, 9 figures. Accepted for publication in A&A

We derive an expression for the angular power spectrum of cosmic microwave background anisotropies due to gravity waves generated by a stochastic magnetic field and compare the result with current observations; we take into account the non-linear nature of the stress energy tensor of the magnetic field. For almost scale invariant spectra, the amplitude of the magnetic field at galactic scales is constrained to be of order 10^{-9} Gauss. If we assume that the magnetic field is damped below the Alfven damping scale, we find that its amplitude at 0.1 h^{-1}Mpc, B_\lambda, is constrained to be B_\lambda<7.9 x10^{-6} e^{3n} Gauss, for n<-3/2, and B_\lambda<9.5x10^{-8} e^{0.37n} Gauss, for n>-3/2, where n is the spectral index of the magnetic field and H_0=100h km s^{-1}Mpc^{-1} is the Hubble constant today., Comment: 6 pages, 1 figure, accepted for publication in Phys. Rev. D

A recently proposed mechanism for large-scale structure in string cosmology --based on massless axionic seeds-- is further analyzed and extended to the acoustic-peak region. Existence, structure, and normalization of the peaks turn out to depend crucially on the overall evolution of extra dimensions during the pre-big bang phase: conversely, precise cosmic microwave background anisotropy data in the acoustic-peak region will provide, within the next decade, a window on string-theory's extra dimensions before their eventual compactification., Comment: 4 pages, 3 figures, to appear in Physical Review Letters

An accurate analytic approximation of the transfer function for the power spectra of primordial density perturbations in mixed dark matter models is presented. The fitting formula in a matter-dominated Universe ($\Omega_0=\Omega_M=1$) is a function of wavenumber $k$, redshift $z$ and four cosmological parameters: the density of massive neutrinos, $\Omega_{\nu}$, the number of massive neutrino species, $N_{\nu}$, the baryon density, $\Omega_{b}$ and the dimensionless Hubble constant, $h$. Our formula is accurate in a broad range of parameters: $k\le 100 h/Mpc$, $z\le 30$, $\Omega_{\nu}\le 0.5$, $N_{\nu}\le 3$, $\Omega_{b}\le 0.3$, $0.3\le h\le 0.7$. The deviation of the variance of density fluctuations calculated with our formula from numerical results obtained with CMBfast is less than 6% for the entire range of parameters. It increases with $\Omega_bh^{2}$ and is less than $\le 3%$ for $\Omega_bh^{2}\le 0.05$. The performance of the analytic approximation of MDM power spectra proposed here is compared with other approximations found in the literature. Our approximation turns out to be closest to numerical results in the parameter space considered here., Comment: 13 pages, 20 figures, LaTeX (l-aa) (accepted by A&A)

A primordial stochastic background of very weakly coupled massless (pseudo-)scalars can seed CMB anisotropy, when large-scale fluctuations of their stress-tensor re-enter the horizon during the matter-dominated era. A general relation between multipole coefficients of the CMB anisotropy and the seed's energy spectrum is derived. Magnitude and tilt of the observed anisotropies can be reproduced for the nearly scale-invariant axion spectra that are predicted in a particularly symmetric class of string cosmology backgrounds., Comment: 9 pages, LATEX

Pre-big bang cosmology predicts tiny first-order dilaton and metric perturbations at very large scales. Here we discuss the possibility that other -- more copiously generated -- perturbations may act, at second order, as scalar seeds of large-scale structure and CMB anisotropies. We study, in particular, the cases of electromagnetic and axionic seeds. We compute the stochastic fluctuations of their energy-momentum tensor and determine the resulting contributions to the multipole expansion of the temperature anisotropy. In the axion case it is possible to obtain a flat or slightly tilted blue spectrum that fits present data consistently, both for massless and for massive (but very light) axions., Comment: 27 pages, LATEX, one figure included using epsf

We compute cosmic microwave background angular power spectra for scaling seed models of structure formation. A generic parameterization of the energy momentum tensor of the seeds is employed. We concentrate on two regions of parameter space inspired by global topological defects: O(4) texture models and the large-N limit of O(N) models. We use $\chi^{2}$ fitting to compare these models to recent flat-band power measurements of the cosmic microwave background. Only scalar perturbations are considered., Comment: LaTeX file 4 pages, 4 postscript figs. revised version, to appear in PRL

We investigate cosmological structure formation seeded by topological defects which may form during a phase transition in the early universe. First we derive a partially new, local and gauge invariant system of perturbation equations to treat microwave background and dark matter fluctuations induced by topological defects or any other type of seeds. We then show that this system is well suited for numerical analysis of structure formation by applying it to seeds induced by fluctuations of a global scalar field. Our numerical results are complementary to previous investigations since we use substantially different methods. The resulting microwave background fluctuations are compatible with older simulations. We also obtain a scale invariant spectrum of fluctuations with about the same amplitude. However, our dark matter results yield a smaller bias parameter compatible with $b\sim 2$ on a scale of $20 Mpc$ in contrast to previous work which yielded to large bias factors. Our conclusions are thus more positive. According to the aspects analyzed in this work, global topological defect induced fluctuations yield viable scenarios of structure formation and do better than standard CDM on large scales., Comment: uuencoded, compressed tar-file containing the text in LaTeX and 12 Postscript Figures, 41 pages

We show that there are inflationary models for which perturbations in the energy momentum tensor, which are of second order in the scalar field, cannot be neglected. We first specify the conditions under which the usual first order perturbations are absent. We then analyze classically, the growth and decay of our new type of perturbations for one mode of fluctuations $\de\phi_k$ in the scalar field. We generalize this analysis, considering the contribution from the whole spectrum of $\de\phi$ to a given wavelength of geometrical perturbations. Finally, we discuss the evolution of the perturbations during the subsequent radiation dominated era and discuss the resulting spectrum of density fluctuations. In the case of a massless scalar field we find a spectral index $n=4$. For massive scalar fields we obtain $n=0$ but the resulting amplitude of fluctuations for inflation around a GUT scale are by far too high. Hence, 'conventional' inflationary models must not be influenced by this new type of perturbations, in order to lead to acceptable matter and CMB fluctuations., Comment: LaTeX file, 15p, 2 Postscript Figs. available on request, Zurich University Preprint ZU-TH9/94

The cosmic microwave anisotropies in a scenario of large scale structure formation with cold dark matter and texture are discussed and compared with recent observational results of the COBE satellite. A couple of important statistical parameters are determined. The fluctuations are slightly non gaussian. The quadrupole anisotropy is $1.5\pm 1.2\times 10^{-5}$ and the fluctuations on a angular scale of 10 degrees are $ (3.8\pm 2.6)\times 10^{-5}$. The COBE are within about one standard deviation of the typical texture + CDM model discussed in this paper. Furthermore, we calculate fluctuations on intermediate scales (about 2 degrees) with the result $\De T/T(\theta \sim 2^o) = 3.9\pm 0.8)\times 10^{-5}$. Collapsing textures are modeled by spherically symmetric field configurations. This leads to uncertainties of about a factor of~2., Comment: 16p, LaTex, ZU-TH 32/92