arXiv subjects

Wayne Hu

Publications and source records attributed to Wayne Hu.

248 records · Page 14Linked to original sources

arXiv1996

Small Scale Cosmological Perturbations: An Analytic Approach

Through analytic techniques verified by numerical calculations, we establish general relations between the matter and cosmic microwave background (CMB) power spectra and their dependence on cosmological parameters on small scales. Fluctuations in the CMB, baryons, cold dark matter (CDM), and neutrinos receive a boost at horizon crossing. Baryon drag on the photons causes alternating acoustic peak heights in the CMB and is uncovered in its bare form under the photon diffusion scale. Decoupling of the photons at last scattering and of the baryons at the end of the Compton drag epoch, freezes the diffusion-damped acoustic oscillations into the CMB and matter power spectra at different scales. We determine the dependence of the respective acoustic amplitudes and damping lengths on fundamental cosmological parameters. The baryonic oscillations, enhanced by the velocity overshoot effect, compete with CDM fluctuations in the present matter power spectrum. We present new exact analytic solutions for the cold dark matter fluctuations in the presence of a growth- inhibiting radiation {\it and} baryon background. Combined with the acoustic contributions and baryonic infall into CDM potential wells, this provides a highly accurate analytic form of the small-scale transfer function in the general case.

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arXiv1995

Concepts in CMB Anisotropy Formation

These lecture notes form a primer on the theory of cosmic microwave background (CMB) anisotropy formation. With emphasis on conceptual aspects rather than technical issues, we examine the physical foundations of anisotropy evolution in relativistic kinetic and perturbation theory as well as the manifestation of these principles in primary and secondary anisotropies. We discuss gauge choice and gauge invariance and their use in understanding the CMB. Acoustic, gravitational redshift and ionization effects have robust signatures in the CMB spectrum and may allow determination of classical cosmological parameters as well as reveal general distinctions between models for structure formation. We develop the tight and weak coupling approximations as analytic tools to help understand these effects and the robustness of their signatures.

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arXiv1995

CMB Anisotropies in the Weak Coupling Limit

We present a new, more powerful and accurate, analytic treatment of cosmic microwave background (CMB) anisotropies in the weakly coupled regime. Three applications are presented: gravitational redshifts in a time dependent potential, the Doppler effect in reionized scenarios, and the Vishniac effect. The Vishniac effect can dominate primary anisotropies at small angles even in late and minimally reionized models in flat dark-matter dominated universes with Harrison-Zel'dovich initial conditions. The techniques developed here refine previous calculations yielding a larger coherence angle for the Vishniac effect and moreover can be applied to non-trivial ionization histories. These analytic expressions may be used to modify results for the standard cold dark matter model to its cosmological constant and reionized extensions without detailed and time consuming recalculation.

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arXiv1995

The Effect of Physical Assumptions on the Calculation of Microwave Background Anisotropies

As the data on CMB anisotropies improve and potential cosmological applications are realized, it will be increasingly important for theoretical calculations to be as accurate as possible. All modern calculations for inflationary-inspired fluctuations involve the numerical solution of coupled Boltzmann equations. There are many assumptions and choices to be made when carrying out such calculations. We go through each in turn, pointing out the best selections to make, and the level of inaccuracy expected through incorrect choice: (1) neglecting the effects of neutrinos or polarization has a 10% effect; (2) varying radiation temperature and He fraction can have smaller, but noticeable effects; (3) numerical issues, such as k-range and smoothing are discussed; (4) short-cut methods, e.g. free-streaming and tilt approximations, are generally inadequate at the few % level; (5) at the 1% level somewhat baroque effects are important, such as He recombination and even minimal reionization; (6) at smaller angular scales there are secondary effects which will ultimately have to be considered. Extracting information from the subsidiary acoustic peaks and the damping region will be an extremely challenging problem. However, given the prospect of measuring just such information on the sky, it will be important to meet this challenge. In principle we can obtain details about reionization history, neutrino contribution, helium abundance, non-power-law initial conditions etc.

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arXiv1995

The Physics of Microwave Background Anisotropies

Cosmic microwave background anisotropies provide a vast amount of information on both structure formation in the universe and the background dynamics and geometry. The full physical content and detailed structure of anisotropies can be understood in a simple and intuitive fashion through a systematic investigation of the individual mechanisms for anisotropy formation, based on elementary gravitational and fluid dynamics.

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arXiv1995

COBE Constraints on Baryon Isocurvature Models

We consider Bayesian constraints on standard isocurvature baryon models from the slope and normalization of the anisotropy power spectrum detected by the COBE DMR experiment in their two year maps. In conjunction with either the amplitude of matter fluctuations $σ_8$ {\it or} its slope, all open models are ruled out at greater than 95\% confidence, whereas cosmological constant $Λ$ dominated models are constrained to be highly ionized. By including the COBE FIRAS 95\% confidence upper limit on spectral distortion, we further reduce the available parameter space for $Λ$ models by excluding these highly ionized models. These constraints define a single class of barely viable standard models which makes definite and testable predictions for degree scale anisotropies and large scale structure.

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arXiv1994

Toward Understanding CMB Anisotropies and Their Implications

Working toward a model independent understanding of cosmic microwave background (CMB) anisotropies and their significance, we undertake a comprehensive and self-contained study of scalar perturbation theory. Initial conditions, evolution, thermal history, matter content, background dynamics, and geometry all play a role in determining the anisotropy. By employing {\it analytic} techniques to illuminate the numerical results, we are able to separate and identify each contribution. We thus bring out the nature of the {\it total} Sachs-Wolfe effect, acoustic oscillations, diffusion damping, Doppler shifts, and reionization, as well as their particular manifestation in a critical, curvature, or cosmological constant dominated universe. By studying the full angular {\it and} spatial content of the resultant anisotropies, we isolate the signature of these effects from the dependence on initial conditions. Whereas structure in the Sachs-Wolfe anisotropy depends strongly on the underlying power spectra, the acoustic oscillations provide features which are nearly model independent. This may allow for future determination of the matter content of the universe as well as the adiabatic and/or isocurvature nature of the initial fluctuations.

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arXiv1994

Anisotropies in the Cosmic Microwave Background: An Analytic Approach

We introduce a simple yet powerful {\it analytic} method which obtains the structure of cosmic microwave background anisotropies to better than 5-10\% in temperature fluctuations on {\it all} scales. It is applicable to {\it any} model in which the potential fluctuations at recombination are both linear and known. Moreover, it recovers and explains the presence of the ``Doppler peaks'' at degree scales as {\it driven} acoustic oscillations of the photon-baryon fluid. We treat in detail such subtleties as the time dependence of the gravitational driving force, anisotropic stress from the neutrino quadrupole, and damping during the recombination process, again all from an analytic standpoint. We apply this formalism to the standard cold dark matter model to gain physical insight into the anisotropies, including the dependence of the peak locations and heights on cosmological parameters such as $Ω_b$ and $h$, as well as model parameters such as the ionization history. Damping due to the finite thickness of the last scattering surface and photon diffusion are further more shown to be identical. In addition to being a powerful probe into the nature of anisotropies, this treatment can be used in place of the standard Boltzmann code where 5-10\% accuracy in temperature fluctuations is satisfactory and/or speed is essential. Equally importantly, it can be used as a portable standard by which numerical codes can be tested and compared.

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arXiv1994

The Nature versus Nurture of Anisotropies

With the rapidly growing number of cosmic microwave background measurements on various scales, there is real hope that the number of acceptable models for structure formation will be limited to a very few in the near future. Yet any given model can always be saved by introducing and tuning extraneous free parameters. To better understand this question of ``nature versus nurture'' for temperature fluctuations, it is useful to know not only the general features of anisotropy predictions but also their causes. Extracting the physical content of our other works, we present here a {\it simple} account of cosmic microwave background anisotropies on all scales. In particular, we show that analytic approximations can trace the structure of the so-called ``Doppler peaks,'' which arise due to the {\it adiabatic} oscillations in the photon-baryon fluid. We also show how the finite thickness of the last scattering surface and the Silk damping mechanism can be described in a unified way by photon diffusion. In order to present a specific example, we focus on comparing the primordial isocurvature baryon (PIB) model with the standard cold dark matter model (CDM). In particular, we explain why PIB generically predicts larger {\it non}-oscillatory anisotropies from the 1$^\circ$ to 10$^\circ$ scale which may already be in conflict with experiments.

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arXiv1994

Thermal History Constraints on the Isocurvature Baryon Model

We present a thorough and detailed investigation of baryon isocurvature models including realistic thermal histories, \ie, late or partial reionization of the universe and compact object formation after standard recombination. Constraints on these models are imposed from spectral distortion in the cosmic microwave background (CMB), number fluctuations in galaxy counts $σ_8$, and recent CMB anisotropy observations. Since the status of degree scale anisotropies is as yet unclear, the lack of spectral distortions is the most serious constraint on the spectral index of initial fluctuations: $-1.2 \simlt n \simlt -0.5$ in partially ionized models and $-1.2 \simlt n \simlt -0.9$ in compact object dominated universes in order to avoid significant bias in galaxy formation. Full ionization of the universe before $z = 300$ is also forbidden by this constraint. Intermediate scale CMB fluctuations which are significantly larger than standard CDM is a {\it robust} prediction of these models. Many models are consequently in conflict with the recent degree scale detections by Python, ARGO, and MSAM, \eg, compact object dominated models with $Ω_0 \simlt 0.2$. Moreover, {\it all} models will be ruled out if the low CMB fluctuations on degree scales as detected by the SP91 13 point scan are confirmed. On the other hand, most models fare well compared with the high Tenerife and MAX detections.

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arXiv1994

Power Spectrum Constraints from Spectral Distortions in the Cosmic Microwave Background

%The content of this replacement paper is identical to the original. %We have attempted to fix the postscript so that it will print out on %a larger number of printers. Using recent experimental limits on $μ$ distortions from COBE FIRAS, and the large lever-arm spanning the damping of sub-Jeans scale fluctuations to the scale of the COBE DMR fluctuations, we set a constraint on the slope of the primordial power spectrum $n$. It is possible to analytically calculate the contribution over the full range of scales and redshifts, correctly taking into account fluctuation growth and damping as well as thermalization processes. We find that the 95\% upper limit is weakly dependent on cosmological parameters, e.g. $n<1.54 (h=0.5)$ and $n<1.56 (h=1.0)$ for $Ω_0=1$ with marginally weaker constraints for $Ω_0<1$ in a flat $Ω_0 +Ω_Λ=1$ universe.

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arXiv1993

Power Spectrum Independent Constraints on Cosmological Models

A formalism is presented that allows cosmological experiments to be tested for consistency, and allows a simple frequentist interpretation of the resulting significance levels. As an example of an application, this formalism is used to place constraints on bulk flows of galaxies using the results of the microwave background anisotropy experiments COBE and SP91, and a few simplifying approximations about the experimental window functions. It is found that if taken at face value, with the quoted errors, the recent detection by Lauer and Postman of a bulk flow of 689 km/s on scales of 150$h^{-1}$Mpc is inconsistent with SP91 at a 95\% confidence level within the framework of a Cold Dark Matter (CDM) model. The same consistency test is also used to place constraints that are completely model-independent, in the sense that they hold for any power spectrum whatsoever --- the only assumption being that the random fields are Gaussian. It is shown that the resulting infinite-dimensional optimization problem reduces to a set of coupled non-linear equations that can readily be solved numerically. Applying this technique to the above-mentioned example, we find that the Lauer and Postman result is inconsistent with SP91 even if no assumptions whatsoever are made about the power spectrum.

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arXiv1993

The Small Scale Integrated Sachs-Wolfe Effect

The integrated Sachs-Wolfe effect (ISW) can be an important factor in the generation of Cosmic Microwave Background anisotropies on all scales, especially in a reionized curvature or lambda dominated universe. We present an analytic treatment of the ISW effect, which is analogous to thick last scattering surface techniques for the Doppler effect, that compares quite well with the full numerical calculations. The power spectrum of temperature fluctuations due to the small scale ISW effect has wave number dependence k^{-5} times that of the matter power spectrum.

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arXiv1993

Reionization and cosmic microwave background distortions: a complete treatment of second order Compton scattering

The ionization history of the universe provides a major source of ambiguity in constraining cosmological models using small angular scale microwave background anisotropies. To clarify these issues, we consider a complete treatment of Compton scattering to second order, an approach which may be applicable to other astrophysical situations. We find that only the ${\cal O} (v)$ Doppler effect, and the ${\cal O} (vδ)$ Vishniac effect are important for recent last scattering epochs; the ${\cal O} (v^2)$ Doppler effect is not significant on any angular scale, and other higher-order effects are completely negligible. However the ${\cal O}(v^2)$ effect does lead to \Cy\ distortions, which although generally below current constraints, set an unavoidable minimum level in reionization models. We consider the small-angle approximation for the Vishniac effect in detail, and show several improvements over previous treatments, particularly for low $Ω_0$. For standard cold dark matter models, the effect of reionization is to redistribute the anisotropies to arcminute scales; late reionization leads to partially erased primary fluctuations and a secondary contribution of comparable magnitude. Using recent anisotropy limits from the ATCA experiment, we set new constraints on baryonic dark matter models. Stronger constraints are imposed (in second order) upon models with higher Hubble constant, steeper $n$, and higher density. These limits depend on the specific ionization history assumed, but the factor gained by lowering the ionization fraction is generally small, and may be tested by currently-planned

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