Showing papers on "Spectral density published in 2016"

Vector Dark Matter from Inflationary Fluctuations

Abstract: We calculate the production of a massive vector boson by quantum fluctuations during inflation. This gives a novel dark-matter production mechanism quite distinct from misalignment or thermal production. While scalars and tensors are typically produced with a nearly scale-invariant spectrum, surprisingly the vector is produced with a power spectrum peaked at intermediate wavelengths. Thus dangerous, long-wavelength, isocurvature perturbations are suppressed. Further, at long wavelengths the vector inherits the usual adiabatic, nearly scale-invariant perturbations of the inflaton, allowing it to be a good dark-matter candidate. The final abundance can be calculated precisely from the mass and the Hubble scale of inflation, ${H}_{I}$. Saturating the dark-matter abundance we find a prediction for the mass $m\ensuremath{\approx}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{eV}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}({10}^{14}\text{ }\text{ }\mathrm{GeV}/{H}_{I}{)}^{4}$. High-scale inflation, potentially observable in the cosmic microwave background, motivates an exciting mass range for recently proposed direct-detection experiments for hidden photon dark matter. Such experiments may be able to reconstruct the distinctive, peaked power spectrum, verifying that the dark matter was produced by quantum fluctuations during inflation and providing a direct measurement of the scale of inflation. Thus a detection would not only be the discovery of dark matter, it would also provide an unexpected probe of inflation itself.

Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model

Abstract: We study spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, a variant of the $k$-body embedded random ensembles studied for several decades in the context of nuclear physics and quantum chaos. We show analytically that the fourth- and sixth-order energy cumulants vanish in the limit of a large number of particles $N\ensuremath{\rightarrow}\ensuremath{\infty}$, which is consistent with a Gaussian spectral density. However, for finite $N$, the tail of the average spectral density is well approximated by a semicircle law. The specific heat coefficient, determined numerically from the low-temperature behavior of the partition function, is consistent with the value obtained by previous analytical calculations. For energy scales of the order of the mean level spacing we show that level statistics are well described by random matrix theory. Due to the underlying Clifford algebra of the model, the universality class of the spectral correlations depends on $N$. For larger energy separations we identify an energy scale that grows with $N$, reminiscent of the Thouless energy in mesoscopic physics, where deviations from random matrix theory are observed. Our results are a further confirmation that the Sachdev-Ye-Kitaev model is quantum chaotic for all time scales. According to recent claims in the literature, this is an expected feature in field theories with a gravity dual.

Dark energy at early times, the Hubble parameter, and the string axiverse

Abstract: Precise measurements of the cosmic microwave background (CMB) power spectrum are in excellent agreement with the predictions of the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmological model. However, there is some tension between the value of the Hubble parameter ${H}_{0}$ inferred from the CMB and that inferred from observations of the Universe at lower redshifts, and the unusually small value of the dark-energy density is a puzzling ingredient of the model. In this paper, we explore a scenario with a new exotic energy density that behaves like a cosmological constant at early times and then decays quickly at some critical redshift ${z}_{c}$. An exotic energy density like this is motivated by some string-axiverse-inspired scenarios for dark energy. By increasing the expansion rate at early times, the very precisely determined angular scale of the sound horizon at decoupling can be preserved with a larger Hubble constant. We find, however, that the Planck temperature power spectrum tightly constrains the magnitude of the early dark-energy density and thus any shift in the Hubble constant obtained from the CMB. If the reionization optical depth is required to be smaller than the Planck 2016 $2\ensuremath{\sigma}$ upper bound $\ensuremath{\tau}\ensuremath{\lesssim}0.0774$, then early dark energy allows a Hubble-parameter shift of at most $1.6\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ (at ${z}_{c}\ensuremath{\simeq}1585$), too small to fully alleviate the Hubble-parameter tension. Only if $\ensuremath{\tau}$ is increased by more than $5\ensuremath{\sigma}$ can the CMB Hubble parameter be brought into agreement with that from local measurements. In the process, we derive strong constraints to the contribution of early dark energy at the time of recombination---it can never exceed $\ensuremath{\sim}2%$ of the radiation/matter density for $10\ensuremath{\lesssim}{z}_{c}\ensuremath{\lesssim}1{0}^{5}$.

Planck 2015 results. IX. Diffuse component separation: CMB maps

Abstract: We present foreground-reduced cosmic microwave background (CMB) maps derived from the full Planck data set in both temperature and polarization. Compared to the corresponding Planck 2013 temperature sky maps, the total data volume is larger by a factor of 3.2 for frequencies between 30 and 70 GHz, and by 1.9 for frequencies between 100 and 857 GHz. In addition, systematic errors in the forms of temperature-to-polarization leakage, analogue-to-digital conversion uncertainties, and very long time constant errors have been dramatically reduced, to the extent that the cosmological polarization signal may now be robustly recovered on angular scales l ≳ 40. On the very largest scales, instrumental systematic residuals are still non-negligible compared to the expected cosmological signal, and modes with l< 20 are accordingly suppressed in the current polarization maps by high-pass filtering. As in 2013, four different CMB component separation algorithms are applied to these observations, providing a measure of stability with respect to algorithmic and modelling choices. The resulting polarization maps have rms instrumental noise ranging between 0.21 and 0.27μK averaged over 55′ pixels, and between 4.5 and 6.1μK averaged over pixels. The cosmological parameters derived from the analysis of temperature power spectra are in agreement at the 1σ level with the Planck 2015 likelihood. Unresolved mismatches between the noise properties of the data and simulations prevent a satisfactory description of the higher-order statistical properties of the polarization maps. Thus, the primary applications of these polarization maps are those that do not require massive simulations for accurate estimation of uncertainties, for instance estimation of cross-spectra and cross-correlations, or stacking analyses. However, the amplitude of primordial non-Gaussianity is consistent with zero within 2σ for all local, equilateral, and orthogonal configurations of the bispectrum, including for polarization E-modes. Moreover, excellent agreement is found regarding the lensing B-mode power spectrum, both internally among the various component separation codes and with the best-fit Planck 2015 Λ cold dark matter model.

Accurate estimators of correlation functions in Fourier space

Abstract: Efficient estimators of Fourier-space statistics for large number of objects rely on Fast Fourier Transforms (FFTs), which are affected by aliasing from unresolved small scale modes due to the finite FFT grid. Aliasing takes the form of a sum over images, each of them corresponding to the Fourier content displaced by increasing multiples of the sampling frequency of the grid. These spurious contributions limit the accuracy in the estimation of Fourier-space statistics, and are typically ameliorated by simultaneously increasing grid size and discarding high-frequency modes. This results in inefficient estimates for e.g. the power spectrum when desired systematic biases are well under per-cent level. We show that using interlaced grids removes odd images, which include the dominant contribution to aliasing. In addition, we discuss the choice of interpolation kernel used to define density perturbations on the FFT grid and demonstrate that using higher-order interpolation kernels than the standard Cloud in Cell algorithm results in significant reduction of the remaining images. We show that combining fourth-order interpolation with interlacing gives very accurate Fourier amplitudes and phases of density perturbations. This results in power spectrum and bispectrum estimates that have systematic biases below 0.01% all the way to the Nyquist frequency of the grid, thus maximizing the use of unbiased Fourier coefficients for a given grid size and greatly reducing systematics for applications to large cosmological datasets.

Planck intermediate results. LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters

Abstract: The six parameters of the standard $\Lambda$CDM model have best-fit values derived from the Planck temperature power spectrum that are shifted somewhat from the best-fit values derived from WMAP data. These shifts are driven by features in the Planck temperature power spectrum at angular scales that had never before been measured to cosmic-variance level precision. We investigate these shifts to determine whether they are within the range of expectation and to understand their origin in the data. Taking our parameter set to be the optical depth of the reionized intergalactic medium $\tau$, the baryon density $\omega_{\rm b}$, the matter density $\omega_{\rm m}$, the angular size of the sound horizon $\theta_*$, the spectral index of the primordial power spectrum, $n_{\rm s}$, and $A_{\rm s}e^{-2\tau}$ (where $A_{\rm s}$ is the amplitude of the primordial power spectrum), we examine the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment $\ell 800$, or splitting at a different multipole, yields similar results. We examine the $\ell 800$ power spectrum data and find that the features there... [abridged]

Observation of Noise Correlated by the Hawking Effect in a Water Tank

Abstract: We measured the power spectrum and two-point correlation function for the randomly fluctuating free surface on the downstream side of a stationary flow with a maximum Froude number ${F}_{\mathrm{max}}\ensuremath{\approx}0.85$ reached above a localized obstacle. On such a flow the scattering of incident long wavelength modes is analogous to that responsible for black hole radiation (the Hawking effect). Our measurements of the noise show a clear correlation between pairs of modes of opposite energies. We also measure the scattering coefficients by applying the same analysis of correlations to waves produced by a wave maker.

Approximating Spectral Densities of Large Matrices

Abstract: In physics, it is sometimes desirable to compute the so-called density of states (DOS), also known as the spectral density, of a real symmetric matrix $A$. The spectral density can be viewed as a probability density distribution that measures the likelihood of finding eigenvalues near some point on the real line. The most straightforward way to obtain this density is to compute all eigenvalues of $A$, but this approach is generally costly and wasteful, especially for matrices of large dimension. There exist alternative methods that allow us to estimate the spectral density function at much lower cost. The major computational cost of these methods is in multiplying $A$ with a number of vectors, which makes them appealing for large-scale problems where products of the matrix $A$ with arbitrary vectors are relatively inexpensive. This article defines the problem of estimating the spectral density carefully and discusses how to measure the accuracy of an approximate spectral density. It then surveys a few kno...

Connecting CO intensity mapping to molecular gas and star formation in the epoch of galaxy assembly

Abstract: Intensity mapping, which images a single spectral line from unresolved galaxies across cosmological volumes, is a promising technique for probing the early universe. Here we present predictions for the intensity map and power spectrum of the CO(1–0) line from galaxies at $$z\sim 2.4$$–2.8, based on a parameterized model for the galaxy–halo connection, and demonstrate the extent to which properties of high-redshift galaxies can be directly inferred from such observations. We find that our fiducial prediction should be detectable by a realistic experiment. Motivated by significant modeling uncertainties, we demonstrate the effect on the power spectrum of varying each parameter in our model. Using simulated observations, we infer constraints on our model parameter space with an MCMC procedure, and show corresponding constraints on the $${L}_{\mathrm{IR}}$$–$${L}_{\mathrm{CO}}$$ relation and the CO luminosity function. These constraints would be complementary to current high-redshift galaxy observations, which can detect the brightest galaxies but not complete samples from the faint end of the luminosity function. Furthermore, by probing these populations in aggregate, CO intensity mapping could be a valuable tool for probing molecular gas and its relation to star formation in high-redshift galaxies.

Eliminating the optical depth nuisance from the CMB with 21 cm cosmology

Abstract: Amongst standard model parameters that are constrained by cosmic microwave background (CMB) observations, the optical depth $\ensuremath{\tau}$ stands out as a nuisance parameter. While $\ensuremath{\tau}$ provides some crude limits on reionization, it also degrades constraints on other cosmological parameters. Here we explore how 21 cm cosmology---as a direct probe of reionization---can be used to independently predict $\ensuremath{\tau}$ in an effort to improve CMB parameter constraints. We develop two complementary schemes for doing so. The first uses 21 cm power spectrum observations in conjunction with semianalytic simulations to predict $\ensuremath{\tau}$. The other uses global 21 cm measurements to directly constrain low redshift (post-reheating) contributions to $\ensuremath{\tau}$ in a relatively model-independent way. Forecasting the performance of the upcoming hydrogen epoch of reionization array, we find that significant reductions in the errors on $\ensuremath{\tau}$ can be achieved. These results are particularly effective at breaking the CMB degeneracy between $\ensuremath{\tau}$ and the amplitude of the primordial fluctuation spectrum ${A}_{s}$, with errors on $\mathrm{ln}({10}^{10}{A}_{s})$ reduced by up to a factor of 4. Stage 4 CMB constraints on the neutrino mass sum are also improved, with errors potentially reduced to 12 meV regardless of whether CMB experiments can precisely measure the reionization bump in polarization power spectra. Observations of the 21 cm line are therefore capable of improving not only our understanding of reionization astrophysics, but also of cosmology in general.

CHIPS: The COSMOLOGICAL H i POWER SPECTRUM ESTIMATOR

Abstract: Detection of the cosmological neutral hydrogen signal from the Epoch of Reionization (EoR) and estimation of its basic physical parameters are principal scientific aims of many current low-frequency radio telescopes. Here we describe the Cosmological H i Power Spectrum Estimator (CHIPS), an algorithm developed and implemented with data from the Murchison Widefield Array, to compute the two-dimensional and spherically-averaged power spectrum of brightness temperature fluctuations. The principal motivations for CHIPS are the application of realistic instrumental and foreground models to form the optimal estimator, thereby maximizing the likelihood of unbiased signal estimation, and allowing a full covariant understanding of the outputs. CHIPS employs an inverse-covariance weighting of the data through the maximum likelihood estimator, thereby allowing use of the full parameter space for signal estimation ("foreground suppression"). We describe the motivation for the algorithm, implementation, application to real and simulated data, and early outputs. Upon application to a set of 3 hr of data, we set a 2σ upper limit on the EoR dimensionless power at Mpc-1 of mK2 in the redshift range z = [6.2-6.6], consistent with previous estimates.

Cosmological constraints on exotic injection of electromagnetic energy

Abstract: We compute cosmic microwave background (CMB) anisotropy constraints on exotic forms of energy injection in electromagnetic (e.m.) channels over a large range of timescales. These constraints are very powerful around or just after recombination, although CMB keeps some sensitivity e.g. to decaying species with lifetimes as long as $10^{25}\,$s. We review here complementary with CMB spectral distortions and primordial nucleosynthesis bounds, which dominate at earlier timescales. For the first time, we describe the effects of the e.m. energy injection on the CMB power spectra as a function of the injection epoch, using the lifetime of a decaying particle as proxy. We identify a suitable on-the-spot approximation. Our results are of interest not only for early universe relics constituting (a fraction of) the dark matter, but also for other exotic injection of e.m. radiation. For illustration, we apply our formalism to: i) Primordial black holes of mass $\in [10^{13.5},10^{16.8}]$ g, showing that the constraints are comparable to the ones obtained from gamma-ray background studies and even dominate below $\sim 10^{14}$g. ii) To a peculiar mass-mixing range in the sterile neutrino parameter space, complementary to other astrophysical and laboratory probes. iii) Finally, we provide a first estimate of the room for improvement left for forthcoming 21 cm experiments, comparing it with the reach of proposed CMB spectral distortion (PiXiE) and CMB angular power spectrum (CORE) missions. We show that the best and most realistic opportunity to look for this signal (or to improve over current constraints) in the 21 cm probe is to focus on the Cosmic Dawn epoch, $15\lesssim z\lesssim30$, where the qualitatively unambiguous signature of a spectrum in emission can be expected for models that evade all current constraints.

Coherent events and spectral shape at ion kinetic scales in the fast solar wind turbulence

Abstract: In this paper we investigate spectral and phase coherence properties of magnetic fluctuations in the vicinity of the spectral transition from large, magnetohydrodynamic (MHD) to sub-ion scales using in-situ measurements of the Wind spacecraft in a fast stream. For the time interval investigated by Leamon et al. (1998) the phase-coherence analysis shows the presence of sporadic quasi-parallel Alfv\'en Ion Cyclotron (AIC) waves as well as coherent structures in the form of large-amplitude, quasi-perpendicular Alfv\'en vortex-like structures and current sheets. These waves and structures importantly contribute to the observed power spectrum of magnetic fluctuations around ion scales; AIC waves contribute to the spectrum in a narrow frequency range whereas the coherent structures contribute to the spectrum over a wide frequency band from the inertial range to the sub-ion frequency range. We conclude that a particular combination of waves and coherent structures determines the spectral shape of the magnetic field spectrum around ion scales. This phenomenon provides a possible explanation for a high variability of the magnetic power spectra around ion scales observed in the solar wind.

Cosmological N-body simulations with suppressed variance

Abstract: We present and test a method that dramatically reduces variance arising from the sparse sampling of wavemodes in cosmological simulations. The method uses two simulations which are fixed (the initial Fourier mode amplitudes are fixed to the ensemble average power spectrum) and paired (with initial modes exactly out of phase). We measure the power spectrum, monopole and quadrupole redshift-space correlation functions, halo mass function and reduced bispectrum at $z=1$. By these measures, predictions from a fixed pair can be as precise on non-linear scales as an average over 50 traditional simulations. The fixing procedure introduces a non-Gaussian correction to the initial conditions; we give an analytic argument showing why the simulations are still able to predict the mean properties of the Gaussian ensemble. We anticipate that the method will drive down the computational time requirements for accurate large-scale explorations of galaxy bias and clustering statistics, enabling more precise comparisons with theoretical models, and facilitating the use of numerical simulations in cosmological data interpretation.

A Fault Diagnosis Scheme for Rolling Bearing Based on Particle Swarm Optimization in Variational Mode Decomposition

Abstract: Variational mode decomposition (VMD) is a new method of signal adaptive decomposition. In the VMD framework, the vibration signal is decomposed into multiple mode components by Wiener filtering in Fourier domain, and the center frequency of each mode component is updated as the center of gravity of the mode’s power spectrum. Therefore, each decomposed mode is compact around a center pulsation and has a limited bandwidth. In view of the situation that the penalty parameter and the number of components affect the decomposition effect in VMD algorithm, a novel method of fault feature extraction based on the combination of VMD and particle swarm optimization (PSO) algorithm is proposed. In this paper, the numerical simulation and the measured fault signals of the rolling bearing experiment system are analyzed by the proposed method. The results indicate that the proposed method is much more robust to sampling and noise. Additionally, the proposed method has an advantage over the EMD in complicated signal decomposition and can be utilized as a potential method in extracting the faint fault information of rolling bearings compared with the common method of envelope spectrum analysis.

Axion inflation with an SU(2) gauge field: detectable chiral gravity waves

Abstract: We study a single field axion inflation model in the presence of an SU(2) gauge field with a small vev. In order to make the analysis as model-independent as possible, we consider an arbitrary potential for the axion that is able to support the slow-roll inflation. The gauge field is coupled to the axion with a Chern-Simons interaction $$ \frac{\lambda }{f}{F}_{\mu u}^a{\tilde{F}}_a^{\mu u } $$ where $$ \frac{\lambda }{f}\sim \frac{\mathcal{O}(10)}{M_{\mathrm{pl}}} $$ . It has a negligible effect on the background evolution, $$ \frac{\rho \mathrm{Y}\mathrm{M}}{M_{\mathrm{pl}}^2{H}^2}\lesssim {\upepsilon}^2 $$ . However, its quantum fluctuations make a significant contribution to the cosmic perturbation. In particular, the gauge field has a spin-2 fluctuation which explicitly breaks the parity between the left- and right-handed polarization states. The chiral tensor modes are linearly coupled to the gravitational waves and lead to a circularly polarized tensor power spectrum comparable to the unpolarized vacuum power spectrum. Moreover, the scalar sector is modified by the linear scalar fluctuations of the gauge field. Since the spin-0 and spin-2 fluctuations of the SU(2) gauge field are independent, the gauge field can, at the same time, generate a detectable chiral gravitational wave signal and have a negligible contribution to the scalar fluctuations, in agreement with the current CMB observations.

The Gaussian streaming model and convolution Lagrangian effective field theory

Abstract: Author(s): Vlah, Z; Castorina, E; White, M | Abstract: We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.

FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

Abstract: We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.

Reliable and Efficient Sub-Nyquist Wideband Spectrum Sensing in Cooperative Cognitive Radio Networks

Abstract: The rising popularity of wireless services resulting in spectrum shortage has motivated dynamic spectrum sharing to facilitate efficient usage of the underutilized spectrum. Wideband spectrum sensing is a critical functionality to enable dynamic spectrum access by enhancing the opportunities of exploring spectral holes, but entails a major implementation challenge in compact commodity radios that only have limited energy and computation capabilities. In contrast to the traditional sub-Nyquist approaches where a wideband signal or its power spectrum is first reconstructed from compressed samples, this paper proposes a sub-Nyquist wideband spectrum sensing scheme that locates occupied channels blindly by recovering the signal support, based on the jointly sparse nature of multiband signals. Exploiting the common signal support shared among multiple secondary users (SUs), an efficient cooperative spectrum sensing scheme is developed, in which the energy consumption on wideband signal acquisition, processing, and transmission is reduced with detection performance guarantee. Based on subspace decomposition, the low-dimensional measurement matrix, computed at each SU from local sub-Nyquist samples, is deployed to reduce the transmission and computation overhead while improving noise robustness. The theoretical analysis of the proposed sub-Nyquist wideband sensing algorithm is derived and verified by numerical analysis and further tested on real-world TV white space signals. It shows that the proposed scheme can achieve good detection performance as well as reduce the computation and implementation complexity, in comparison with the conventional cooperative wideband spectrum sensing schemes.

CHIPS: The Cosmological HI Power Spectrum Estimator

Abstract: Detection of the cosmological neutral hydrogen signal from the Epoch of Reionization, and estimation of its basic physical parameters, is the principal scientific aim of many current low-frequency radio telescopes. Here we describe the Cosmological HI Power Spectrum Estimator (CHIPS), an algorithm developed and implemented with data from the Murchison Widefield Array (MWA), to compute the two-dimensional and spherically-averaged power spectrum of brightness temperature fluctuations. The principal motivations for CHIPS are the application of realistic instrumental and foreground models to form the optimal estimator, thereby maximising the likelihood of unbiased signal estimation, and allowing a full covariant understanding of the outputs. CHIPS employs an inverse-covariance weighting of the data through the maximum likelihood estimator, thereby allowing use of the full parameter space for signal estimation ("foreground suppression"). We describe the motivation for the algorithm, implementation, application to real and simulated data, and early outputs. Upon application to a set of 3 hours of data, we set a 2$\sigma$ upper limit on the EoR dimensionless power at $k=0.05$~h.Mpc$^{-1}$ of $\Delta_k^2<7.6\times{10^4}$~mK$^2$ in the redshift range $z=[6.2-6.6]$, consistent with previous estimates.

Frequency-dependent dispersion measures and implications for pulsar timing

Abstract: We analyze the frequency dependence of the dispersion measure (DM), the column density of free electrons to a pulsar, caused by multipath scattering from small scale electron-density fluctuations. The DM is slightly different along each propagation path and the transverse spread of paths varies greatly with frequency, yielding time-of-arrival (TOA) perturbations that scale differently than the inverse square of the frequency, the expected dependence for a cold, unmagnetized plasma. We quantify DM and TOA perturbations analytically for thin phase screens and extended media and verify the results with simulations of thin screens. The rms difference between DMs across an octave band near 1.5~GHz $\sim 4\times10^{-5}\,{\rm pc\ cm^{-3}}$ for pulsars at $\sim 1$~kpc distance. TOA errors from chromatic DMs are of order a few to hundreds of nanoseconds for pulsars with DM $\lesssim 30$~pc~cm$^{-3}$ observed across an octave band but increase rapidly to microseconds or larger for larger DMs and wider frequency ranges. Frequency-dependent DMs introduce correlated noise into timing residuals whose power spectrum is `low pass' in form. The correlation time is of order the geometric mean of the refraction times for the highest and lowest radio frequencies used and thus ranges from days to years, depending on the pulsar. We discuss the implications for methodologies that use large frequency separations or wide bandwidth receivers for timing measurements. Chromatic DMs are partially mitigable by using an additional chromatic term in arrival time models. Without mitigation, our results provide an additional term in the noise model for pulsar timing; they also indicate that in combination with measurement errors from radiometer noise, an arbitrary increase in total frequency range (or bandwidth) will yield diminishing benefits and may be detrimental to overall timing precision.

Planck intermediate results. XLIX. Parity-violation constraints from polarization data

Abstract: Parity violating extensions of the standard electromagnetic theory cause in vacuo rotation of the plane of polarization of propagating photons. This effect, also known as cosmic birefringence, impacts the cosmic microwave background (CMB) anisotropy angular power spectra, producing non-vanishing $T$--$B$ and $E$--$B$ correlations that are otherwise null when parity is a symmetry. Here we present new constraints on an isotropic rotation, parametrized by the angle $\alpha$, derived from Planck 2015 CMB polarization data. To increase the robustness of our analyses, we employ two complementary approaches, in harmonic space and in map space, the latter based on a peak stacking technique. The two approaches provide estimates for $\alpha$ that are in agreement within statistical uncertainties and very stable against several consistency tests. Considering the $T$--$B$ and $E$--$B$ information jointly, we find $\alpha = 0.31^{\circ} \pm 0.05^{\circ} \, ({\rm stat.})\, \pm 0.28^{\circ} \, ({\rm syst.})$ from the harmonic analysis and $\alpha = 0.35^{\circ} \pm 0.05^{\circ} \, ({\rm stat.})\, \pm 0.28^{\circ} \, ({\rm syst.})$ from the stacking approach. These constraints are compatible with no parity violation and are dominated by the systematic uncertainty in the orientation of Planck's polarization-sensitive bolometers.

The effect of baryons on redshift space distortions and cosmic density and velocity fields in the EAGLE simulation

Abstract: We use the EAGLE galaxy formation simulation to study the effects of baryons on the power spectrum of the total matter and dark matter distributions and on the velocity fields of dark matter and galaxies. On scales $k{\stackrel{>}{{}_\sim}} 4{h\,{\rm Mpc}^{-1}}$ the effect of baryons on the amplitude of the total matter power spectrum is greater than $1\%$. The back-reaction of baryons affects the density field of the dark matter at the level of $\sim3\%$ on scales of $1\leq k/({h\,{\rm Mpc}^{-1}})\leq 5$. The dark matter velocity divergence power spectrum at $k{\stackrel{ }{{}_\sim}} 1{h\,{\rm Mpc}^{-1}}$ (for $\mu>0.5$), but for $|\vec{k}|\leq 0.4{h\,{\rm Mpc}^{-1}}$ it differs by less than $1\%$. We report vanishingly small baryonic velocity bias for haloes: the peculiar velocities of haloes with $M_{200}>3\times10^{11}{{\rm M}_{\odot}}$ (hosting galaxies with $M_{*}>10^9{{\rm M}_{\odot}}$) are affected at the level of at most $1~$km/s, which is negligible for $1\%$-precision cosmology. We caution that since EAGLE overestimates cluster gas fractions it may also underestimate the impact of baryons, particularly for the total matter power spectrum. Nevertheless, our findings suggest that for theoretical modelling of redshift space distortions and galaxy velocity-based statistics, baryons and their back-reaction can be safely ignored at the current level of observational accuracy. However, we confirm that the modelling of the total matter power spectrum in weak lensing studies needs to include realistic galaxy formation physics in order to achieve the accuracy required in the precision cosmology era.

Linear response to long wavelength fluctuations using curvature simulations

Abstract: We study the local response to long wavelength fluctuations in cosmological N-body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, more direct, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the response of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naive derivation assuming a universal mass function by approximately 8–20%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.

Effective Theory of Dark Energy at Redshift Survey Scales

Abstract: We explore the phenomenological consequences of general late-time modifications of gravity in the quasi-static approximation, in the case where baryons and cold dark matter have distinct couplings to the gravitational sector. Assuming spectroscopic and photometric surveys with configuration parameters similar to those of the Euclid mission, we derive constraints on our effective description from three observables: the galaxy power spectrum in redshift space, tomographic weak-lensing shear power spectrum and the correlation spectrum between the integrated Sachs-Wolfe effect and the galaxy distribution. In particular, with $\Lambda$CDM as fiducial model and a specific choice for the time dependence of our effective functions, we perform a Fisher matrix analysis and find that the unmarginalized $68\%$ CL errors on the three parameters describing the modifications of gravity are of order $\sigma\sim10^{-3}$. We also consider two other fiducial models. A nonminimal coupling of CDM enhances the effects of modified gravity and reduces the above statistical errors accordingly. In all cases, we find that the parameters are highly degenerate, which prevents the inversion of the Fisher matrices. Although all three observational probes are complementary in breaking some of the degeneracies, the ISW-galaxy correlation stands out as a promising probe to constrain the modifications of gravity.

Impact of post-Born lensing on the CMB

Abstract: Lensing of the CMB is affected by post-Born lensing, producing corrections to the convergence power spectrum and introducing field rotation. We show numerically that the lensing convergence power spectrum is affected at the lesssim 0.2% level on accessible scales, and that this correction and the field rotation are negligible for observations with arcminute beam and noise levels gsim 1 μK arcmin. The field rotation generates ~ 2.5% of the total lensing B-mode polarization amplitude (0.2% in power on small scales), but has a blue spectrum on large scales, making it highly subdominant to the convergence B modes on scales where they are a source of confusion for the signal from primordial gravitational waves. Since the post-Born signal is non-linear, it also generates a bispectrum with the convergence. We show that the post-Born contributions to the bispectrum substantially change the shape predicted from large-scale structure non-linearities alone, and hence must be included to estimate the expected total signal and impact of bispectrum biases on CMB lensing reconstruction quadratic estimators and other observables. The field-rotation power spectrum only becomes potentially detectable for noise levels Lt 1 μK arcmin, but its bispectrum with the convergence may be observable at ~ 3σ with Stage IV observations. Rotation-induced and convergence-induced B modes are slightly correlated by the bispectrum, and the bispectrum also produces additional contributions to the lensed BB power spectrum.

Perturbation theory, effective field theory, and oscillations in the power spectrum

Abstract: We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[−k2Σ2(q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ~ 0.5h/Mpc at z = 0.

A global view of velocity fluctuations in the corona below 1.3r⊙ with comp

Abstract: The Coronal Multi-channel Polarimeter (CoMP) has previously demonstrated the presence of Doppler velocity fluctuations in the solar corona. The observed fluctuations are thought to be transverse waves, i.e., highly incompressible motions whose restoring force is dominated by the magnetic tension, some of which demonstrate clear periodicity. We aim to exploit CoMP’s ability to provide high cadence observations of the off-limb corona to investigate the properties of velocity fluctuations in a range of coronal features, providing insight into how (whether) the properties of the waves are influenced by the varying magnetic topology in active regions, quiet Sun and open field regions. An analysis of Doppler velocity time-series of the solar corona from the 10747 A Iron XIII line is performed, determining the velocity power spectrum and using it as a tool to probe wave behavior. Further, the average phase speed and density for each region are estimated and used to compute the spectra for energy density and energy flux. In addition, we assess the noise levels associated with the CoMP data, deriving analytic formulae for the uncertainty on Doppler velocity measurements and providing a comparison by estimating the noise from the data. It is found that the entire corona is replete with transverse wave behavior. The corresponding power spectra indicate that the observed velocity fluctuations are predominately generated by stochastic processes,with the spectral slope of the power varying between the different magnetic regions. Most strikingly, all power spectra reveal the presence of enhanced power occurring at ∼3 mHz, potentially implying that the excitation of coronal transverse waves by p-modes is a global phenomenon.

Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms

Abstract: Author(s): Schmittfull, M; Vlah, Z; McDonald, P | Abstract: The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e.; Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a few orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g.; the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. The method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.