In General Relativity, the constraint equation relating metric and density perturbations is inher... more In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the density field on large scales -even if the primordial metric perturbation is Gaussian. This imprints a relativistic signature in large-scale structure which is potentially observable, for example via a scale-dependent galaxy bias. The effect has been derived and then confirmed by independent calculations, using second-order perturbation theory. Recently, the physical reality of this relativistic effect has been disputed. The counterargument is based on the claim that a very long wavelength curvature perturbation can be removed by a coordinate transformation. We argue that while this is true locally, the large-scale curvature cannot be removed by local coordinate transformations. The transformation itself contains the longwavelength modes and thus includes the correlation. We show how the separate universe approach can be used to understand this correlation, confirming the results of perturbation theory.
We point out that the theoretical predictions for the inflationary observables may be generically... more We point out that the theoretical predictions for the inflationary observables may be generically altered by the presence of fields which are heavier than the Hubble rate during inflation and whose dynamics is usually neglected. They introduce corrections which may be easily larger than both the second-order contributions in the slow-roll parameters and the accuracy expected in the forthcoming experiments.
We obtain exact expressions for the effect of primordial non-Gaussianity on the matter density pe... more We obtain exact expressions for the effect of primordial non-Gaussianity on the matter density perturbation up to second order in a ΛCDM cosmology, fully accounting for the general relativistic corrections arising on scales comparable with the Hubble radius. We present our results both in the Poisson gauge and in the comoving and synchronous gauge, which are relevant for comparison to different cosmological observables.
We investigate how well future large-scale radio surveys could measure different shapes of primor... more We investigate how well future large-scale radio surveys could measure different shapes of primordial non-Gaussianity; in particular we focus on angle-dependent non-Gaussianity arising from primordial anisotropic sources, whose bispectrum has an angle dependence between the three wavevectors that is characterized by Legendre polynomials PL and expansion coefficients cL. We provide forecasts for measurements of galaxy power spectrum, finding that Large-Scale Structure (LSS) data could allow measurements of primordial non-Gaussianity competitive or improving upon current constraints set by CMB experiments, for all the shapes considered. We argue that the best constraints will come from the possibility to assign redshift information to radio galaxy surveys, and investigate a few possible scenarios for the EMU and SKA surveys. A realistic (futuristic) modeling could provide constraints of f loc NL ≈ 1(0.5) for the local shape, fNL of O(10)(O(1)) for the orthogonal, equilateral and folded shapes, and cL=1 ≈ 80(2), cL=2 ≈ 400(10) for angle-dependent non-Gaussianity. The more futuristic forecasts show the potential of LSS analyses to considerably improve current constraints on non-Gaussianity, and so on models of the primordial Universe. Finally, we find the minimum requirements that would be needed to reach σ(cL=1) = 10, which can be considered as a typical (lower) value predicted by some (inflationary) models. arXiv:1507.05903v1 [astro-ph.CO] 21 Jul 2015 2 These values correspond to the Planck 2015 limits [5]: f L=1 NL = −49 ± 43 and f L=2 NL = 0.5 ± 2.7, where the f L NL parameters in the Planck papers [4, 5] are related to c L in Eq. (1) as c 1 = −(12/5)f L=1 NL and c 2 = −(48/5)f L=2 NL . 3 This paper focuses on the isotropic angle-averaged bispectrum effects on the scale-dependent bias due to primordial vector fields. See [31] for the analysis including the statistically-anisotropic effects. For the analysis of the effects sourced from large-scale vector fields existing in the radiation dominated era, see [32]. 4 In this paper we only take into account the contributions from the bispectrum. See [62, 63] for discussions on the higher-order effects.
We discuss the question of gauge choice when analysing second-order relativistic perturbations an... more We discuss the question of gauge choice when analysing second-order relativistic perturbations and when defining the galaxy bias at second order. Some misconceptions in the recent literature on the comoving-synchronous gauge are addressed and we show that this gauge is appropriate at second order to describe the matter overdensity and to define local Lagrangian bias.
The polarized thermal emission from diffuse Galactic dust is the main foreground present in measu... more The polarized thermal emission from diffuse Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100 GHz. In this paper we exploit the uniqueness of the Planck HFI polarization data from 100 to 353 GHz to measure the polarized dust angular power spectra C EE and C BB over the multipole range 40 < < 600 well away from the Galactic plane. These measurements will bring new insights into interstellar dust physics and allow a precise determination of the level of contamination for CMB polarization experiments. Despite the non-Gaussian and anisotropic nature of Galactic dust, we show that general statistical properties of the emission can be characterized accurately over large fractions of the sky using angular power spectra. The polarization power spectra of the dust are well described by power laws in multipole, C ∝ α , with exponents α EE,BB = −2.42 ± 0.02. The amplitudes of the polarization power spectra vary with the average brightness in a way similar to the intensity power spectra. The frequency dependence of the dust polarization spectra is consistent with modified blackbody emission with β d = 1.59 and T d = 19.6 K down to the lowest Planck HFI frequencies. We find a systematic difference between the amplitudes of the Galactic B-and E-modes, C BB /C EE = 0.5. We verify that these general properties are preserved towards high Galactic latitudes with low dust column densities. We show that even in the faintest dust-emitting regions there are no "clean" windows in the sky where primordial CMB B-mode polarization measurements could be made without subtraction of foreground emission. Finally, we investigate the level of dust polarization in the specific field recently targeted by the BICEP2 experiment. Extrapolation of the Planck 353 GHz data to 150 GHz gives a dust power D BB ≡ ( + 1)C BB /(2π) of 1.32 × 10 −2 µK 2 CMB over the multipole range of the primordial recombination bump (40 < < 120); the statistical uncertainty is ±0.29 × 10 −2 µK 2 CMB and there is an additional uncertainty (+0.28, −0.24) × 10 −2 µK 2 CMB from the extrapolation. This level is the same magnitude as reported by BICEP2 over this range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky. The present uncertainties are large and will be reduced through an ongoing, joint analysis of the Planck and BICEP2 data sets.
We present all-sky dust modelling of the high resolution Planck, IRAS and WISE infrared (IR) obse... more We present all-sky dust modelling of the high resolution Planck, IRAS and WISE infrared (IR) observations using the physical dust model presented by Draine & Li in 2007 (DL). We study the performance of this model and present implications for future dust modelling. The present work extends to the full sky the dust modelling carried out on nearby galaxies using Herschel and Spitzer data. We employ the DL dust model to generate maps of the dust mass surface density Σ M d , the dust optical extinction A V , and the starlight intensity heating the bulk of the dust, parametrized by U min . We test the model by comparing these maps with independent estimates of the dust optical extinction A V . The DL model reproduces the observed spectral energy distribution (SED) satisfactorily over most of the sky, with small deviations in the inner Galactic disk, and in low ecliptic latitude areas, presumably due to zodiacal light contamination. In the Andromeda galaxy (M31), the present dust mass estimates agree remarkably well (within 10 %) with DL estimates based on independent Spitzer and Herschel data. In molecular clouds, we compare the DL A V estimates with maps generated from stellar optical observations from the 2MASS survey. The DL A V estimates are a factor of about 3 larger than values estimated from 2MASS observations. In the diffuse interstellar medium (ISM) we compare the DL optical extinction A V estimates with optical estimates from approximately 2 × 10 5 quasi-stellar objects (QSOs) observed in the Sloan digital sky survey. The DL A V estimates are larger than those determined from the QSOs, and this discrepancy depends on U min . We propose an empirical renormalization of the DL A V estimate, dependent of U min , which compensates for the systematic differences found here. This renormalization, bringing into agreement the A V estimates on QSOs, also brings into agreement the A V estimates on molecular clouds. In the diffuse ISM, the DL fitting parameter U min , effectively determined by the wavelength where the SED peaks, appears to trace variations in the far-IR opacity of the dust grains. Therefore, some of the physical assumptions of the DL model need to be revised. We provide a family of SEDs normalized by optical reddening, parameterized by U min ; these will be the constraints for a next generation of dust models.
We summarize the utility of precise cosmic microwave background (CMB) polarization measurements a... more We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B-mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super-Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale-dependence and non-Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters. †
The European Space Agency's Planck satellite, dedicated to studying the early Universe and its su... more The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14 May 2009 and has been scanning the microwave and submillimetre sky continuously since 12 August 2009. In March 2013, ESA and the Planck Collaboration released the initial cosmology products based on the first 15.5 months of Planck data, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the mission and its performance, the processing, analysis, and characteristics of the data, the scientific results, and the science data products and papers in the release. The science products include maps of the cosmic microwave background (CMB) and diffuse extragalactic foregrounds, a catalogue of compact Galactic and extragalactic sources, and a list of sources detected through the Sunyaev-Zeldovich effect. The likelihood code used to assess cosmological models against the Planck data and a lensing likelihood are described. Scientific results include robust support for the standard six-parameter ΛCDM model of cosmology and improved measurements of its parameters, including a highly significant deviation from scale invariance of the primordial power spectrum. The Planck values for these parameters and others derived from them are significantly different from those previously determined. Several large-scale anomalies in the temperature distribution of the CMB, first detected by WMAP, are confirmed with higher confidence. Planck sets new limits on the number and mass of neutrinos, and has measured gravitational lensing of CMB anisotropies at greater than 25σ. Planck finds no evidence for non-Gaussianity in the CMB. Planck's results agree well with results from the measurements of baryon acoustic oscillations. Planck finds a lower Hubble constant than found in some more local measures. Some tension is also present between the amplitude of matter fluctuations (σ 8 ) derived from CMB data and that derived from Sunyaev-Zeldovich data. The Planck and WMAP power spectra are offset from each other by an average level of about 2% around the first acoustic peak. Analysis of Planck polarization data is not yet mature, therefore polarization results are not released, although the robust detection of E-mode polarization around CMB hot and cold spots is shown graphically.
Journal of Cosmology and Astroparticle Physics, 2009
We consider a primordial SU (2) vector multiplet during inflation in models where quantum fluctua... more We consider a primordial SU (2) vector multiplet during inflation in models where quantum fluctuations of vector fields are involved in producing the curvature perturbation. Recently, a lot of attention has been paid to models populated by vector fields, given the interesting possibility of generating some level of statistical anisotropy in the cosmological perturbations. The scenario we propose is strongly motivated by the fact that, for non-Abelian gauge fields, self-interactions are responsible for generating extra terms in the cosmological correlation functions, which are naturally absent in the Abelian case. We compute these extra contributions to the bispectrum of the curvature perturbation, using the δN formula and the Schwinger-Keldysh formalism. The primordial violation of rotational invariance (due to the introduction of the SU (2) gauge multiplet) leaves its imprint on the correlation functions introducing, as expected, some degree of statistical anisotropy in our results. We calculate the non-Gaussianity parameter f N L , proving that the new contributions derived from gauge bosons self-interactions can be important, and in some cases the dominat ones. We study the shape of the bispectrum and we find that it turns out to peak in the local configuration, with an amplitude that is modulated by the preferred directions that break statistical isotropy.
We present the first computation of the cosmological perturbations generated during inflation up ... more We present the first computation of the cosmological perturbations generated during inflation up to second order in deviations from the homogeneous background solution. Our results, which fully account for the inflaton self-interactions as well as for the second-order fluctuations of the background metric, provide the exact expression for the gauge-invariant curvature perturbation bispectrum produced during inflation in terms of the slow-roll parameters. The bispectrum represents a specific non-Gaussian signature of fluctuations generated by quantum oscillations during slow-roll inflation. However, our findings indicate that detecting the non-Gaussianity in the cosmic microwave background anisotropies emerging from the second-order calculation will be a challenge for the forthcoming satellite experiments.
We study the evolution of cosmological perturbations on large scales, up to second order, for a p... more We study the evolution of cosmological perturbations on large scales, up to second order, for a perfect fluid with generic equation of state. Taking advantage of super-horizon conservation laws, it is possible to follow the evolution of the non-Gaussianity of perturbations through the different stages after inflation. We find that a large non-linearity is generated by the gravitational dynamics from the original inflationary quantum fluctuations. This leads to a significant enhancement of the tiny intrinsic non-Gaussianity produced during inflation in single-field slow-roll models. 1
Preprint submitted to Elsevier Science 5.1 The first-order curvature perturbation 67 5.2 Reheatin... more Preprint submitted to Elsevier Science 5.1 The first-order curvature perturbation 67 5.2 Reheating after inflation 69 5.3 The second-order curvature perturbation and non-Gaussianity during inflation 70 5.4 Reheating after inflation 75 5.5 Post-inflationary evolution of the second-order curvature perturbation 76 6 The curvaton scenario 78 6.1 Generating the curvature perturbation at linear order 79 6.2 Second-order curvature perturbation from the curvaton fluctuations 82 7 The inhomogeneous reheating scenario: δΓ = 0 85 7.1 Generating the curvature perturbation at linear order from decay rate fluctuations 86 7.2 Second-order curvature perturbation from inhomogeneous reheating 87 8 Non-linearities in the gravitational potential 89 8.1 The standard scenario 90 8.2 The curvaton scenario 93 8.3 The inhomogeneous reheating scenario 94 8.4 Second-order temperature fluctuations on large scales and the correct definition of the measured f NL 96 9
We provide the gauge-invariant expression for large-scale cosmic microwave background temperature... more We provide the gauge-invariant expression for large-scale cosmic microwave background temperature fluctuations at second-order in perturbation theory. It enables to unambiguously define the nonlinearity parameter fNL which is used by experimental collaborations to pin down the level of Non-Gaussianity in the temperature fluctuations. Furthermore, it contains a primordial term encoding all the information about the Non-Gaussianity generated at primordial epochs and about the mechanism which gave rise to cosmological perturbations, thus neatly disentangling the primordial contribution to Non-Gaussianity from the one caused by the post-inflationary evolution.
We obtain the equation governing the evolution of the cosmological gravitational-wave background,... more We obtain the equation governing the evolution of the cosmological gravitational-wave background, accounting for the presence of cosmic neutrinos, up to second order in perturbation theory. In particular, we focus on the epoch during radiation dominance, after neutrino decoupling, when neutrinos yield a relevant contribution to the total energy density and behave as collisionless ultrarelativistic particles. Besides recovering the standard damping effect due to neutrinos, a new source term for gravitational waves is shown to arise from the neutrino anisotropic stress tensor. The importance of such a source term, so far completely disregarded in the literature, is related to the high velocity dispersion of neutrinos in the considered epoch; its computation requires solving the full second-order Boltzmann equation for collisionless neutrinos.
In General Relativity, the constraint equation relating metric and density perturbations is inher... more In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the density field on large scales -even if the primordial metric perturbation is Gaussian. This imprints a relativistic signature in large-scale structure which is potentially observable, for example via a scale-dependent galaxy bias. The effect has been derived and then confirmed by independent calculations, using second-order perturbation theory. Recently, the physical reality of this relativistic effect has been disputed. The counterargument is based on the claim that a very long wavelength curvature perturbation can be removed by a coordinate transformation. We argue that while this is true locally, the large-scale curvature cannot be removed by local coordinate transformations. The transformation itself contains the longwavelength modes and thus includes the correlation. We show how the separate universe approach can be used to understand this correlation, confirming the results of perturbation theory.
We point out that the theoretical predictions for the inflationary observables may be generically... more We point out that the theoretical predictions for the inflationary observables may be generically altered by the presence of fields which are heavier than the Hubble rate during inflation and whose dynamics is usually neglected. They introduce corrections which may be easily larger than both the second-order contributions in the slow-roll parameters and the accuracy expected in the forthcoming experiments.
We obtain exact expressions for the effect of primordial non-Gaussianity on the matter density pe... more We obtain exact expressions for the effect of primordial non-Gaussianity on the matter density perturbation up to second order in a ΛCDM cosmology, fully accounting for the general relativistic corrections arising on scales comparable with the Hubble radius. We present our results both in the Poisson gauge and in the comoving and synchronous gauge, which are relevant for comparison to different cosmological observables.
We investigate how well future large-scale radio surveys could measure different shapes of primor... more We investigate how well future large-scale radio surveys could measure different shapes of primordial non-Gaussianity; in particular we focus on angle-dependent non-Gaussianity arising from primordial anisotropic sources, whose bispectrum has an angle dependence between the three wavevectors that is characterized by Legendre polynomials PL and expansion coefficients cL. We provide forecasts for measurements of galaxy power spectrum, finding that Large-Scale Structure (LSS) data could allow measurements of primordial non-Gaussianity competitive or improving upon current constraints set by CMB experiments, for all the shapes considered. We argue that the best constraints will come from the possibility to assign redshift information to radio galaxy surveys, and investigate a few possible scenarios for the EMU and SKA surveys. A realistic (futuristic) modeling could provide constraints of f loc NL ≈ 1(0.5) for the local shape, fNL of O(10)(O(1)) for the orthogonal, equilateral and folded shapes, and cL=1 ≈ 80(2), cL=2 ≈ 400(10) for angle-dependent non-Gaussianity. The more futuristic forecasts show the potential of LSS analyses to considerably improve current constraints on non-Gaussianity, and so on models of the primordial Universe. Finally, we find the minimum requirements that would be needed to reach σ(cL=1) = 10, which can be considered as a typical (lower) value predicted by some (inflationary) models. arXiv:1507.05903v1 [astro-ph.CO] 21 Jul 2015 2 These values correspond to the Planck 2015 limits [5]: f L=1 NL = −49 ± 43 and f L=2 NL = 0.5 ± 2.7, where the f L NL parameters in the Planck papers [4, 5] are related to c L in Eq. (1) as c 1 = −(12/5)f L=1 NL and c 2 = −(48/5)f L=2 NL . 3 This paper focuses on the isotropic angle-averaged bispectrum effects on the scale-dependent bias due to primordial vector fields. See [31] for the analysis including the statistically-anisotropic effects. For the analysis of the effects sourced from large-scale vector fields existing in the radiation dominated era, see [32]. 4 In this paper we only take into account the contributions from the bispectrum. See [62, 63] for discussions on the higher-order effects.
We discuss the question of gauge choice when analysing second-order relativistic perturbations an... more We discuss the question of gauge choice when analysing second-order relativistic perturbations and when defining the galaxy bias at second order. Some misconceptions in the recent literature on the comoving-synchronous gauge are addressed and we show that this gauge is appropriate at second order to describe the matter overdensity and to define local Lagrangian bias.
The polarized thermal emission from diffuse Galactic dust is the main foreground present in measu... more The polarized thermal emission from diffuse Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100 GHz. In this paper we exploit the uniqueness of the Planck HFI polarization data from 100 to 353 GHz to measure the polarized dust angular power spectra C EE and C BB over the multipole range 40 < < 600 well away from the Galactic plane. These measurements will bring new insights into interstellar dust physics and allow a precise determination of the level of contamination for CMB polarization experiments. Despite the non-Gaussian and anisotropic nature of Galactic dust, we show that general statistical properties of the emission can be characterized accurately over large fractions of the sky using angular power spectra. The polarization power spectra of the dust are well described by power laws in multipole, C ∝ α , with exponents α EE,BB = −2.42 ± 0.02. The amplitudes of the polarization power spectra vary with the average brightness in a way similar to the intensity power spectra. The frequency dependence of the dust polarization spectra is consistent with modified blackbody emission with β d = 1.59 and T d = 19.6 K down to the lowest Planck HFI frequencies. We find a systematic difference between the amplitudes of the Galactic B-and E-modes, C BB /C EE = 0.5. We verify that these general properties are preserved towards high Galactic latitudes with low dust column densities. We show that even in the faintest dust-emitting regions there are no "clean" windows in the sky where primordial CMB B-mode polarization measurements could be made without subtraction of foreground emission. Finally, we investigate the level of dust polarization in the specific field recently targeted by the BICEP2 experiment. Extrapolation of the Planck 353 GHz data to 150 GHz gives a dust power D BB ≡ ( + 1)C BB /(2π) of 1.32 × 10 −2 µK 2 CMB over the multipole range of the primordial recombination bump (40 < < 120); the statistical uncertainty is ±0.29 × 10 −2 µK 2 CMB and there is an additional uncertainty (+0.28, −0.24) × 10 −2 µK 2 CMB from the extrapolation. This level is the same magnitude as reported by BICEP2 over this range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky. The present uncertainties are large and will be reduced through an ongoing, joint analysis of the Planck and BICEP2 data sets.
We present all-sky dust modelling of the high resolution Planck, IRAS and WISE infrared (IR) obse... more We present all-sky dust modelling of the high resolution Planck, IRAS and WISE infrared (IR) observations using the physical dust model presented by Draine & Li in 2007 (DL). We study the performance of this model and present implications for future dust modelling. The present work extends to the full sky the dust modelling carried out on nearby galaxies using Herschel and Spitzer data. We employ the DL dust model to generate maps of the dust mass surface density Σ M d , the dust optical extinction A V , and the starlight intensity heating the bulk of the dust, parametrized by U min . We test the model by comparing these maps with independent estimates of the dust optical extinction A V . The DL model reproduces the observed spectral energy distribution (SED) satisfactorily over most of the sky, with small deviations in the inner Galactic disk, and in low ecliptic latitude areas, presumably due to zodiacal light contamination. In the Andromeda galaxy (M31), the present dust mass estimates agree remarkably well (within 10 %) with DL estimates based on independent Spitzer and Herschel data. In molecular clouds, we compare the DL A V estimates with maps generated from stellar optical observations from the 2MASS survey. The DL A V estimates are a factor of about 3 larger than values estimated from 2MASS observations. In the diffuse interstellar medium (ISM) we compare the DL optical extinction A V estimates with optical estimates from approximately 2 × 10 5 quasi-stellar objects (QSOs) observed in the Sloan digital sky survey. The DL A V estimates are larger than those determined from the QSOs, and this discrepancy depends on U min . We propose an empirical renormalization of the DL A V estimate, dependent of U min , which compensates for the systematic differences found here. This renormalization, bringing into agreement the A V estimates on QSOs, also brings into agreement the A V estimates on molecular clouds. In the diffuse ISM, the DL fitting parameter U min , effectively determined by the wavelength where the SED peaks, appears to trace variations in the far-IR opacity of the dust grains. Therefore, some of the physical assumptions of the DL model need to be revised. We provide a family of SEDs normalized by optical reddening, parameterized by U min ; these will be the constraints for a next generation of dust models.
We summarize the utility of precise cosmic microwave background (CMB) polarization measurements a... more We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B-mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super-Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale-dependence and non-Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters. †
The European Space Agency's Planck satellite, dedicated to studying the early Universe and its su... more The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14 May 2009 and has been scanning the microwave and submillimetre sky continuously since 12 August 2009. In March 2013, ESA and the Planck Collaboration released the initial cosmology products based on the first 15.5 months of Planck data, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the mission and its performance, the processing, analysis, and characteristics of the data, the scientific results, and the science data products and papers in the release. The science products include maps of the cosmic microwave background (CMB) and diffuse extragalactic foregrounds, a catalogue of compact Galactic and extragalactic sources, and a list of sources detected through the Sunyaev-Zeldovich effect. The likelihood code used to assess cosmological models against the Planck data and a lensing likelihood are described. Scientific results include robust support for the standard six-parameter ΛCDM model of cosmology and improved measurements of its parameters, including a highly significant deviation from scale invariance of the primordial power spectrum. The Planck values for these parameters and others derived from them are significantly different from those previously determined. Several large-scale anomalies in the temperature distribution of the CMB, first detected by WMAP, are confirmed with higher confidence. Planck sets new limits on the number and mass of neutrinos, and has measured gravitational lensing of CMB anisotropies at greater than 25σ. Planck finds no evidence for non-Gaussianity in the CMB. Planck's results agree well with results from the measurements of baryon acoustic oscillations. Planck finds a lower Hubble constant than found in some more local measures. Some tension is also present between the amplitude of matter fluctuations (σ 8 ) derived from CMB data and that derived from Sunyaev-Zeldovich data. The Planck and WMAP power spectra are offset from each other by an average level of about 2% around the first acoustic peak. Analysis of Planck polarization data is not yet mature, therefore polarization results are not released, although the robust detection of E-mode polarization around CMB hot and cold spots is shown graphically.
Journal of Cosmology and Astroparticle Physics, 2009
We consider a primordial SU (2) vector multiplet during inflation in models where quantum fluctua... more We consider a primordial SU (2) vector multiplet during inflation in models where quantum fluctuations of vector fields are involved in producing the curvature perturbation. Recently, a lot of attention has been paid to models populated by vector fields, given the interesting possibility of generating some level of statistical anisotropy in the cosmological perturbations. The scenario we propose is strongly motivated by the fact that, for non-Abelian gauge fields, self-interactions are responsible for generating extra terms in the cosmological correlation functions, which are naturally absent in the Abelian case. We compute these extra contributions to the bispectrum of the curvature perturbation, using the δN formula and the Schwinger-Keldysh formalism. The primordial violation of rotational invariance (due to the introduction of the SU (2) gauge multiplet) leaves its imprint on the correlation functions introducing, as expected, some degree of statistical anisotropy in our results. We calculate the non-Gaussianity parameter f N L , proving that the new contributions derived from gauge bosons self-interactions can be important, and in some cases the dominat ones. We study the shape of the bispectrum and we find that it turns out to peak in the local configuration, with an amplitude that is modulated by the preferred directions that break statistical isotropy.
We present the first computation of the cosmological perturbations generated during inflation up ... more We present the first computation of the cosmological perturbations generated during inflation up to second order in deviations from the homogeneous background solution. Our results, which fully account for the inflaton self-interactions as well as for the second-order fluctuations of the background metric, provide the exact expression for the gauge-invariant curvature perturbation bispectrum produced during inflation in terms of the slow-roll parameters. The bispectrum represents a specific non-Gaussian signature of fluctuations generated by quantum oscillations during slow-roll inflation. However, our findings indicate that detecting the non-Gaussianity in the cosmic microwave background anisotropies emerging from the second-order calculation will be a challenge for the forthcoming satellite experiments.
We study the evolution of cosmological perturbations on large scales, up to second order, for a p... more We study the evolution of cosmological perturbations on large scales, up to second order, for a perfect fluid with generic equation of state. Taking advantage of super-horizon conservation laws, it is possible to follow the evolution of the non-Gaussianity of perturbations through the different stages after inflation. We find that a large non-linearity is generated by the gravitational dynamics from the original inflationary quantum fluctuations. This leads to a significant enhancement of the tiny intrinsic non-Gaussianity produced during inflation in single-field slow-roll models. 1
Preprint submitted to Elsevier Science 5.1 The first-order curvature perturbation 67 5.2 Reheatin... more Preprint submitted to Elsevier Science 5.1 The first-order curvature perturbation 67 5.2 Reheating after inflation 69 5.3 The second-order curvature perturbation and non-Gaussianity during inflation 70 5.4 Reheating after inflation 75 5.5 Post-inflationary evolution of the second-order curvature perturbation 76 6 The curvaton scenario 78 6.1 Generating the curvature perturbation at linear order 79 6.2 Second-order curvature perturbation from the curvaton fluctuations 82 7 The inhomogeneous reheating scenario: δΓ = 0 85 7.1 Generating the curvature perturbation at linear order from decay rate fluctuations 86 7.2 Second-order curvature perturbation from inhomogeneous reheating 87 8 Non-linearities in the gravitational potential 89 8.1 The standard scenario 90 8.2 The curvaton scenario 93 8.3 The inhomogeneous reheating scenario 94 8.4 Second-order temperature fluctuations on large scales and the correct definition of the measured f NL 96 9
We provide the gauge-invariant expression for large-scale cosmic microwave background temperature... more We provide the gauge-invariant expression for large-scale cosmic microwave background temperature fluctuations at second-order in perturbation theory. It enables to unambiguously define the nonlinearity parameter fNL which is used by experimental collaborations to pin down the level of Non-Gaussianity in the temperature fluctuations. Furthermore, it contains a primordial term encoding all the information about the Non-Gaussianity generated at primordial epochs and about the mechanism which gave rise to cosmological perturbations, thus neatly disentangling the primordial contribution to Non-Gaussianity from the one caused by the post-inflationary evolution.
We obtain the equation governing the evolution of the cosmological gravitational-wave background,... more We obtain the equation governing the evolution of the cosmological gravitational-wave background, accounting for the presence of cosmic neutrinos, up to second order in perturbation theory. In particular, we focus on the epoch during radiation dominance, after neutrino decoupling, when neutrinos yield a relevant contribution to the total energy density and behave as collisionless ultrarelativistic particles. Besides recovering the standard damping effect due to neutrinos, a new source term for gravitational waves is shown to arise from the neutrino anisotropic stress tensor. The importance of such a source term, so far completely disregarded in the literature, is related to the high velocity dispersion of neutrinos in the considered epoch; its computation requires solving the full second-order Boltzmann equation for collisionless neutrinos.
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Papers by Nicola Bartolo