Cosmological hydrogen recombination: The effect of extremely high-n states

Calculations of cosmological hydrogen recombination are vital for the extraction of cosmological parameters from cosmic microwave background (CMB) observations, and for imposing constraints to inflation and re-ionization. The Planck} mission and future experiments will make high precision measurements of CMB anisotropies at angular scales as small as l~2500, necessitating a calculation of recombination with fractional accuracy of ~10^{-3}. Recent work on recombination includes two-photon transitions from high excitation states and many radiative transfer effects. Modern recombination calculations separately follow angular momentum sublevels of the hydrogen atom to accurately treat non-equilibrium effects at late times (z<900). The inclusion of extremely high-n (n>100) states of hydrogen is then computationally challenging, preventing until now a determination of the maximum n needed to predict CMB anisotropy spectra with sufficient accuracy for Planck. Here, results from a new multi-level-atom code (RecSparse) are presented. For the first time, `forbidden' quadrupole transitions of hydrogen are included, but shown to be negligible. RecSparse is designed to quickly calculate recombination histories including extremely high-n states in hydrogen. Histories for a sequence of values as high as n_max=250 are computed, keeping track of all angular momentum sublevels and energy shells of the hydrogen atom separately. Use of an insufficiently high n_max value (e.g., n_max=64) leads to errors (e.g., 1.8 sigma for Planck) in the predicted CMB power spectrum. Extrapolating errors, the resulting CMB anisotropy spectra are converged to 0.5 sigma at Fisher-matrix level for n_max=128, in the purely radiative case.Comment: 19 pages, 12 figures, replaced with version published in Physical Review D (added discussion of collisions)

Lower Limit to the Scale of an Effective Quantum Theory of Gravitation

An effective quantum theory of gravitation in which gravity weakens at energies higher than ~10^-3 eV is one way to accommodate the apparent smallness of the cosmological constant. Such a theory predicts departures from the Newtonian inverse-square force law on distances below ~0.05 mm. However, it is shown that this modification also leads to changes in the long-range behavior of gravity and is inconsistent with observed gravitational lenses

Do baryons trace dark matter in the early universe?

Baryon-density perturbations of large amplitude may exist if they are compensated by dark-matter perturbations so that the total density remains unchanged. Big-bang nucleosynthesis and galaxy clusters allow the amplitudes of these compensated isocurvature perturbations (CIPs) to be as large as $\sim10$. CIPs will modulate the power spectrum of cosmic microwave background (CMB) fluctuations---those due to the usual adiabatic perturbations---as a function of position on the sky. This leads to correlations between different spherical-harmonic coefficients of the temperature/polarization map, and it induces B modes in the CMB polarization. Here, the magnitude of these effects is calculated and techniques to measure them are introduced. While a CIP of this amplitude can be probed on the largest scales with WMAP, forthcoming CMB experiments should improve the sensitivity to CIPs by at least an order of magnitude.Comment: 4 pages, 3 figures, updated with version published in Phys. Rev. Lett. Results unchanged. Added expanded discussion of how to disentangle compensated isocurvature perturbations from weak lensing of the CMB. Expanded discussion of early universe motivation for compensated isocurvature perturbation

Compensated isocurvature perturbations in the curvaton model

Primordial fluctuations in the relative number densities of particles, or isocurvature perturbations, are generally well constrained by cosmic microwave background (CMB) data. A less probed mode is the compensated isocurvature perturbation (CIP), a fluctuation in the relative number densities of cold dark matter and baryons. In the curvaton model, a subdominant field during inflation later sets the primordial curvature fluctuation $\zeta$. In some curvaton-decay scenarios, the baryon and cold dark matter isocurvature fluctuations nearly cancel, leaving a large CIP correlated with $\zeta$. This correlation can be used to probe these CIPs more sensitively than the uncorrelated CIPs considered in past work, essentially by measuring the squeezed bispectrum of the CMB for triangles whose shortest side is limited by the sound horizon. Here, the sensitivity of existing and future CMB experiments to correlated CIPs is assessed, with an eye towards testing specific curvaton-decay scenarios. The planned CMB Stage 4 experiment could detect the largest CIPs attainable in curvaton scenarios with more than 3$\sigma$ significance. The significance could improve if small-scale CMB polarization foregrounds can be effectively subtracted. As a result, future CMB observations could discriminate between some curvaton-decay scenarios in which baryon number and dark matter are produced during different epochs relative to curvaton decay. Independent of the specific motivation for the origin of a correlated CIP perturbation, cross-correlation of CIP reconstructions with the primary CMB can improve the signal-to-noise ratio of a CIP detection. For fully correlated CIPs the improvement is a factor of $\sim$2$-$3.Comment: 20 pages, 8 figures, minor changes matching publicatio

Lensing Bias to CMB Measurements of Compensated Isocurvature Perturbations

Compensated isocurvature perturbations (CIPs) are modes in which the baryon and dark matter density fluctuations cancel. They arise in the curvaton scenario as well as some models of baryogenesis. While they leave no observable effects on the cosmic microwave background (CMB) at linear order, they do spatially modulate two-point CMB statistics and can be reconstructed in a manner similar to gravitational lensing. Due to the similarity between the effects of CMB lensing and CIPs, lensing contributes nearly Gaussian random noise to the CIP estimator that approximately doubles the reconstruction noise power. Additionally, the cross correlation between lensing and the integrated Sachs-Wolfe (ISW) effect generates a correlation between the CIP estimator and the temperature field even in the absence of a correlated CIP signal. For cosmic-variance limited temperature measurements out to multipoles $l \leq 2500$, subtracting a fixed lensing bias degrades the detection threshold for CIPs by a factor of $1.3$, whether or not they are correlated with the adiabatic mode.Comment: 10 pages, 12 figures; one of the authors Chen He Heinrich was previously known as Chen H

An improved estimator for non-Gaussianity in cosmic microwave background observations

An improved estimator for the amplitude fnl of local-type non-Gaussianity from the cosmic microwave background (CMB) bispectrum is discussed. The standard estimator is constructed to be optimal in the zero-signal (i.e., Gaussian) limit. When applied to CMB maps which have a detectable level of non-Gaussianity the standard estimator is no longer optimal, possibly limiting the sensitivity of future observations to a non-Gaussian signal. Previous studies have proposed an improved estimator by using a realization-dependent normalization. Under the approximations of a flat sky and a vanishingly thin last-scattering surface, these studies showed that the variance of this improved estimator can be significantly smaller than the variance of the standard estimator when applied to non-Gaussian CMB maps. Here this technique is generalized to the full sky and to include the full radiation transfer function, yielding expressions for the improved estimator that can be directly applied to CMB maps. The ability of this estimator to reduce the variance as compared to the standard estimator in the face of a significant non-Gaussian signal is re-assessed using the full CMB transfer function. As a result of the late time integrated Sachs-Wolfe effect, the performance of the improved estimator is degraded. If CMB maps are first cleaned of the late-time ISW effect using a tracer of foreground structure, such as a galaxy survey or a measurement of CMB weak lensing, the new estimator does remove a majority of the excess variance, allowing a higher significance detection of fnl.Comment: 21 pages, 7 figure

CMB spectral distortions from small-scale isocurvature fluctuations

The damping of primordial perturbations at small scales gives rise to distortions of the cosmic microwave background (CMB). Here, the dependence of the distortion on the different types of cosmological initial conditions is explored, covering adiabatic, baryon/cold dark matter isocurvature, neutrino density/velocity isocurvature modes and some mixtures. The radiation transfer functions for each mode are determined and then used to compute the dissipative heating rates and spectral distortion signatures, utilizing both analytic estimates and numerical results from the thermalization code CosmoTherm. Along the way, the early-time super-horizon behavior for the resulting fluid modes is derived in conformal Newtonian gauge, and tight-coupling transfer function approximations are given. CMB spectral distortions caused by different perturbation modes can be estimated using simple k-space window functions which are provided here. Neutrinos carry away some fraction of the primordial perturbation power, introducing an overall efficiency factor that depends on the perturbation type. It is shown that future measurements of the CMB frequency spectrum have the potential to probe different perturbation modes at very small scales (corresponding to wavenumbers 1 Mpc^{-1} < k < few x 10^4 Mpc^{-1}). These constraints are complementary to those obtained at large scales and hence provide an exciting new window to early-universe physics.Comment: 16 pages, 5 figures, minor changes, accepted versio

Thermal axion constraints in non-standard thermal histories

There is no direct evidence for radiation domination prior to big-bang nucleosynthesis, and so it is useful to consider how constraints to thermally-produced axions change in non-standard thermal histories. In the low-temperature-reheating scenario, radiation domination begins at temperatures as low as 1 MeV, and is preceded by significant entropy generation. Axion abundances are then suppressed, and cosmological limits to axions are significantly loosened. In a kination scenario, a more modest change to axion constraints occurs. Future possible constraints to axions and low-temperature reheating are discussed.Comment: Submitted conference proceedings, based on a talk presented at Dark Matter '08 in Marina del Rey. Based on work discussed in Phys.Rev.D77:085020,2008, as well as arXiv:0711.1352. Updated to correct titl

Constraining mixing in massive stars in the Small Magellanic Cloud

Context. The evolution of massive stars is strongly influenced by internal mixing processes such as semiconvection, convective core overshooting, and rotationally induced mixing. None of these is currently well constrained. Aims. We investigate models for massive stars in the Small Magellanic Cloud (SMC). We aim to constrain the various mixing efficiencies by comparing model results to observations. Methods. We use the stellar evolution code MESA to compute more than 60 grids of detailed evolutionary models for stars with initial masses of 9 to 100 Msol, in each grid assuming different combinations of mixing efficiencies. Results. We find that for most of the combinations of the mixing efficiencies, models in a wide mass range spend core-helium burning either only as blue supergiants, or only as red supergiants. The latter case corresponds to models that maintain a shallow slope of the hydrogen/helium (H/He) gradient separating the core and the envelope of the models. Only a small part of the mixing parameter space leads to models that produce a significant number of blue and red supergiants, which both exist abundantly in the SMC. Interestingly, these models contain steep H/He gradients, as is required to understand the hot, hydrogen-rich Wolf-Rayet stars in the SMC. We find that unless it is very fast, rotation has a limited effect on the H/He profiles in our models. Conclusions. While we use specific implementations of the considered mixing processes, they comprehensively probe the two first order structural parameters: the core mass and the H/He gradient in the core-envelope interface. Our results imply that, in massive stars, the H/He gradients above the helium cores become very steep. Our model grids can be tested with future observational surveys of the massive stars in the SMC, and thereby help to considerably reduce the uncertainties in models of massive star evolution.Comment: Accepted for publication in Astronomy and Astrophysics. 16 pages, 14 figure