Showing papers on "Spectral density published in 2017"

Shape of the acoustic gravitational wave power spectrum from a first order phase transition

Abstract: We present results from large-scale numerical simulations of a first order thermal phase transition in the early Universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted k−3 behavior, where k is the wave number, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper high-k decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wave number behavior of the velocity power spectrum is consistent with a causal k3, except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISA-like mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about 0.05c, produced from bubbles with a mean separation of about 10−2 of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.

Primordial black holes and slow-roll violation

Abstract: For primordial black holes (PBH) to be the dark matter in single-field inflation, the slow-roll approximation must be violated by at least $\mathcal{O}(1)$ in order to enhance the curvature power spectrum within the required number of $e$-folds between cosmic microwave background scales and PBH mass scales. Power spectrum predictions which rely on the inflaton remaining on the slow-roll attractor can fail dramatically leading to qualitatively incorrect conclusions in models like an inflection potential and misestimate the mass scale in a running mass model. We show that an optimized temporal evaluation of the Hubble slow-roll parameters to second order remains a good description for a wide range of PBH formation models where up to a $1{0}^{7}$ amplification of power occurs in 10 $e$-folds or more.

KiDS-450: the tomographic weak lensing power spectrum and constraints on cosmological parameters

Abstract: We present measurements of the weak gravitational lensing shear power spectrum based on $450$ sq. deg. of imaging data from the Kilo Degree Survey. We employ a quadratic estimator in two and three redshift bins and extract band powers of redshift auto-correlation and cross-correlation spectra in the multipole range $76 \leq \ell \leq 1310$. The cosmological interpretation of the measured shear power spectra is performed in a Bayesian framework assuming a $\Lambda$CDM model with spatially flat geometry, while accounting for small residual uncertainties in the shear calibration and redshift distributions as well as marginalising over intrinsic alignments, baryon feedback and an excess-noise power model. Moreover, massive neutrinos are included in the modelling. The cosmological main result is expressed in terms of the parameter combination $S_8 \equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$ yielding $S_8 = \ 0.651 \pm 0.058$ (3 z-bins), confirming the recently reported tension in this parameter with constraints from Planck at $3.2\sigma$ (3 z-bins). We cross-check the results of the 3 z-bin analysis with the weaker constraints from the 2 z-bin analysis and find them to be consistent. The high-level data products of this analysis, such as the band power measurements, covariance matrices, redshift distributions, and likelihood evaluation chains are available at http://kids.strw.leidenuniv.nl/

Analytical spectral density of the Sachdev-Ye-Kitaev model at finite N

Abstract: We derive an approximate analytical formula for the spectral density of the $q$-body Sachdev-Ye-Kitaev (SYK) model obtained by summing a class of diagrams representing leading intersecting contractions. This expression agrees with that of $Q$-Hermite polynomials, with $Q$ a nontrivial function of $q\ensuremath{\ge}2$ and the number of Majorana fermions $N$. Numerical results, obtained by exact diagonalization, are in excellent agreement with this approximate analytical spectral density even for relatively small $N\ensuremath{\sim}8$. For $N\ensuremath{\gg}1$ and not close to the edge of the spectrum, we find that the approximate analytical spectral density simplifies to ${\ensuremath{\rho}}_{\mathrm{asym}}(E)=\mathrm{exp}[2{\mathrm{arcsin}}^{2}(E/{E}_{0})/\mathrm{log}\ensuremath{\eta}]$, where $\ensuremath{\eta}(N,q)$ is the suppression factor of the contribution of intersecting Wick contractions relative to nested contractions and ${E}_{0}$ is the ground-state energy per particle. This spectral density reproduces the known result for the free energy in the large-$q$ and large-$N$ limit at arbitrary values of the temperature. In the infrared region, where the SYK model is believed to have a gravity dual, the analytical spectral density is given by $\ensuremath{\rho}(E)\ensuremath{\sim}\mathrm{sinh}[2\ensuremath{\pi}\sqrt{2}\sqrt{(1\ensuremath{-}E/{E}_{0})/(\ensuremath{-}\mathrm{log}\ensuremath{\eta})}]$. It therefore has a square-root edge, as in random matrix ensembles, followed by an exponential growth, a distinctive feature of black holes and also of low-energy nuclear excitations. Results for level statistics in this region confirm the agreement with random matrix theory. Physically this is a signature that, for sufficiently long times, the SYK model and its gravity dual evolve to a fully ergodic state whose dynamics only depends on the global symmetry of the system. Our results strongly suggest that random matrix correlations are a universal feature of quantum black holes and that the SYK model, combined with holography, may be relevant to modeling certain aspects of the nuclear dynamics.

Inflationary primordial black holes for the LIGO gravitational wave events and pulsar timing array experiments

Abstract: Primordial black holes (PBHs) are one of the candidates to explain the gravitational wave (GW) signals observed by the LIGO detectors. Among several phenomena in the early universe, cosmic inflation is a major example to generate PBHs from large primordial density perturbations. In this paper, we discuss the possibility to interpret the observed GW events as mergers of PBHs that are produced by cosmic inflation. The primordial curvature perturbation should be large enough to produce a sizable amount of PBHs, and thus we have several other probes to test this scenario. We point out that the current pulsar timing array (PTA) experiments already put severe constraints on GWs generated via the second-order effects, and that the observation of the cosmic microwave background puts severe restriction on its $\ensuremath{\mu}$ distortion. In particular, it is found that the scalar power spectrum should have a very sharp peak at $k\ensuremath{\sim}1{0}^{6}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ to fulfill the required abundance of PBHs while evading constraints from the PTA experiments together with the $\ensuremath{\mu}$ distortion. We propose a mechanism that can realize such a sharp peak. In the future, simple inflation models that generate PBHs via almost Gaussian fluctuations could be probed/excluded.

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 ΛCDM 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 have investigated 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 τ, the baryon density ωb, the matter density ωm, the angular size of the sound horizon θ∗, the spectral index of the primordial power spectrum, ns, and Ase− 2τ (where As is the amplitude of the primordial power spectrum), we have examined the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment l 800, or splitting at a different multipole, yields similar results. We examined the l 800 power spectrum data and find that the features there that drive these shifts are a set of oscillations across a broad range of angular scales. Although they partly appear similar to the effects of enhanced gravitational lensing, the shifts in ΛCDM parameters that arise in response to these features correspond to model spectrum changes that are predominantly due to non-lensing effects; the only exception is τ, which, at fixed Ase− 2τ, affects the l> 800 temperature power spectrum solely through the associated change in As and the impact of that on the lensing potential power spectrum. We also ask, “what is it about the power spectrum at l < 800 that leads to somewhat different best-fit parameters than come from the full l range?” We find that if we discard the data at l < 30, where there is a roughly 2σ downward fluctuation in power relative to the model that best fits the full l range, the l < 800 best-fit parameters shift significantly towards the l < 2500 best-fit parameters. In contrast, including l < 30, this previously noted “low-l deficit” drives ns up and impacts parameters correlated with ns, such as ωm and H0. As expected, the l < 30 data have a much greater impact on the l < 800 best fit than on the l < 2500 best fit. So although the shifts are not very significant, we find that they can be understood through the combined effects of an oscillatory-like set of high-l residuals and the deficit in low-l power, excursions consistent with sample variance that happen to map onto changes in cosmological parameters. Finally, we examine agreement between PlanckTT data and two other CMB data sets, namely the Planck lensing reconstruction and the TT power spectrum measured by the South Pole Telescope, again finding a lack of convincing evidence of any significant deviations in parameters, suggesting that current CMB data sets give an internally consistent picture of the ΛCDM model.Key words: cosmology: observations / cosmic background radiation / cosmological parameters / cosmology: theory

The gravitational wave background from massive black hole binaries in Illustris: spectral features and time to detection with pulsar timing arrays

Abstract: Pulsar Timing Arrays (PTA) around the world are using the incredible consistency of millisecond pulsars to measure low frequency gravitational waves from (super)Massive Black Hole (MBH) binaries. We use comprehensive MBH merger models based on cosmological hydrodynamic simulations to predict the spectrum of the stochastic Gravitational-Wave Background (GWB). We use real Time-of-Arrival (TOA) specifications from the European, NANOGrav, Parkes, and International PTA (IPTA) to calculate realistic times to detection of the GWB across a wide range of model parameters. In addition to exploring the parameter space of environmental hardening processes (in particular: stellar scattering efficiencies), we have expanded our models to include eccentric binary evolution which can have a strong effect on the GWB spectrum. Our models show that strong stellar scattering and high characteristic eccentricities enhance the GWB strain amplitude near the PTA sensitive "sweet-spot" (near the frequency $f = 1 \, \mathrm{yr}^{-1}$), slightly improving detection prospects in these cases. While the GWB $amplitude$ is degenerate between cosmological and environmental parameters, the location of a spectral turnover at low frequencies ($f \lesssim 0.1 \, \mathrm{yr}^{-1}$) is strongly indicative of environmental coupling. At high frequencies ($f\gtrsim 1 \, \mathrm{yr}^{-1}$), the GWB spectral index can be used to infer the number density of sources and possibly their eccentricity distribution. Even with merger models that use pessimistic environmental and eccentricity parameters, if the current rate of PTA expansion continues, we find that the International PTA is highly likely to make a detection within about 10 years.

Towards optimal extraction of cosmological information from nonlinear data

Abstract: One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics of clusters, density peaks or voids etc.), along with the corresponding covariance matrices. However, this approach is computationally prohibitive and has not been shown to be exhaustive in terms of information content. Here we instead develop a hierarchical Bayesian approach, expanding the likelihood around the maximum posterior of linear modes, which we solve for using optimization methods. By integrating out the modes using perturbative expansion of the likelihood we construct an initial power spectrum estimator, which for a fixed forward model contains all the cosmological information if the initial modes are gaussian distributed. We develop a method to construct the window and covariance matrix such that the estimator is explicitly unbiased and nearly optimal. We then generalize the method to include the forward model parameters, including cosmological and nuisance parameters, and primordial non-gaussianity. We apply the method in the simplified context of nonlinear structure formation, using either simplified 2-LPT dynamics or N-body simulations as the nonlinear mapping between linear and nonlinear density, and 2-LPT dynamics in the optimization steps used to reconstruct the initial density modes. We demonstrate that the method gives an unbiased estimator of the initial power spectrum, providing among other a near optimal reconstruction of linear baryonic acoustic oscillations.

A Measurement of the Cosmic Microwave Background $B$-Mode Polarization Power Spectrum at Sub-Degree Scales from 2 years of POLARBEAR Data

Abstract: We report an improved measurement of the cosmic microwave background (CMB) $B$-mode polarization power spectrum with the POLARBEAR experiment at 150 GHz. By adding new data collected during the second season of observations (2013-2014) to re-analyzed data from the first season (2012-2013), we have reduced twofold the band-power uncertainties. The band powers are reported over angular multipoles $500 \leq \ell \leq 2100$, where the dominant $B$-mode signal is expected to be due to the gravitational lensing of $E$-modes. We reject the null hypothesis of no $B$-mode polarization at a confidence of 3.1$\sigma$ including both statistical and systematic uncertainties. We test the consistency of the measured $B$-modes with the $\Lambda$ Cold Dark Matter ($\Lambda$CDM) framework by fitting for a single lensing amplitude parameter $A_L$ relative to the Planck best-fit model prediction. We obtain $A_L = 0.60 ^{+0.26} _{-0.24} ({\rm stat}) ^{+0.00} _{-0.04}({\rm inst}) \pm 0.14 ({\rm foreground}) \pm 0.04 ({\rm multi})$, where $A_{L}=1$ is the fiducial $\Lambda$CDM value, and the details of the reported uncertainties are explained later in the manuscript.

Anisotropy of the astrophysical gravitational wave background: Analytic expression of the angular power spectrum and correlation with cosmological observations

Abstract: Unresolved sources of gravitational waves are at the origin of a stochastic gravitational wave background. While the computation of its mean density as a function of frequency in a homogeneous and isotropic universe is standard lore, the computation of its anisotropies requires understanding the coarse graining from local systems, to galactic scales and then to cosmology. An expression of the gravitational wave energy density valid in any general spacetime is derived. It is then specialized to a perturbed Friedmann-Lema\^{\i}tre spacetime in order to determine the angular power spectrum of this stochastic background as well as its correlation with other cosmological probes, such as the galaxy number counts and weak lensing. Our result for the angular power spectrum also provides an expression for the variance of the gravitational wave background.

The Potential of Using Large Antenna Arrays on Intelligent Surfaces

Abstract: In this paper, we consider capacities of single- antenna terminals communicating to large antenna arrays that are deployed on surfaces. That is, the entire surface is used as an intelligent receiving antenna array. Under the condition that the surface area is sufficiently large, the received signal after matched-filtering (MF) can be well approximated by an intersymbol interference (ISI) channel where channel taps are closely related to a sinc function. Based on such an approximation, we have derived the capacities for both one- dimensional (terminals on a line) and high dimensional (terminals on a plane or in a cube) terminal-deployments. In particular, we analyze the normalized capacity $\bar{\mathcal{C}}$, measured in nats/s/Hz/m$^2$, under the constraint that the transmit power per m$^2$, $\bar{P}$, is fixed. We show that when the user-density increases, the limit of $\bar{\mathcal{C}}$, achieved as the wavelength $\lambda$ approaches 0, is $\bar{P}/(2N_0)$ nats/s/Hz/m$^2$, where $N_0$ is the spatial power spectral density (PSD) of noise. In addition, we also show that the number of signal dimensions is $2/\lambda$ per meter deployed surface for the one-dimensional case, and $\pi/\lambda^2$ per m$^2$ deployed surface for two and three dimensional terminal-deployments.

Iterative initial condition reconstruction

Abstract: Motivated by recent developments in perturbative calculations of the nonlinear evolution of large-scale structure, we present an iterative algorithm to reconstruct the initial conditions in a given volume starting from the dark matter distribution in real space. In our algorithm, objects are first moved back iteratively along estimated potential gradients, with a progressively reduced smoothing scale, until a nearly uniform catalog is obtained. The linear initial density is then estimated as the divergence of the cumulative displacement, with an optional second-order correction. This algorithm should undo nonlinear effects up to one-loop order, including the higher-order infrared resummation piece. We test the method using dark matter simulations in real space. At redshift $z=0$, we find that after eight iterations the reconstructed density is more than 95% correlated with the initial density at $k\ensuremath{\le}0.35\text{ }\text{ }h{\mathrm{Mpc}}^{\ensuremath{-}1}$. The reconstruction also reduces the power in the difference between reconstructed and initial fields by more than 2 orders of magnitude at $k\ensuremath{\le}0.2\text{ }\text{ }h{\mathrm{Mpc}}^{\ensuremath{-}1}$, and it extends the range of scales where the full broadband shape of the power spectrum matches linear theory by a factor of 2--3. As a specific application, we consider measurements of the baryonic acoustic oscillation (BAO) scale that can be improved by reducing the degradation effects of large-scale flows. In our idealized dark matter simulations, the method improves the BAO signal-to-noise ratio by a factor of 2.7 at $z=0$ and by a factor of 2.5 at $z=0.6$, improving standard BAO reconstruction by 70% at $z=0$ and 30% at $z=0.6$, and matching the optimal BAO signal and signal-to-noise ratio of the linear density in the same volume. For BAO, the iterative nature of the reconstruction is the most important aspect.

Constraints from Ly-$\alpha$ forests on non-thermal dark matter including resonantly-produced sterile neutrinos

Abstract: We use BOSS DR9 quasars to constrain 2 cases of dark matter models: cold-plus-warm (C+WDM) where the warm component is a thermal relic, and sterile neutrinos resonantly produced in the presence of a lepton asymmetry (RPSN). We establish constraints on the relic mass m_x and its relative abundance $F=\Omega_{wdm}/\Omega_{dm}$ using a suite of hydrodynamical simulations in 28 C+WDM configurations. We find that the 3 sigma bounds approximately follow F ~ $0.35 (keV/m_x)^{-1.37}$ from BOSS alone. We also establish constraints on sterile neutrino mass and mixing angle by producing the non-linear flux power spectrum of 8 RPSN models, where the input linear power spectrum is computed directly from the particles distribution functions. We find values of lepton asymmetries for which sterile neutrinos as light as 6.5 keV (resp. 3.5 keV) are consistent with BOSS at the 2 sigma (resp. 3sigma) level. These limits tighten by close to a factor of 2 for lepton asymmetries departing from those yielding the coolest distribution functions. Our Ly-a forest bounds can be strengthened if we include higher-resolution data from XQ-100, HIRES and MIKE. At these smaller scales, the flux power spectrum exhibits a suppression that can be due to Doppler broadening, IGM pressure smoothing or free-streaming of WDM particles. In the current work, we show that if one extrapolates temperatures from lower redshifts via broken power laws in T_0 and gamma, then our 3 sigma C+WDM bounds strengthen to F~ $0.20 (keV/m_x)^{-1.37}$, and the lightest RPSN consistent with our extended data set have masses of 7.0 keV at the 3 sigma level. Using dedicated hydrodynamical simulations, we show that a 7 keV sterile neutrino produced in a lepton asymmetry $L = 8 \times 10^{-6}$ is consistent at 1.9 sigma (resp. 3.1 sigma) with BOSS (resp. BOSS + higher-resolution), for the thermal history models tested in this work.

Assessment of the information content of the power spectrum and bispectrum

Abstract: The covariance matrix of the matter and halo power spectrum and bispectrum are studied Using a large suite of simulations, we find that the non-Gaussianity in the covariance is significant already at mildly nonlinear scales We compute the leading disconnected non-Gaussian correction to the matter bispectrum covariance using perturbation theory, and find that the corrections result in good agreement in the mildly nonlinear regime The shot noise contribution to the halo power spectrum and bispectrum covariance is computed using the Poisson model, and the model yields decent agreement with simulation results However, when the shot noise is estimated from the individual realization, which is usually done in reality, we find that the halo covariance is substantially reduced and gets close to the Gaussian covariance This is because most of the non-Gaussianity in the covariance arises from the fluctuations in the Poisson shot noise We use the measured non-Gaussian covariance to access the information content of the power spectrum and bispectrum The signal-to-noise ratio (S/N) of the matter and halo power spectrum levels off in the mildly nonlinear regime, $k\ensuremath{\sim}01--02\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}h$ In the nonlinear regime the S/N of the matter and halo bispectrum increases but much slower than the Gaussian results suggest We find that both the S/N for power spectrum and bispectrum are overestimated by the Gaussian covariances, but the problem is much more serious for the bispectrum Because the bispectrum is affected strongly by nonlinearity and shot noise, inclusion of the bispectrum only adds a modest amount of S/N compared to that of the power spectrum

Observational constraints on generalized Proca theories

Abstract: In a model of the late-time cosmic acceleration within the framework of generalized Proca theories, there exists a de Sitter attractor preceded by the dark energy equation of state ${w}_{\mathrm{DE}}=\ensuremath{-}1\ensuremath{-}s$, where $s$ is a positive constant. We run the Markov-chain--Monte Carlo code to confront the model with the observational data of the cosmic microwave background (CMB), baryon acoustic oscillations, supernovae type Ia, and local measurements of the Hubble expansion rate for the background cosmological solutions and obtain the bound $s={0.254}_{\ensuremath{-}0.097}^{+0.118}$ at 95% confidence level (C.L.). Existence of the additional parameter $s$ to those in the $\mathrm{\ensuremath{\Lambda}}$-cold-dark-matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model allows to reduce tensions of the Hubble constant ${H}_{0}$ between the CMB and the low-redshift measurements. Including the cosmic growth data of redshift-space distortions in the galaxy power spectrum and taking into account no-ghost and stability conditions of cosmological perturbations, we find that the bound on $s$ is shifted to $s=0.1{6}_{\ensuremath{-}0.08}^{+0.08}$ (95% C.L.) and hence the model with $sg0$ is still favored over the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Apart from the quantities $s,{H}_{0}$ and the today's matter density parameter ${\mathrm{\ensuremath{\Omega}}}_{m0}$, the constraints on other model parameters associated with perturbations are less stringent, reflecting the fact that there are different sets of parameters that give rise to a similar cosmic expansion and growth history.

Experimental Investigation of All-Optical Relay-Assisted 10 Gb/s FSO Link Over the Atmospheric Turbulence Channel

Abstract: This paper presents novel experimental results for a 10 Gb/s triple-hop relay-based all-optical free space optical (FSO) system by employing the amplify-and-forward relaying scheme. We provide a mathematical framework for the end–end signal-to-noise ratio (SNR) and the bit-error rate (BER) performance and confirm that the derived analytical results reasonably match experimental results especially at relatively high SNR. The evaluated BER performances under different atmospheric turbulence regimes (modeled by the Gamma–Gamma distribution) show that the considered relay-assisted FSO system offers a significant performance improvement for weak-to-strong turbulence regimes, even without knowledge of the channel state information. More precisely, at a target BER of 10–5 , the proposed scheme offers ∼5 and ∼4 dB of SNR gains compared to the direct transmission for turbulence strengths $\ {\boldsymbol C}_{\boldsymbol n}^2$ of $3.8 \times {10^{ - 10}}\,{{\rm{m}}^{ - 2/3}}$ and $5.4\times 10^{-12}\,{{\rm{m}}^{ - 2/3}}$ , respectively.

Rapid modelling of the redshift-space power spectrum multipoles for a masked density field

Abstract: In this work, we reformulate the forward modelling of the redshift-space power spectrum multipole moments for a masked density field, as encountered in galaxy redshift surveys. Exploiting the symmetries of the redshift-space correlation function, we provide a masked-field generalization of the Hankel transform relation between the multipole moments in real and Fourier space. Using this result, we detail how a likelihood analysis requiring computation for a broad range of desired P(k) models may be executed 10^3–10^4 times faster than with other common approaches, together with significant gains in spectral resolution. We present a concrete application to the complex angular geometry of the VIMOS Public Extragalactic Redshift Survey PDR-1 release and discuss the validity of this technique for finite-angle surveys.

Cumulative effects in inflation with ultra-light entropy modes

Abstract: In multi-field inflation one or more non-adiabatic modes may become light, potentially inducing large levels of isocurvature perturbations in the cosmic microwave background. If in addition these light modes are coupled to the adiabatic mode, they influence its evolution on super horizon scales. Here we consider the case in which a non-adiabatic mode becomes approximately massless (``ultralight") while still coupled to the adiabatic mode, a typical situation that arises with pseudo-Nambu-Goldstone bosons or moduli. This ultralight mode freezes on super-horizon scales and acts as a constant source for the curvature perturbation, making it grow linearly in time and effectively suppressing the isocurvature component. We identify a Stuckelberg-like emergent shift symmetry that underlies this behavior. As inflation lasts for many e-folds, the integrated effect of this source enhances the power spectrum of the adiabatic mode, while keeping the non-adiabatic spectrum approximately untouched. In this case, towards the end of inflation all the fluctuations, adiabatic and non-adiabatic, are dominated by a single degree of freedom.

The impact of modelling errors on interferometer calibration for 21 cm power spectra

Abstract: We study the impact of sky-based calibration errors from source mismodeling on 21\,cm power spectrum measurements with an interferometer and propose a method for suppressing their effects. While emission from faint sources that are not accounted for in calibration catalogs is believed to be spectrally smooth, deviations of true visibilities from model visibilities are not, due to the inherent chromaticity of the interferometer's sky-response (the "wedge"). Thus, unmodeled foregrounds, below the confusion limit of many instruments, introduce frequency structure into gain solutions on the same line-of-sight scales on which we hope to observe the cosmological signal. We derive analytic expressions describing these errors using linearized approximations of the calibration equations and estimate the impact of this bias on measurements of the 21\,cm power spectrum during the Epoch of Reionization (EoR). Given our current precision in primary beam and foreground modeling, this noise will significantly impact the sensitivity of existing experiments that rely on sky-based calibration. Our formalism describes the scaling of calibration with array and sky-model parameters and can be used to guide future instrument design and calibration strategy. We find that sky-based calibration that down-weights long baselines can eliminate contamination in most of the region outside of the wedge with only a modest increase in instrumental noise.

The impact of turbulent renewable energy production on power grid stability and quality

Abstract: Feed-in fluctuations induced by renewables are one of the key challenges to the stability and quality of electrical power grids. In particular short-term fluctuations disturb the system on a time scale, on which load balancing does not operate yet and the system is intrinsically governed by self-organized synchronization. Wind and solar power are known to be strongly non-Gaussian with intermittent increment statistics in these time scales. We investigate the impact of short-term wind fluctuations on the basis of a Kuramoto-like power grid model considering stability in terms of desynchronization and frequency and voltage quality aspects. We present a procedure to generate realistic feed-in fluctuations with temporal correlations, Kolmogorov power spectrum and intermittent increments. By comparison to correlated Gaussian noise of the same spectrum and Gaussian white noise, we found out that while the correlations are essential to capture the likelihood of severe outages, the intermittent nature of wind power has significant consequences on power quality: intermittency is directly transferred into frequency and voltage fluctuations yielding a novel type of fluctuations, which is beyond engineering status of knowledge.

Fourier transform spectrometer on silicon with thermo-optic non-linearity and dispersion correction

Abstract: The integration of miniaturized optical spectrometers into mobile platforms will have an unprecedented impact on applications ranging from unmanned aerial vehicles (UAVs) to mobile phones. To address this demand, silicon photonics stands out as a platform capable of delivering compact and cost-effective devices. The Fourier transform spectrometer (FTS) is largely used in free-space spectroscopy, and its implementation in silicon photonics will contribute to bringing broadband operation and fine resolution to the chip scale. The implementation of an integrated silicon photonics FTS (Si-FTS) must nonetheless take into account effects such as waveguide dispersion and non-linearity of refractive index tuning mechanisms. Here we present the modeling and experimental demonstration of a silicon-on-insulator (SOI) Si-FTS with integrated microheaters. We show how the power spectral density (PSD) of a light source and the interferogram measured with the Si-FTS can be related through a simple Fourier transform (FT), provided the optical frequency and time delay are corrected to account for dispersion, thermo-optic non-linearity and thermal expansion. We calibrate the Si-FTS, including the correction parameters, using a tunable laser source and we successfully retrieve the PSD of a broadband source. The aforementioned effects are shown to effectively enhance the Si-FTS resolution when properly accounted for. Finally, we discuss the Si-FTS resilience to chip-scale fabrication variations, a major advantage for large-scale manufacturing. Providing design flexibility and robustness, the Si-FTS is poised to become a fundamental building-block for on-chip spectroscopy

The limits of cosmic shear

Abstract: In this paper we discuss the commonly-used limiting cases, or approximations, for two-point cosmic shear statistics. We discuss the most prominent assumptions in this statistic: the flat-sky (small angle limit), the Limber (Bessel-to-delta function limit) and the Hankel transform (large l-mode limit) approximations; that the vast majority of cosmic shear results to date have used simultaneously. We find that the combined effect of these approximations can suppress power by >1% on scales of l<40. A fully non-approximated cosmic shear study should use a spherical-sky, non-Limber-approximated power spectrum analysis; and a transform involving Wigner small-d matrices in place of the Hankel transform. These effects, unaccounted for, would constitute at least 11% of the total budget for systematic effects for a power spectrum analysis of a Euclid-like experiment; but they are unnecessary.

Analysing the 21 cm signal from the epoch of reionization with artificial neural networks

Abstract: The 21 cm signal from the Epoch of Reionization should be observed within the next decade. While a simple statistical detection is expected with SKA pathfinders, the SKA will hopefully produce a full 3D mapping of the signal. To extract from the observed data constraints on the parameters describing the underlying astrophysical processes, inversion methods must be developed. For example, the Markov Chain Monte Carlo method has been successfully applied. Here we test another possible inversion method: artificial neural networks (ANN). We produce a training set which consists of 70 individual sample. Each sample is made of the 21 cm power spectrum at different redshifts produced with the 21cmFast code plus the value of three parameters used in the semi-numerical simulations that describe astrophysical processes. Using this set we train the network to minimize the error between the parameter values it produces as an output and the true values. We explore the impact of the architecture of the network on the quality of the training. Then we test the trained network on the new set of 54 test samples with different values of the parameters. We find that the quality of the parameter reconstruction depends on the sensitivity of the power spectrum to the different parameters at a given redshift, that including thermal noise and sample variance decreases the quality of the reconstruction and that using the power spectrum at several redshifts as an input to the ANN improves the quality of the reconstruction. We conclude that ANNs are a viable inversion method whose main strength is that they require a sparse exploration of the parameter space and thus should be usable with full numerical simulations.

Planck 2015 constraints on the non-flat $\Lambda$CDM inflation model

Abstract: We study Planck 2015 cosmic microwave background (CMB) anisotropy data using the energy density inhomogeneity power spectrum generated by quantum fluctuations during an early epoch of inflation in the non-flat $\Lambda$CDM model. Unlike earlier analyses of non-flat models, which assumed an inconsistent power-law power spectrum of energy density inhomogeneities, we find that the Planck 2015 data alone, and also in conjunction with baryon acoustic oscillation measurements, are reasonably well fit by a closed $\Lambda$CDM model in which spatial curvature contributes a few percent of the current cosmological energy density budget. In this model, the measured Hubble constant and non-relativistic matter density parameter are in good agreement with values determined using most other data. Depending on parameter values, the closed $\Lambda$CDM model has reduced power, relative to the tilted, spatially-flat $\Lambda$CDM case, and can partially alleviate the low multipole CMB temperature anisotropy deficit and can help partially reconcile the CMB anisotropy and weak lensing $\sigma_8$ constraints, at the expense of somewhat worsening the fit to higher multipole CMB temperature anisotropy data. Our results are interesting but tentative; a more thorough analysis is needed to properly gauge their significance.

Learning Power Spectrum Maps From Quantized Power Measurements

Abstract: Power spectral density (PSD) maps providing the distribution of RF power across space and frequency are constructed using power measurements collected by a network of low-cost sensors. By introducing linear compression and quantization to a small number of bits, sensor measurements can be communicated to the fusion center with minimal bandwidth requirements. Strengths of data- and model-driven approaches are combined to develop estimators capable of incorporating multiple forms of spectral and propagation prior information while fitting the rapid variations of shadow fading across space. To this end, novel nonparametric and semiparametric formulations are investigated. It is shown that PSD maps can be obtained using support vector machine-type solvers. In addition to batch approaches, an online algorithm attuned to real-time operation is developed. Numerical tests assess the performance of the novel algorithms.

Axion minicluster power spectrum and mass function

Abstract: When Peccei-Quinn (PQ) symmetry breaking happens after inflation, the axion field takes random values in causally disconnected regions. This leads to fluctuations of order one in the axion energy density around the QCD epoch. These over-densities eventually decouple from the Hubble expansion and form so-called miniclusters. We present a semi-analytical method to calculate the average axion energy density, as well as the power spectrum, from the re-alignment mechanism in this scenario. Furthermore, we develop a modified Press & Schechter approach, suitable to describe the collapse of non-linear density fluctuations during radiation domination, which is relevant for the formation of axion miniclusters. It allows us to calculate the double differential distribution of gravitationally collapsed miniclusters as a function of their mass and size. For instance, assuming a PQ scale of $10^{11}$ GeV, minicluster masses range from about $5 \times 10^{-16}$ to $3 \times 10^{-13}$ solar masses and have sizes from about $4\times 10^4$ to $7\times 10^5$ km at the time they start to collapse.

Extending the modeling of the anisotropic galaxy power spectrum to $k = 0.4 \ h\mathrm{Mpc}^{-1}$

Abstract: We present a new model for the redshift-space power spectrum of galaxies and demonstrate its accuracy in modeling the monopole, quadrupole, and hexadecapole of the galaxy density field down to scales of $k = 0.4 \ h\mathrm{Mpc}^{-1}$. The model describes the clustering of galaxies in the context of a halo model and the clustering of the underlying halos in redshift space using a combination of Eulerian perturbation theory and $N$-body simulations. The modeling of redshift-space distortions is done using the so-called distribution function approach. The final model has 13 free parameters, and each parameter is physically motivated rather than a nuisance parameter, which allows the use of well-motivated priors. We account for the Finger-of-God effect from centrals and both isolated and non-isolated satellites rather than using a single velocity dispersion to describe the combined effect. We test and validate the accuracy of the model on several sets of high-fidelity $N$-body simulations, as well as realistic mock catalogs designed to simulate the BOSS DR12 CMASS data set. The suite of simulations covers a range of cosmologies and galaxy bias models, providing a rigorous test of the level of theoretical systematics present in the model. The level of bias in the recovered values of $f \sigma_8$ is found to be small. When including scales to $k = 0.4 \ h\mathrm{Mpc}^{-1}$, we find 15-30\% gains in the statistical precision of $f \sigma_8$ relative to $k = 0.2 \ h\mathrm{Mpc}^{-1}$ and a roughly 10-15\% improvement for the perpendicular Alcock-Paczynski parameter $\alpha_\perp$. Using the BOSS DR12 CMASS mocks as a benchmark for comparison, we estimate an uncertainty on $f \sigma_8$ that is $\sim$10-20\% larger than other similar Fourier-space RSD models in the literature that use $k \leq 0.2 \ h\mathrm{Mpc}^{-1}$, suggesting that these models likely have a too-limited parametrization.

The full-sky relativistic correlation function and power spectrum of galaxy number counts: I. Theoretical aspects

Abstract: We derive an exact expression for the correlation function in redshift shells including all the relativistic contributions. This expression, which does not rely on the distant-observer or flat-sky approximation, is valid at all scales and includes both local relativistic corrections and integrated contributions, like gravitational lensing. We present two methods to calculate this correlation function, one which makes use of the angular power spectrum C_ell(z1,z2) and a second method which evades the costly calculations of the angular power spectra. The correlation function is then used to define the power spectrum as its Fourier transform. In this work theoretical aspects of this procedure are presented, together with quantitative examples. In particular, we show that gravitational lensing modifies the multipoles of the correlation function and of the power spectrum by a few percent at redshift z=1 and by up to 30% and more at z=2. We also point out that large-scale relativistic effects and wide-angle corrections generate contributions of the same order of magnitude and have consequently to be treated in conjunction. These corrections are particularly important at small redshift, z=0.1, where they can reach 10%. This means in particular that a flat-sky treatment of relativistic effects, using for example the power spectrum, is not consistent.

Gauge Dependence of Gravitational Waves Generated from Scalar Perturbations

Abstract: A tensor-type cosmological perturbation, defined as a transverse and traceless spatial fluctuation, is often interpreted as the gravitational waves. While decoupled from the scalar-type perturbations in linear order, the tensor perturbations can be sourced from the scalar-type in the nonlinear order. The tensor perturbations generated by the quadratic combination of linear scalar-type cosmological perturbation are widely studied in the literature, but all previous studies are based on zero-shear gauge without proper justification. Here, we show that, being second order in perturbation, such an induced tensor perturbation is generically gauge dependent. In particular, the gravitational wave power spectrum depends on the hypersurface (temporal gauge) condition taken for the linear scalar perturbation. We further show that, during the matter-dominated era, the induced tensor modes dominate over the linearly evolved primordial gravitational waves amplitude for $k\gtrsim10^{-2}~[h/{\rm Mpc}]$ even for the gauge that gives lowest induced tensor modes with the optimistic choice of primordial gravitational waves ($r=0.1$). The induced tensor modes, therefore, must be modeled correctly specific to the observational strategy for the measurement of primordial gravitational waves from large-scale structure via, for example, parity-odd mode of weak gravitational lensing, or clustering fossils.