Background Power Spectrum Research Articles

True cosmic microwave background power spectrum estimation

Aims. The cosmic microwave background (CMB) power spectrum is a powerful cosmological probe as it entails almost the entire statistical information of CMB perturbations. Having access to only one sky, the CMB power spectrum measured by our experiments is only a realization of the true underlying angular power spectrum. We aim to recover the true underlying CMB power spectrum from the one realization that we have without knowing the cosmological parameters. Methods. The sparsity of the CMB power spectrum is rst investigated in two dictionaries; discrete cosine transform (DCT) and wavelet transform (WT). The CMB power spectrum can be recovered with very few coe cients in these two dictionaries and hence is very compressible. Results. We studied the performance of these dictionaries in smoothing a set of simulated power spectra. Based on this, we developed a technique that estimates the true underlying CMB power spectrum from data, i.e., without a need to know the cosmological parameters. Conclusions. This smooth estimated spectrum can be used to simulate CMB maps with similar properties as the true CMB simulations with the correct cosmological parameters. This allows us to perform Monte Carlo simulations in a given project without having to know the cosmological parameters. The developed IDL code, TOUSI, for theoretical power spectrum using sparse estimation, will be released with the next version of ISAP.

Cosmography beyond standard candles and rulers

We perform a cosmographic analysis using several cosmological observables such as the luminosity distance moduli, the volume distance, the angular diameter distance and the Hubble parameter. These quantities are determined using different data sets: Supernovae type Ia and Gamma Ray Bursts, the Baryonic Acoustic Oscillations, the cosmic microwave background power spectrum and the Hubble parameter as measured from surveys of galaxies. This data set allows to put constraints on the cosmographic expansion with unprecedented precision. We also present forecasts for the coefficients of the kinematic expansion using future but realistic data sets: constraints on the coefficients of the expansions are likely to improve by a factor ten with the upcoming large scale structure probes. Finally, we derive the set of the cosmographic parameters for several cosmological models (including $\Lambda$CDM) and compare them with our best fit set. While distance measurements are unable to discriminate among these models, we show that the inclusion of the Hubble data set leads to strong constraints on the lowest order coefficients and in particular it is incompatible with $\Lambda$CDM at 3-$\sigma$ confidence level. We discuss the reliability of this determination and suggest further observations which might be of crucial importance for the viability of cosmographic tests in the next future.

Probing the Ricci dark energy model with perturbations by using WMAP seven-year cosmic microwave background measurements, baryon acoustic oscillations, and type Ia supernovae

In this paper, we investigate the Ricci dark energy model with perturbations through the joint constraints of current cosmological data sets from dynamical and geometrical perspectives. We use the full cosmic microwave background information from WMAP seven-year data, the baryon acoustic oscillations from the Sloan Digital Sky Survey and the Two Degree Galaxy Redshift Survey, and type Ia supernovae from the Union2 compilation of the Supernova Cosmology Project Collaboration. A global constraint is performed by employing the Markov chain Monte Carlo method. With the best-fitting results, we show the differences of cosmic microwave background power spectra and background evolutions for the cosmological constant model and Ricci dark energy model with perturbations.

Predicted constraints on cosmic string tension from Planck and future CMB polarization measurements

We perform a Fisher matrix calculation of the predicted uncertainties on estimates of the cosmic string tension Gmu from upcoming observational data (namely, cosmic microwave background power spectra from the Planck satellite and an idealized future polarization experiment). We employ simulations that are more general than others commonly used in the literature, leaving the mean velocity of strings, correlation length of the string network, and "wiggliness" (which parametrizes smaller-scale structure along the strings) as free parameters that can be observationally measured. In a new code, StringFast, we implement a method for efficient computation of the C_l spectra induced by a network of strings, which is fast enough to be used in Markov Chain Monte Carlo analyses of future data. Performing a calculation with the string parameters left free results in projected constraints on Gmu that are larger than those obtained by fixing their values a priori, typically by a factor of ~2-7. We also find that if Gmu is equal to the current observational maximum, Planck will be able to make a confident detection of strings. However, if Gmu is two orders of magnitude smaller, even a perfect, lensing-free measurement of polarization power spectra will not be able to detect a nonzero string tension at better than 2 sigma confidence.

IMPROVED CONSTRAINTS ON COSMIC MICROWAVE BACKGROUND SECONDARY ANISOTROPIES FROM THE COMPLETE 2008 SOUTH POLE TELESCOPE DATA

We report measurements of the cosmic microwave background (CMB) power spectrum from the complete 2008 South Pole Telescope (SPT) data set. We analyze twice as much data as the first SPT power spectrum analysis, using an improved cosmological parameter estimator which fits multi-frequency models to the SPT 150 and $220\,$GHz bandpowers. We find an excellent fit to the measured bandpowers with a model that includes lensed primary CMB anisotropy, secondary thermal (tSZ) and kinetic (kSZ) Sunyaev-Zel'dovich anisotropies, unclustered synchrotron point sources, and clustered dusty point sources. In addition to measuring the power spectrum of dusty galaxies at high signal-to-noise, the data primarily constrain a linear combination of the kSZ and tSZ anisotropy contributions at $150\,$GHz and $\ell=3000$: $D^{tSZ}_{3000} + 0.5\,D^{kSZ}_{3000} = 4.5\pm 1.0 \,\mu{\rm K}^2$. The 95% confidence upper limits on secondary anisotropy power are $D^{tSZ}_{3000} < 5.3\,\mu{\rm K}^2$ and $D^{kSZ}_{3000} < 6.5\,\mu{\rm K}^2$. We also consider the potential correlation of dusty and tSZ sources, and find it incapable of relaxing the tSZ upper limit. These results increase the significance of the lower than expected tSZ amplitude previously determined from SPT power spectrum measurements. We find that models including non-thermal pressure support in groups and clusters predict tSZ power in better agreement with the SPT data. Combining the tSZ power measurement with primary CMB data halves the statistical uncertainty on $\sigma_8$. However, the preferred value of $\sigma_8$ varies significantly between tSZ models. Improved constraints on cosmological parameters from tSZ power spectrum measurements require continued progress in the modeling of the tSZ power.

Detecting relic gravitational waves in the CMB: A statistical bias

Analyzing the imprint of relic gravitational waves (RGWs) on the cosmic microwave background (CMB) power spectra provides a way to determine the signal of RGWs. In this Letter, we discuss a statistical bias, which could exist in the data analysis and has the tendency to overlook the RGWs. We also explain why this bias exists, and how to avoid it.

Galaxy peculiar velocities from large-scale supernova surveys as a dark energy probe

Upcoming imaging surveys such as the Large Synoptic Survey Telescope will repeatedly scan large areas of sky and have the potential to yield million-supernova catalogs. Type Ia supernovae are excellent standard candles and will provide distance measures that suffice to detect mean pairwise velocities of their host galaxies. We show that when combining these distance measures with photometric redshifts for either the supernovae or their host galaxies, the mean pairwise velocities of the host galaxies will provide a dark energy probe which is competitive with other widely discussed methods. Adding information from this test to type Ia supernova photometric luminosity distances from the same experiment, plus the cosmic microwave background power spectrum from the Planck satellite, improves the Dark Energy Task Force figure of merit by a factor of 1.8. Pairwise velocity measurements require no additional observational effort beyond that required to perform the traditional supernova luminosity distance test, but may provide complementary constraints on dark energy parameters and the nature of gravity. Incorporating additional spectroscopic redshift follow-up observations could provide important dark energy constraints from pairwise velocities alone. Mean pairwise velocities are much less sensitive to systematic redshift errors than the luminosity distance test or weak lensing techniques, and also are only mildly affected by systematic evolution of supernova luminosity.

THE ATACAMA COSMOLOGY TELESCOPE: A MEASUREMENT OF THE COSMIC MICROWAVE BACKGROUND POWER SPECTRUM AT 148 AND 218 GHz FROM THE 2008 SOUTHERN SURVEY

We present measurements of the cosmic microwave background (CMB) power spectrum made by the Atacama Cosmology Telescope at 148 GHz and 218 GHz, as well as the cross-frequency spectrum between the two channels. Our results clearly show the second through the seventh acoustic peaks in the CMB power spectrum. The measurements of these higher-order peaks provide an additional test of the {\Lambda}CDM cosmological model. At l > 3000, we detect power in excess of the primary anisotropy spectrum of the CMB. At lower multipoles 500 < l < 3000, we find evidence for gravitational lensing of the CMB in the power spectrum at the 2.8{\sigma} level. We also detect a low level of Galactic dust in our maps, which demonstrates that we can recover known faint, diffuse signals.

Perceived Motion is Influenced by Random Dynamic Information

Distortions of the local spatial-frequency power spectrum caused by motion blur may be used by the visual system to improve motion analysis (e.g., Barlow and Olshausen, 2004 Journal of Vision 4415-426). We tested this hypothesis by measuring the error of perceived motion direction of moving patterns in the presence of random noncoherent motion manipulated to create different spatial power spectra. The results showed that error increased when the background power spectrum was similar to the motion power spectrum; however, when the background power spectrum had an anisotropy consistent with motion blur, the error was reduced. Shifting the power spectrum away from the motion power spectrum reduced the error.

Measuring information content from observations for data assimilations: utilities of spectral formulations demonstrated with radar observations

Utilities of the spectral formulations for measuring information content from observations are explored and demonstrated with real radar data. It is shown that the spectral formulations can be used (i) to precisely compute the information contents from one-dimensional radar data uniformly distributed along the radar beam, (ii) to approximately estimate the information contents from two-dimensional radar observations non-uniformly distributed on the conical surface of radar scan and thus (iii) to estimate the information losses caused by super-observations generated by local averaging with a series of successively coarsened resolutions to find an optimally coarsened resolution for radar data compression with zero or near-zero minimal loss of information. The results obtained from the spectral formulations are verified against the results computed accurately but costly from the singular-value formulations. As the background and observation error power spectra can be derived analytically for the above utilities, the spectral formulations are computationally much more efficient and affordable than the singular-value formulations, even and especially when the background space and observation space are both extremely large and too large to be computed by the singular-value formulations.

COSMOLOGY WITH MIRROR DARK MATTER

Mirror matter is a stable self-collisional dark matter candidate. If parity is a conserved unbroken symmetry of nature, there could exist a parallel hidden (mirror) sector of the universe composed of particles with the same masses and obeying the same physical laws as our (visible) sector, except for the opposite-handedness of weak interactions. The two sectors interact predominantly via gravity, therefore mirror matter is naturally "dark". Here I review the cosmological signatures of mirror dark matter, concerning thermodynamics of the early universe, big bang nucleosynthesis, primordial structure formation and evolution, cosmic microwave background and large scale structure power spectra. Besides gravity, the effects on primordial nucleosynthesis of the kinetic mixing between photons and mirror photons are considered. Summarizing the present status of research and comparing theoretical results with observations/experiments, it emerges that mirror matter is not just a viable, but a promising dark matter candidate.

IMPACT OF CLUSTER PHYSICS ON THE SUNYAEV-ZEL'DOVICH POWER SPECTRUM

We use an analytic model to investigate the theoretical uncertainty on the thermal Sunyaev-Zel'dovich (SZ) power spectrum due to astrophysical uncertainties in the thermal structure of the intracluster medium. Our model accounts for star formation and energy feedback (from supernovae and active galactic nuclei) as well as radially dependent non-thermal pressure support due to random gas motions, the latter calibrated by recent hydrodynamical simulations. We compare the model against X-ray observations of low redshift clusters, finding excellent agreement with observed pressure profiles. Varying the levels of feedback and non-thermal pressure support can significantly change both the amplitude and shape of the thermal SZ power spectrum. Increasing the feedback suppresses power at small angular scales, shifting the peak of the power spectrum to lower ell. On the other hand, increasing the non-thermal pressure support has the opposite effect, significantly reducing power at large angular scales. In general, including non-thermal pressure at the level measured in simulations has a large effect on the power spectrum, reducing the amplitude by 50% at angular scales of a few arcminutes compared to a model without a non-thermal component. Our results demonstrate that measurements of the shape of the power spectrum can reveal useful information on important physical processes in groups and clusters, especially at high-redshift where there exists little observational data. Comparing with the recent South Pole Telescope measurements of the small-scale cosmic microwave background power spectrum, we find our model reduces the tension between the values of sigma_8 measured from the SZ power spectrum and from cluster abundances.

One Centimetre Receiver Array-prototype observations of the CRATES sources at 30 GHz

Knowledge of the population of radio sources in the range ~2-200 GHz is important for understanding their effects on measurements of the Cosmic Microwave Background power spectrum. We report measurements of the 30 GHz flux densities of 605 radio sources from the Combined Radio All-sky Targeted Eight-GHz Survey (CRATES), which have been made with the One Centimetre Receiver Array prototype (OCRA-p) on the Torun 32-m telescope. The flux densities of sources that were also observed by WMAP and previous OCRA surveys are in broad agreement with those reported here, however a number of sources display intrinsic variability. We find a good correlation between the 30 GHz and Fermi gamma-ray flux densities for common sources. We examine the radio spectra of all observed sources and report a number of Gigahertz-peaked and inverted spectrum sources. These measurements will be useful for comparison to those from the Low Frequency Instrument of the Planck satellite, which will make some of its most sensitive observations in the region covered here.

CMB power spectra from cosmic strings: Predictions for the Planck satellite and beyond

We present a significant improvement over our previous calculations of the cosmic string contribution to cosmic microwave background (CMB) power spectra, with particular focus on sub-WMAP angular scales. These smaller scales are relevant for the now-operational Planck satellite and additional suborbital CMB projects that have even finer resolutions. We employ larger Abelian Higgs string simulations than before and we additionally model and extrapolate the statistical measures from our simulations to smaller length scales. We then use an efficient means of including the extrapolations into our Einstein-Boltzmann calculations in order to yield accurate results over the multipole range $2\ensuremath{\le}\ensuremath{\ell}\ensuremath{\le}4000$. Our results suggest that power-law behavior cuts in for $\ensuremath{\ell}\ensuremath{\gtrsim}3000$ in the case of the temperature power spectrum, which then allows cautious extrapolation to even smaller scales. We find that a string contribution to the temperature power spectrum making up 10% of power at $\ensuremath{\ell}=10$ would be larger than the Silk-damped primary adiabatic contribution for $\ensuremath{\ell}\ensuremath{\gtrsim}3500$. Astrophysical contributions such as the Sunyaev-Zeldovich effect also become important at these scales and will reduce the sensitivity to strings, but these are potentially distinguishable by their frequency-dependence.

Updated constraints on the cosmic string tension

We re-examine the constraints on the cosmic string tension from Cosmic Microwave Background (CMB) and matter power spectra, and also from limits on a stochastic background of gravitational waves provided by pulsar timing. We discuss the different approaches to modeling string evolution and radiation. In particular, we show that the unconnected segment model can describe CMB spectra expected from thin string (Nambu) and field theory (Abelian-Higgs) simulations using the computed values for the correlation length, rms string velocity and small-scale structure relevant to each variety of simulation. Applying the computed spectra in a fit to CMB and SDSS data we find that $G\mu/c^2< 2.6\times 10^{-7}$ ($2 \sigma$) if the Nambu simulations are correct and $G\mu /c^2< 6.4\times 10^{-7}$ in the Abelian-Higgs case. The degeneracy between $G\mu/c^2$ and the power spectrum slope $n_{\rm S}$ is substantially reduced from previous work. Inclusion of constraints on the baryon density from Big Bang Nucleosynthesis (BBN) imply that $n_{\rm S} <1$ at around the $4\sigma$ level for both the Nambu and Abelian-Higgs cases. As a by-product of our results, we find there is "moderate-to-strong" Bayesian evidence that the Harrison-Zel'dovich spectrum is excluded (odds ratio of $\sim 100:1$) by the combination of CMB, SDSS and BBN when compared to the standard 6 parameter fit. Using the contribution to the gravitational wave background from radiation era loops as a conservative lower bound on the signal for specific values of $G\mu/c^2$ and loop production size, $\alpha$, we find that $G\mu /c^2< 7\times 10^{-7} $ for $\alpha c^2/(\Gamma G\mu)\ll1$ and $G\mu/c^2 < 5\times 10^{-11}/\alpha$ for $\alpha c^2/(\Gamma G\mu) \gg1$.

MEASUREMENTS OF SECONDARY COSMIC MICROWAVE BACKGROUND ANISOTROPIES WITH THE SOUTH POLE TELESCOPE

We report cosmic microwave background (CMB) power spectrum measurements from the first 100 sq. deg. field observed by the South Pole Telescope (SPT) at 150 and 220 GHz. On angular scales where the primary CMB anisotropy is dominant, ell ~< 3000, the SPT power spectrum is consistent with the standard LambdaCDM cosmology. On smaller scales, we see strong evidence for a point source contribution, consistent with a population of dusty, star-forming galaxies. After we mask bright point sources, anisotropy power on angular scales of 3000 < ell < 9500 is detected with a signal-to-noise > 50 at both frequencies. We combine the 150 and 220 GHz data to remove the majority of the point source power, and use the point source subtracted spectrum to detect Sunyaev-Zel'dovich (SZ) power at 2.6 sigma. At ell=3000, the SZ power in the subtracted bandpowers is 4.2 +/- 1.5 uK^2, which is significantly lower than the power predicted by a fiducial model using WMAP5 cosmological parameters. This discrepancy may suggest that contemporary galaxy cluster models overestimate the thermal pressure of intracluster gas. Alternatively, this result can be interpreted as evidence for lower values of sigma8. When combined with an estimate of the kinetic SZ contribution, the measured SZ amplitude shifts sigma8 from the primary CMB anisotropy derived constraint of 0.794 +/- 0.028 down to 0.773 +/- 0.025. The uncertainty in the constraint on sigma8 from this analysis is dominated by uncertainties in the theoretical modeling required to predict the amplitude of the SZ power spectrum for a given set of cosmological parameters.

Recombinations to the Rydberg states of hydrogen and their effect during the cosmological recombination epoch

In this paper we discuss the effect of recombinations to highly excited states (n > 100) in hydrogen during the cosmological recombination epoch. For this purpose, we developed a new ordinary differential equation solver for the recombination problem, based on an implicit Gear's method. This solver allows us to include up to 350 l-resolved shells or ∼61 000 separate levels in the hydrogen model and to solve the recombination problem for one cosmology in ∼27 h. This is a huge improvement in performance over our previous recombination code, for which a 100-shell computation (5050 separate states) already required ∼150 h on a single processor. We show that for 350 shells down to redshift z∼ 200, the results for the free electron fraction have practically converged. The final modification in the free electron fraction at z∼ 200 decreases from about ΔNe/Ne∼ 2.8 per cent for 100 shells to ΔNe/Ne∼ 1.6 per cent for 350 shells. However, the associated changes in the cosmic microwave background power spectra at large multipoles l are rather small, so that for accurate computations in connection with the analysis of Planck data already ∼100 shells are expected to be sufficient. Nevertheless, the total value of τ could still be affected at a significant level. We also briefly investigate the effect of collisions on the recombination dynamics. With our current estimates for the collisional rates we find a correction of ΔNe/Ne∼−8.8 × 10−4 at z∼ 700, which is mainly caused by l-changing collisions with protons. Furthermore, we present results on the cosmological recombination spectrum, showing that at low frequencies collisional processes are important. However, the current accuracy of collisional rates is insufficient for precise computations of templates for the recombination spectrum at ν≲ 1 GHz, and also the effect of collisions on the recombination dynamics suffers from the uncertainty in these rates. Improvements in collisional rates will therefore become necessary in order to obtain a final answer regarding their effects during recombination.

Constraints on the neutrino mass and the primordial magnetic field from the matter density fluctuation parameterσ8

We have made an analysis of limits on the neutrino mass based upon the formation of large-scale structure in the presence of a primordial magnetic field. We find that a new upper bound on the neutrino mass is possible based upon fits to the cosmic microwave background and matter power spectrum when the existing independent constraints on the matter density fluctuation parameter $\sigma_8$ and the primordial magnetic field are taken into account.

Constraints on dark energy evolution

We investigate a class of dark energy models in which the equation of state undergoes a rapid transition and for which the Hubble SN Ia diagram is known to be poorly discriminant. Interestingly enough, we find that transitions at high redshift can lead to distortion in the correlation function of dark matter at lower redshift. We therefore use a combination of the SN Ia Hubble diagram, Cosmic Microwave Background data and power spectrum from the Sloan Digital Sky Survey Luminous Red Galaxies (SDSS LRG) to constrain the redshift of a possible transition. We find that the fundamental cosmological parameters are well constrained independently of the presence of a transition. Acceptable transitions from an equation of state close to $w = 0$ to a value close to -1 are strongly rejected at redshifts much higher than those for which Large Scale Structure and SN Ia data are available: the transition redshift can be rejected up to a value as high as 10. We conclude that no preference for a transition appears from present-day data.

Anatomical background and generalized detectability in tomosynthesis and cone-beam CT.

Anatomical background presents a major impediment to detectability in 2D radiography as well as 3D tomosynthesis and cone-beam CT (CBCT). This article incorporates theoretical and experimental analysis of anatomical background "noise" in cascaded systems analysis of 2D and 3D imaging performance to yield "generalized" metrics of noise-equivalent quanta (NEQ) and detectability index as a function of the orbital extent of the (circular arc) source-detector orbit. A physical phantom was designed based on principles of fractal self-similarity to exhibit power-law spectral density (kappa/Fbeta) comparable to various anatomical sites (e.g., breast and lung). Background power spectra [S(B)(F)] were computed as a function of source-detector orbital extent, including tomosynthesis (approximately 10 degrees -180 degrees) and CBCT (180 degrees + fan to 360 degrees) under two acquisition schemes: (1) Constant angular separation between projections (variable dose) and (2) constant total number of projections (constant dose). The resulting S(B) was incorporated in the generalized NEQ, and detectability index was computed from 3D cascaded systems analysis for a variety of imaging tasks. The phantom yielded power-law spectra within the expected spatial frequency range, quantifying the dependence of clutter magnitude (kappa) and correlation (beta) with increasing tomosynthesis angle. Incorporation of S(B) in the 3D NEQ provided a useful framework for analyzing the tradeoffs among anatomical, quantum, and electronic noise with dose and orbital extent. Distinct implications are posed for breast and chest tomosynthesis imaging system design-applications varying significantly in kappa and beta, and imaging task and, therefore, in optimal selection of orbital extent, number of projections, and dose. For example, low-frequency tasks (e.g., soft-tissue masses or nodules) tend to benefit from larger orbital extent and more fully 3D tomographic imaging, whereas high-frequency tasks (e.g., microcalcifications) require careful, application-specific selection of orbital extent and number of projections to minimize negative effects of quantum and electronic noise. The complex tradeoffs among anatomical background, quantum noise, and electronic noise in projection imaging, tomosynthesis, and CBCT can be described by generalized cascaded systems analysis, providing a useful framework for system design and optimization.