There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

WMAP precision data enable accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat � -dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data. For the WMAP data only, the best-fit parameters are h ¼ 0:72 � 0:05, � bh 2 ¼ 0:024 � 0:001, � mh 2 ¼ 0:14 � 0:02, � ¼ 0:166 þ0:076 � 0:071 , ns ¼ 0:99 � 0:04, and � 8 ¼ 0:9 � 0:1. With parameters fixed only by WMAP data, we can fit finer scale cosmic microwave background (CMB) measure- ments and measurements of large-scale structure (galaxy surveys and the Lyforest). This simple model is also consistent with a host of other astronomical measurements: its inferred age of the universe is consistent with stellar ages, the baryon/photon ratio is consistent with measurements of the (D/H) ratio, and the inferred Hubble constant is consistent with local observations of the expansion rate. We then fit the model parameters to a combination of WMAP data with other finer scale CMB experiments (ACBAR and CBI), 2dFGRS measurements, and Lyforest data to find the model's best-fit cosmological parameters: h ¼ 0:71 þ0:04 � 0:03 , � bh 2 ¼ 0:0224 � 0:0009, � mh 2 ¼ 0:135 þ0:008 � 0:009 , � ¼ 0:17 � 0:06, ns(0.05 Mpc � 1 )=0 :93 � 0:03, and � 8 ¼ 0:84 � 0:04. WMAP's best determination of � ¼ 0:17 � 0:04 arises directly from the temperature- polarization (TE) data and not from this model fit, but they are consistent. These parameters imply that the age of the universe is 13:7 � 0:2 Gyr. With the Lyforest data, the model favors but does not require a slowly varying spectral index. The significance of this running index is sensitive to the uncertainties in the Ly� forest. By combining WMAP data with other astronomical data, we constrain the geometry of the universe, � tot ¼ 1:02 � 0:02, and the equation of state of the dark energy, w < � 0:78 (95% confidence limit assuming w �� 1). The combination of WMAP and 2dFGRS data constrains the energy density in stable neutrinos: � � h 2 < 0:0072 (95% confidence limit). For three degenerate neutrino species, this limit implies that their mass is less than 0.23 eV (95% confidence limit). The WMAP detection of early reionization rules out warm dark matter. Subject headings: cosmic microwave background — cosmological parameters — cosmology: observations — early universe On-line material: color figure

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First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters

We present a new model for computing the spectral evolution of stellar populations at ages between 100,000 yr and 20 Gyr at a resolution of 3 A across the whole wavelength range from 3200 to 9500 A for a wide range of metallicities. These predictions are based on a newly available library of observed stellar spectra. We also compute the spectral evolution across a larger wavelength range, from 91 A to 160 micron, at lower resolution. The model incorporates recent progress in stellar evolution theory and an observationally motivated prescription for thermally-pulsing stars on the asymptotic giant branch. The latter is supported by observations of surface brightness fluctuations in nearby stellar populations. We show that this model reproduces well the observed optical and near-infrared colour-magnitude diagrams of Galactic star clusters of various ages and metallicities. Stochastic fluctuations in the numbers of stars in different evolutionary phases can account for the full range of observed integrated colours of star clusters in the Magellanic Clouds. The model reproduces in detail typical galaxy spectra from the Early Data Release (EDR) of the Sloan Digital Sky Survey (SDSS). We exemplify how this type of spectral fit can constrain physical parameters such as the star formation history, metallicity and dust content of galaxies. Our model is the first to enable accurate studies of absorption-line strengths in galaxies containing stars over the full range of ages. Using the highest-quality spectra of the SDSS EDR, we show that this model can reproduce simultaneously the observed strengths of those Lick indices that do not depend strongly on element abundance ratios [abridged].

https://hal.archives-ouvertes.fr/hal-00012948/document

Stellar population synthesis at the resolution of 2003

This paper presents the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the Planck spectra at high multipoles (l ≳ 40) are extremely well described by the standard spatially-flat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the Planck data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be θ∗ = (1.04147 ± 0.00062) × 10-2, Ωbh2 = 0.02205 ± 0.00028, Ωch2 = 0.1199 ± 0.0027, and ns = 0.9603 ± 0.0073, respectively(note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H0 = (67.3 ± 1.2) km s-1 Mpc-1, and a high value of the matter density parameter, Ωm = 0.315 ± 0.017. These values are in tension with recent direct measurements of H0 and the magnitude-redshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using Planck CMB data alone. We use high-resolution CMB data together with Planck to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter ΛCDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured over the standard six-parameter ΛCDM cosmology. The deviation of the scalar spectral index from unity isinsensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r0.002< 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find Neff = 3.30 ± 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of Neff = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = -1.13-0.10+0.13. We also use the Planck data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter ΛCDM model in describing the Planck data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. The unusual shape of the spectrum in the multipole range 20 ≲ l ≲ 40 was seen previously in the WMAP data and is a real feature of the primordial CMB anisotropies. The poor fit to the spectrum at low multipoles is not of decisive significance, but is an “anomaly” in an otherwise self-consistent analysis of the Planck temperature data.

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Planck 2013 results. XVI. Cosmological parameters

Statistics for Spatial Data.

We study spherical collapse in the Quartic and Quintic Covariant Galileon gravity models within the framework of the excursion set formalism. We derive the nonlinear spherically symmetric equations in the quasi-static and weak-field limits, focusing on model parameters that fit current CMB, SNIa and BAO data. We demonstrate that the equations of the Quintic model do not admit physical solutions of the fifth force in high density regions, which prevents the study of structure formation in this model. For the Quartic model, we show that the effective gravitational strength deviates from the standard value at late times (z1), becoming larger if the density is low, but smaller if the density is high. This shows that the Vainshtein mechanism at high densities is not enough to screen all of the modifications of gravity. This makes halos that collapse at z1 feel an overall weaker gravity, which suppresses halo formation. However, the matter density in the Quartic model is higher than in standard ΛCDM, which boosts structure formation and dominates over the effect of the weaker gravity. In the Quartic model there is a significant overabundance of high-mass halos relative to ΛCDM. Dark matter halos are also less biased than in ΛCDM, with the difference increasing appreciably with halo mass. However, our results suggest that the bias may not be small enough to fully reconcile the predicted matter power spectrum with LRG clustering data.

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Spherical collapse in Galileon gravity: fifth force solutions, halo mass function and halo bias

We use the Millennium Simulation, a large, high-resolution N-body simulation of the evolution of structure in a Λ cold dark matter cosmology, to study the properties and fate of substructures within a large sample of dark matter haloes. We find that the subhalo mass function departs significantly from a power law at the high-mass end. We also find that the radial and angular distributions of substructures depend on subhalo mass. In particular, high-mass subhaloes tend to be less radially concentrated and to have angular distributions closer to the direction perpendicular to the spin of the host halo than their less massive counterparts. We find that mergers between subhaloes occur. These tend to be between substructures that were already dynamically associated before accretion into the main halo. For subhaloes larger than 0.001 times the mass of the host halo, it is more likely that the subhalo will merge with the central or main subhalo than with another subhalo larger than itself. For lower masses, subhalo–subhalo mergers become equally likely to mergers with the main subhalo. Our results have implications for the variation of galaxy properties with environment and for the treatment of mergers in galaxy formation models.

The fate of substructures in cold dark matter haloes

We model the linear and nonlinear growth of large scale structure in the Cubic Galileon gravity model, by running a suite of N-body cosmological simulations using the {\tt ECOSMOG} code. Our simulations include the Vainshtein screening effect, which reconciles the Cubic Galileon model with local tests of gravity. In the linear regime, the amplitude of the matter power spectrum increases by $\sim 25%$ with respect to the standard $\Lambda$CDM model today. The modified expansion rate accounts for $\sim 20%$ of this enhancement, while the fifth force is responsible for only $\sim 5%$. This is because the effective unscreened gravitational strength deviates from standard gravity only at late times, even though it can be twice as large today. In the nonlinear regime ($k \gtrsim 0.1 h\rm{Mpc}^{-1}$), the fifth force leads to only a modest increase ($\lesssim 8%$) in the clustering power on all scales due to the very efficient operation of the Vainshtein mechanism. Such a strong effect is typically not seen in other models with the same screening mechanism. The screening also results in the fifth force increasing the number density of halos by less than 10%, on all mass scales. Our results show that the screening does not ruin the validity of linear theory on large scales which anticipates very strong constraints from galaxy clustering data. We also show that, whilst the model gives an excellent match to CMB data on small angular scales ($l \gtrsim 50$), the predicted integrated Sachs-Wolf effect is in tension with Planck/WMAP results.

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Nonlinear structure formation in the Cubic Galileon gravity model

We use an extremely large volume (2.4h 3 Gpc 3 ), high resolution N-body simulation to measure the higher order clustering of dark matter haloes as a function of mass and internal structure. As a result of the large simulation volume and the use of a novel “cross-moment” counts-in-cells technique which suppresses discreteness noise, we are able to measure the clustering of haloes corresponding to rarer peaks than was possible in previous studies; the rarest haloes for which we measure the variance are 100 times more clustered than the dark matter. We are able to extract, for the first time, halo bias parameters from linear up to fourth order. For all orders measured, we find that the bias parameters are a strong function of mass for haloes more massive than the characteristic mass M�. Currently, no theoretical model is able to reproduce this mass dependence closely. We find that the bias parameters also depend on the internal structure of the halo up to fourth order. For haloes more massive than M�, we find that the more concentrated haloes are more weakly clustered than the less concentrated ones. We see no dependence of clustering on concentration for haloes with masses M < M�; this is contrary to the trend reported in the literature when segregating haloes by their formation time. Our results are insensitive to whether haloes are labelled by the total mass returned by the friends-of-friends group finder or by the mass of the most massive substructure. This implies that our conclusions are not an artefact of the particular choice of group finding algorithm. Our results will provide important input to theoretical models of galaxy clustering.

The assembly bias of dark matter haloes to higher orders

We present a new model for the X-ray properties of the intracluster medium that explicitly includes heating of the gas by the energy released during the evolution of cluster galaxies. We calculate the evolution of clusters by combining the semi-analytic model of galaxy formation of Cole et al. with a simple model for the radial profile of the intracluster gas. We focus on the cluster X-ray luminosity function and on the relation between X-ray temperature and luminosity (the T–L relation). Observations of these properties are known to disagree with predictions based on scaling relations that neglect gas cooling and heating processes. We show that cooling alone is not enough to account for the flatness of the observed T–L relation or for the lack of strong redshift evolution in the observed X-ray luminosity function. Gas heating, on the other hand, can solve these two problems: in the Λ cold dark matter cosmology, our model reproduces fairly well the T–L relation and the X-ray luminosity function. Furthermore, it predicts only weak evolution in these two properties out to z=0.5, in agreement with recent observational data. A successful model requires an energy input of 1–2×1049 erg per solar mass of stars formed. This is comparable to the total energy released by the supernovae associated with the formation of the cluster galaxies. Thus, unless the transfer of supernovae energy to the intracluster gas is very (perhaps unrealistically) efficient, additional sources of energy, such as mechanical energy from active galactic nuclei winds are required. However, the amplification of an initial energy input by the response of the intracluster medium to protocluster mergers might ease the energy requirements. Our model makes definite predictions for the X-ray properties of groups and clusters at high redshift. Some of these, such as the T–L relation at z1, may soon be tested with data from the Chandra and Newton satellites.

Carlton M. Baugh

Papers

Spherical collapse in Galileon gravity: fifth force solutions, halo mass function and halo bias

The fate of substructures in cold dark matter haloes

Nonlinear structure formation in the Cubic Galileon gravity model

The assembly bias of dark matter haloes to higher orders

The Impact of Galaxy Formation on the X-ray Evolution of Clusters