arXiv subjects

Eiichiro Komatsu

Publications and source records attributed to Eiichiro Komatsu.

At least 163 records · Page 9Linked to original sources

arXiv2007

Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background

Measurements of primordial non-Gaussianity ($f_{NL}$) open a new window onto the physics of inflation. We describe a fast cubic (bispectrum) estimator of $f_{NL}$, using a combined analysis of temperature and polarization observations. The speed of our estimator allows us to use a sufficient number of Monte Carlo simulations to characterize its statistical properties in the presence of real world issues such as instrumental effects, partial sky coverage, and foreground contamination. We find that our estimator is optimal, where optimality is defined by saturation of the Cramer Rao bound, if noise is homogeneous. Our estimator is also computationally efficient, scaling as $O(N^{3/2})$ compared to the $O(N^{5/2})$ scaling of the brute force bispectrum calculation for sky maps with $N$ pixels. For Planck this translates into a speed-up by factors of millions, reducing the required computing time from thousands of years to just hours and thus making $f_{NL}$ estimation feasible for future surveys. Our estimator in its current form is optimal if noise is homogeneous. In future work our fast polarized bispectrum estimator should be extended to deal with inhomogeneous noise in an analogous way to how the existing fast temperature estimator was generalized.

astro-ph↗

arXiv2006

Angular power spectrum of gamma-ray sources for GLAST: blazars and clusters of galaxies

Blazars, a beamed population of active galactic nuclei, radiate high-energy gamma-rays, and thus are a good target for the Gamma Ray Large Area Space Telescope (GLAST). As the blazars trace the large-scale structure of the universe, one may observe spatial clustering of blazars. We calculate the angular power spectrum of blazars that would be detected by GLAST. We show that we have the best chance of detecting their clustering at large angular scales, θ>~ 10 deg, where shot noise is less important, and the dominant contribution to the correlation comes from relatively low redshift, z <~ 0.1. The GLAST can detect the correlation signal, if the blazars detected by GLAST trace the distribution of low-z quasars observed by optical galaxy surveys, which have the bias of unity. If the bias of blazars is greater than 1.5, GLAST will detect the correlation signal unambiguously. We also find that GLAST may detect spatial clustering of clusters of galaxies in gamma-rays. The shape of the angular power spectrum is different for blazars and clusters of galaxies; thus, we can separate these two contributions on the basis of the shape of the power spectrum.

astro-ph↗

arXiv2006

Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure

We derive analytical formulae for the Minkowski Functions of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a non-linear coupling parameter, f_NL, directly from the CMB and LSS data without relying on numerical simulations of non-Gaussian primordial fluctuations. One can use these formulae to estimate statistical errors on f_NL from Gaussian realizations, which are much faster to generate than non-Gaussian ones, fully taking into account the cosmic/sampling variance, beam smearing, survey mask, etc. We show that the CMB data from the Wilkinson Microwave Anisotropy Probe should be sensitive to |f_NL|\simeq 40 at the 68% confidence level. The Planck data should be sensitive to |f_NL|\simeq 20. As for the LSS data, the late-time non-Gaussianity arising from gravitational instability and galaxy biasing makes it more challenging to detect primordial non-Gaussianity at low redshifts. The late-time effects obscure the primordial signals at small spatial scales. High-redshift galaxy surveys at z>2 covering \sim 10Gpc^3 volume would be required for the LSS data to detect |f_NL|\simeq 100. Minkowski Functionals are nicely complementary to the bispectrum because the Minkowski Functionals are defined in real space and the bispectrum is defined in Fourier space. This property makes the Minksowski Functionals a useful tool in the presence of real-world issues such as anisotropic noise, foreground and survey masks. Our formalism can be extended to scale-dependent f_NL easily.

astro-ph↗

arXiv2006

Perturbation Theory Reloaded: Analytical Calculation of Non-linearity in Baryonic Oscillations in the Real Space Matter Power Spectrum

We compare the non-linear matter power spectrum in real space calculated analytically from 3rd-order perturbation theory with N-body simulations at 1 1, the shape of oscillations is distorted from the linear theory prediction. Nevertheless, our results suggest that one can correct the distortion caused by non-linearity almost exactly. We also find that perturbation theory, which does not contain any free parameters, provides a significantly better fit to the simulations than the conventional approaches based on empirical fitting functions to simulations. The future work would include perturbation theory calculations of non-linearity in redshift space distortion and halo biasing in the weakly non-linear regime.

astro-ph↗

arXiv2006

Cosmology with High-redshift Galaxy Survey: Neutrino Mass and Inflation

(abridged) High-z galaxy redshift surveys open up exciting possibilities for precision determinations of neutrino masses and inflationary models. The high-z surveys are more useful for cosmology than low-z ones owing to much weaker non-linearities in matter clustering, redshift-space distortion and galaxy bias. We can then utilize the two-dimensional information of the linear power spectrum in angular and redshift space to measure the scale-dependent suppression of matter clustering due to neutrino free-streaming as well as the shape of the primordial power spectrum. To illustrate capabilities of high-z surveys for constraining neutrino masses and the primordial power spectrum, we compare three future redshift surveys covering 300 square degrees at 0.5<z<2, 2<z<4, and 3.5<z<6.5. We find that, combined with the cosmic microwave background data expected from the Planck satellite, these surveys allow precision determination of the total neutrino mass with the projected errors of sigma(m_nu)=0.059, 0.043, and 0.025 eV, respectively, thus yielding a positive detection of the neutrino mass rather than an upper limit, as sigma(m_nu) is smaller than the lower limits to the neutrino masses implied from the neutrino oscillation experiments. The accuracies of constraining the tilt and running index of the primordial power spectrum, sigma(n_s)=(3.8, 3.7, 3.0)x10^-3, and sigma(alpha_s)=(5.9, 5.7, 2.4)x10^-3, respectively, are smaller than the current uncertainties by more than an order of magnitude, which will allow us to discriminate between candidate inflationary models. In particular, the error on alpha_s from the highest redshift survey is not very far away from the prediction of a class of simple inflationary models driven by a massive scalar field with self-coupling, alpha_s=-(0.8-1.2)x10^-3.

astro-ph↗

arXiv2006

Angular Trispectrum of CMB Temperature Anisotropy from Primordial Non-Gaussianity with the Full Radiation Transfer Function

We calculate the cosmic microwave background (CMB) angular trispectrum, spherical harmonic transform of the four-point correlation function, from primordial non-Gaussianity in primordial curvature perturbations characterized by a constant non-linear coupling parameter, $f_{\rm NL}$. We fully take into account the effect of the radiation transfer function, and thus provide the most accurate estimate of the signal-to-noise ratio of the angular trispectrum of CMB temperature anisotropy. We find that the predicted signal-to-noise ratio of the trispectrum summed up to a given $l$ is approximately a power-law, $(S/N)(<l)\sim 2.2\times 10^{-9}f^2_{\rm NL}l^2$, up to the maximum multipole that we have reached in our numerical calculation, $l=1200$, assuming that the error is dominated by cosmic variance. Our results indicate that the signal-to-noise ratio of the temperature trispectrum exceeds that of the bispectrum at the critical multipole, $l_c \sim 1500~(50/|f_{\rm NL}|)$. Therefore, the trispectrum of the Planck data is more sensitive to primordial non-Gaussianity than the bispectrum for $|f_{\rm NL}|\gtrsim 50$. We also report the predicted constraints on the amplitude of trispectrum, which may be useful for other non-Gaussian models such as curvaton models.

astro-ph↗

arXiv2006

The Cosmic Near Infrared Background: Remnant Light from Early Stars

The redshifted ultraviolet light from early stars at z ~ 10 contributes to the cosmic near infrared background. We present detailed calculations of its spectrum with various assumptions about metallicity and mass spectrum of early stars. We show that if the near infrared background has a stellar origin, metal-free stars are not the only explanation of the excess near infrared background; stars with metals (e.g. Z=1/50 Z_sun) can produce the same amount of background intensity as the metal-free stars. We quantitatively show that the predicted average intensity at 1-2 microns is essentially determined by the efficiency of nuclear burning in stars, which is not very sensitive to metallicity. We predict νI_ν/ \dotρ_* ~ 4-8 nW m^-2 sr^-1, where \dot{ρ_*} is the mean star formation rate at z=7-15 (in units of M_sun yr^-1 Mpc^-3) for stars more massive than 5 M_sun. On the other hand, since we have very little knowledge about the form of mass spectrum of early stars, uncertainty in the average intensity due to the mass spectrum could be large. An accurate determination of the near infrared background allows us to probe formation history of early stars, which is difficult to constrain by other means. While the star formation rate at z=7-15 inferred from the current data is significantly higher than the local rate at z<5, it does not rule out the stellar origin of the cosmic near infrared background. In addition, we show that a reasonable initial mass function, coupled with this star formation rate, does not over-produce metals in the universe in most cases, and may produce as little as less than 1 % of the metals observed in the universe today.

astro-ph↗

arXiv2006

The Cosmic Reionization History as Revealed by the CMB Doppler--21-cm Correlation

We show that the epoch(s) of reionization when the ionization fraction of the universe is about half can be determined by correlating Cosmic Microwave Background (CMB) temperature maps with 21-cm line maps at degree scales ($l\sim 100$). During reionization peculiar motion of free electrons induces the Doppler anisotropy of the CMB, while density fluctuations of neutral hydrogen induce the 21-cm line anisotropy. In our simplified model of inhomogeneous reionization, a positive correlation arises as the universe reionizes whereas a negative correlation arises as it recombines; thus, the sign of the correlation provides information on the reionization history which cannot be obtained by presently. The signal comes mainly from large scales (k~0.01 Mpc^-1) where linear perturbation theory is valid and complexity due to patchy reionization is averaged out. Since the Doppler signal comes from ionized regions and the 21-cm comes from neutral ones, the correlation has a well-defined peak(s) in redshift when the ionization fraction of the universe is about half. Furthermore, the cross-correlation is much less sensitive to systematic errors, especially foreground emission, than the auto-correlation of 21-cm lines: this is analogous to the temperature-polarization correlation of the CMB being more immune to systematic errors than the polarization-polarization. Therefore, we argue that the Doppler-21cm correlation provides a robust measurement of the 21-cm anisotropy, which can also be used as a diagnostic tool for detected signals in the 21-cm data -- detection of the cross-correlation provides the strongest confirmation that the signal is of cosmological origin. We show that the Square Kilometer Array can easily measure the predicted correlation signal for 1~year of survey observation.

astro-ph↗

arXiv2006

Improved Calculation of the Primordial Gravitational Wave Spectrum in the Standard Model

We show that the energy density spectrum of the primordial gravitational waves has characteristic features due to the successive changes in the relativistic degrees of freedom during the radiation era. These changes make the evolution of radiation energy density deviate from the conventional adiabatic evolution, ρ_r~ a^{-4}, and thus cause the expansion rate of the universe to change suddenly at each transition which, in turn, modifies the spectrum of primordial gravitational waves. We take into account all the particles in the Standard Model of elementary particles. In addition, free-streaming of neutrinos damps the amplitude of gravitational waves, leaving characteristic features in the energy density spectrum. Our calculations are solely based on the standard model of cosmology and particle physics, and therefore these features must exist. Our calculations significantly improve the previous ones which ignored these effects and predicted a smooth, featureless spectrum.

astro-ph↗

arXiv2006

Anisotropy of the cosmic gamma-ray background from dark matter annihilation

High-energy photons from dark matter annihilation contribute to the cosmic gamma-ray background (CGB). Since dark matter particles are weakly interacting, annihilation can happen only in high density regions such as dark matter halos. The precise shape of the energy spectrum of CGB depends on the nature of dark matter particles, as well as the cosmological evolution of dark matter halos. In order to discriminate between the signals from dark matter annihilation and other astrophysical sources, however, the information from the energy spectrum may not be sufficient. We show that dark matter annihilation also produces a characteristic anisotropy of the CGB, which provides a powerful tool for testing the origin. We develop the formalism based on a halo model approach to calculate the three-dimensional power spectrum of dark matter clumping, which determines the power spectrum of annihilation signals. We show that the sensitivity of future gamma-ray detectors such as GLAST should allow us to measure the angular power spectrum of CGB anisotropy, if dark matter particles are supersymmetric neutralinos and they account for most of the observed mean intensity of CGB in GeV region. On the other hand, if dark matter has a relatively small mass, and accounts for most of the CGB in MeV region, then the future Advanced Compton Telescope should be able to measure the anisotropy in MeV region. As the intensity of photons from annihilation is proportional to the density squared, we show that the predicted shape of the angular power spectrum of gamma rays from dark matter annihilation is different from that due to other astrophysical sources such as blazars. Therefore, the angular power spectrum of the CGB provides a smoking-gun signature of dark matter annihilation.

astro-ph↗

arXiv2005

Dark Matter Annihilation: the origin of cosmic gamma-ray background at 1-20 MeV

The origin of the cosmic gamma-ray background at 1-20 MeV remains a mystery. We show that gamma-ray emission accompanying annihilation of 20 MeV dark matter particles explains most of the observed signal. Our model satisfies all of the current observational constraints, and naturally provides the origin of "missing" gamma-ray background at 1-20 MeV and 511 keV line emission from the Galactic center. We conclude that gamma-ray observations support the existence of 20 MeV dark matter particles. Improved measurements of the gamma-ray background in this energy band undoubtedly test our proposal.

astro-ph↗

arXiv2005

Measuring primordial non-Gaussianity in the cosmic microwave background

We derive a fast way for measuring primordial non-Gaussianity in a nearly full-sky map of the cosmic microwave background. We find a cubic combination of sky maps combining bispectrum configurations to capture a quadratic term in primordial fluctuations. Our method takes only N^1.5 operations rather than N^2.5 of the bispectrum analysis (1000 times faster for l=512), retaining the same sensitivity. A key component is a map of underlying primordial fluctuations, which can be more sensitive to the primordial non-Gaussianity than a temperature map. We also derive a fast and accurate statistic for measuring non-Gaussian signals from foreground point sources. The statistic is 10^6 times faster than the full bispectrum analysis, and can be used to estimate contamination from the sources. Our algorithm has been successfully applied to the Wilkinson Microwave Anisotropy Probe sky maps by Komatsu et al. (2003).

astro-ph↗

arXiv2005

Cosmic gamma-ray background from Type Ia supernovae revisited: Evidence for missing gamma-rays at MeV

The observed cosmic gamma-ray background at ~ MeV has often been attributed to Type Ia supernovae (SNIa). Since SNIa is close to a standard candle, one can calculate the gamma-ray intensity of SNIa integrated over redshifts fairly accurately, once the evolution of the SNIa rate is known. The latest SNIa rate measured at z < ~1.6 (Dahlen et al. 2004) indicates that the previous calculations of the gamma-ray background consistently overestimated the SNIa rate. With the new rate, we find that the SNIa contribution is an order of magnitude smaller than observed, and thus new population(s) of sources should be invoked.

astro-ph↗

arXiv2004

Cosmological Lower Bound on Dark Matter Masses from the Soft Gamma-ray Background

Motivated by a recent detection of 511 keV photons from the center of our Galaxy, we calculate the spectrum of the soft gamma-ray background of the redshifted 511 keV photons from cosmological halos. Annihilation of dark matter particles into electron-positron pairs makes a substantial contribution to the gamma-ray background. Mass of such dark matter particles must be <~ 100 MeV so that resulting electron-positron pairs are on-relativistic. On the other hand, we show that in order for the annihilation not to exceed the observed background, the dark matter mass needs to be >~ 20 MeV. We include the contribution from the active galactic nuclei and supernovae. The halo substructures may increase the lower bound to >~ 60 MeV.

astro-ph↗

arXiv2003

Constraining the Topology of the Universe

The first year data from the Wilkinson Microwave Anisotropy Probe are used to place stringent constraints on the topology of the Universe. We search for pairs of circles on the sky with similar temperature patterns along each circle. We restrict the search to back-to-back circle pairs, and to nearly back-to-back circle pairs, as this covers the majority of the topologies that one might hope to detect in a nearly flat universe. We do not find any matched circles with radius greater than 25 degrees. For a wide class of models, the non-detection rules out the possibility that we live in a universe with topology scale smaller than 24 Gpc.

astro-ph↗

arXiv2002

The Sunyaev-Zel'dovich angular power spectrum as a probe of cosmological parameters

The angular power spectrum of the SZ effect, C_l, is a powerful probe of cosmology. It is easier to detect than individual clusters in the field, is insensitive to observational selection effects and does not require a calibration between cluster mass and flux, reducing the systematic errors which dominate the cluster-counting constraints. It receives a dominant contribution from cluster region between 20-40% of the virial radius and is thus insensitive to the poorly known gas physics in the cluster centre, such as cooling or (pre)heating. In this paper we derive a refined analytic prediction for C_l using the universal gas-density and temperature profile and the dark-matter halo mass function. The predicted C_l has no free parameters and fits all of the published hydrodynamic simulation results to better than a factor of two around l=3000. We find that C_l scales as (sigma_8)^7 times (Omega_b h)^2 and is almost independent of all of the other cosmological parameters. This differs from the local cluster abundance studies, which give a relation between sigma_8 and Omega_m. We also compute the covariance matrix of C_l using the halo model and find a good agreement relative to the simulations. We estimate how well we can determine sigma_8 with sampling-variance-limited observations and find that for a several-square-degree survey with 1-2 arcminute resolution one should be able to determine sigma_8 to within a few percent, with the remaining uncertainty dominated by theoretical modelling. If the recent excess of the CMB power on small scales reported by the CBI experiment is due to the SZ effect, then we find sigma_8(Omega_b h/0.029)^0.3 = 1.04 +- 0.12 at the 95% confidence level (statistical) and with a residual 10% systematic (theoretical) uncertainty.

astro-ph↗

arXiv2002

The Pursuit of Non-Gaussian Fluctuations in the Cosmic Microwave Background

We present theoretical and observational studies of non-Gaussian fluctuations in CMB, by using the angular bispectrum and trispectrum. We predict the primary angular bispectrum from inflation, and forecast how well we can measure the primordial non-Gaussian signal. In addition to that, secondary anisotropy sources in the low-redshift universe also produce non-Gaussianity, so do foreground emissions from extragalactic or interstellar microwave sources. We study how well we can measure these non-Gaussian signals, including the primordial signal. We find that slow-roll inflation produces too small bispectrum to be detected by any experiments; thus, any detection strongly constrains this class of models. We also find that the secondary bispectrum from coupling between the SZ effect and the weak lensing effect, and the foreground bispectrum from extragalactic point sources, give detectable non-Gaussian signals on small angular scales. We test Gaussianity of the COBE DMR sky maps, by measuring all the modes of the angular bispectrum down to the DMR beam size. We find no significant signal of the bispectrum. We also find that the previously reported detection of the bispectrum is consistent with a statistical fluctuation. By fitting the theoretical prediction to the data for the primary bispectrum, we put a constraint on non-linearity in inflation. We conclude that the angular bispectrum finds no significant non-Gaussian signals in the DMR data. We present the first measurement of the angular trispectrum on the DMR sky maps, further testing Gaussianity of the DMR data. We find no significant non-Gaussian signals in the trispectrum. Therefore, the angular bispectrum and trispectrum show that the DMR sky map is comfortably consistent with Gaussianity.

astro-ph↗

arXiv2001

Measurement of the cosmic microwave background bispectrum on the COBE DMR sky maps

We measure the angular bispectrum of the cosmic microwave background (CMB) radiation anisotropy from the COBE Differential Microwave Radiometer (DMR) four-year sky maps. The angular bispectrum is the harmonic transform of the three-point correlation function, analogous to the angular power spectrum, the harmonic transform of the two-point correlation function. First, we study statistical properties of the bispectrum and the normalized bispectrum. We find the latter more useful for statistical analysis; the distribution of the normalized bispectrum is very much Gaussian, while the bare bispectrum distribution is highly non-Gaussian. Then, we measure 466 modes of the normalized bispectrum, all independent combinations of three-point configurations up to a maximum multipole of 20, the mode corresponding to the DMR beam size. By measuring 10 times as many modes as the sum of previous work, we test Gaussianity of the DMR maps. We compare the data with the simulated Gaussian realizations, finding no significant detection of the normalized bispectrum on the mode-by-mode basis. We also find that the previously reported detection of the normalized bispectrum is consistent with a statistical fluctuation. By fitting a theoretical prediction to the data for the primary CMB bispectrum, which is motivated by slow-roll inflation, we put a weak constraint on a parameter characterizing non-linearity in inflation. Simultaneously fitting the foreground bispectra estimated from interstellar dust and synchrotron template maps shows that neither dust nor synchrotron emissions significantly contribute to the bispectrum at high Galactic latitude. We conclude that the DMR map is consistent with Gaussianity.

astro-ph↗