scholarly journals Second-order power spectra of CMB anisotropies due to primordial random perturbations in flat cosmological models

2008 ◽  
Vol 77 (10) ◽  
Author(s):  
Kenji Tomita
Keyword(s):  
Power Spectra ◽  
Cosmological Models ◽  
Second Order ◽  
Random Perturbations

scholarly journals Second-order differential equations with random perturbations and small parameters

2017 ◽  
Vol 147 (4) ◽  
pp. 763-779
Author(s):  
M. Kamenskii ◽  
S. Pergamenchtchikov ◽  
M. Quincampoix
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Random Perturbation ◽  
Stochastic Averaging ◽  
Second Order ◽  
Random Perturbations ◽  
Existence And Uniqueness Theorem ◽  
Second Order Differential Equations ◽  
Averaging Theorem ◽  
Small Parameters

We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small parameter goes to zero and show the stochastic averaging theorem for such equations. We find the explicit limits for the solutions as the small parameter goes to zero.

G-INFLATION: INFLATION WITH THE MOST GENERAL SECOND-ORDER FIELD EQUATIONS

2012 ◽  
Vol 10 ◽  
pp. 77-84
Author(s):  
TSUTOMU KOBAYASHI ◽  
MASAHIDE YAMAGUCHI ◽  
JUN'ICHI YOKOYAMA
Keyword(s):  
Power Spectra ◽  
Second Order ◽  
Stability Criteria ◽  
Cosmological Perturbations ◽  
Field Equations ◽  
Special Cases ◽  
Single Field ◽  
The Stability

In this talk, we have discussed generalized Galileons as a framework to develop the most general single-field inflation models ever, (Generalized) G-inflation, containing previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases. We have also investigated the background and perturbation evolution in this model, calculating the most general quadratic actions for tensor and scalar cosmological perturbations to give the stability criteria and the power spectra of primordial fluctuations.

scholarly journals K-inflationary power spectra at second order

2013 ◽  
Vol 2013 (06) ◽  
pp. 021-021 ◽  
Author(s):  
Jérôme Martin ◽  
Christophe Ringeval ◽  
Vincent Vennin
Keyword(s):  
Power Spectra ◽  
Second Order

Spatial nonlinearities in the instantaneous perception of textures with identical power spectra

1980 ◽  
Vol 290 (1038) ◽  
pp. 83-94 ◽  
Keyword(s):  
Order Statistics ◽  
Power Spectra ◽  
Building Blocks ◽  
Second Order ◽  
Perceptual System ◽  
Higher Order Statistics ◽  
Line Segments ◽  
Second Order Statistics ◽  
Local Structures ◽  
Perception System

In 1962, Julesz observed that texture pairs with identical second-order statistics but different third- and higher-order statistics were usually not discriminable without scrutiny. Since second-order (dipole) statistics determine the autocorrelation functions and hence the power spectra, this observation also meant that in preattentive perception of texture the phase (position) spectra were ignored. In the last two decades many new classes of texture pairs with identical power spectra have been invented that were not effortlessly discriminable; however, recently (Caelli & Julesz 1978; Caelli et al . 1978; Julesz et al . 1978) several counterexamples were found. In these texture pairs with identical power spectra some local structures of ‘quasi-collinearity’, ‘corner’, ‘closure’ and ‘granularity’ yielded strong discrimination. These features can be regarded as the fundamental building blocks of form, that is, the essential nonlinearities of the preattentive perceptual system. Here, it will be shown that these counterexamples are not independent of each other, but can be described by two elementary units: bars (line segments) and their terminators. Furthermore, the preattentive texture perception system can count the number of terminators but ignores their positions.

scholarly journals THE DEGENERACY PROBLEM IN LAMBDA-CDM COSMOLOGICAL MODELS

2011 ◽  
Vol 03 ◽  
pp. 246-253
Author(s):  
ARMANDO BERNUI
Keyword(s):  
Power Spectrum ◽  
Background Radiation ◽  
Cosmological Parameters ◽  
Power Spectra ◽  
Cosmological Models ◽  
Microwave Background ◽  
Angular Power Spectrum ◽  
Statistical Property ◽  
Microwave Background Radiation ◽  
Degeneracy Problem

Recent measurements of the cosmic microwave background radiation (CMB) from the WMAP satellite led to formulate a successful concordance cosmological model, termed ΛCDM. This model satisfactorily explains the origin and structure of the CMB temperature fluctuations, from small to large angular scales, and moreover it accurately fits –with only six parameters– the CMB angular power spectrum. Despite of their triumphs in describing the observed WMAP data, we notice that some ΛCDM cosmological parameters can attain, due to their error bars, slightly different values and this degree of freedom could produce a significant impact in our understanding of the primordial universe. We are talking about the degeneracy problem, that is cosmological models with parameters that are a little bit different from those given by the ΛCDM model but fits equally well the angular power spectrum of the CMB data. Our interest here is to investigate the Gaussian statistical property, at large angular scales, in two sets of Monte Carlo CMB maps produced by seeding them with slightly different ΛCDM angular power spectra.

scholarly journals Clustering and halo abundances in early dark energy cosmological models

2021 ◽  
Vol 504 (1) ◽  
pp. 769-781
Author(s):  
Anatoly Klypin ◽  
Vivian Poulin ◽  
Francisco Prada ◽  
Joel Primack ◽  
Marc Kamionkowski ◽  
...  
Keyword(s):  
Dark Energy ◽  
Cold Dark Matter ◽  
Power Spectra ◽  
Hubble Constant ◽  
Cosmological Models ◽  
Acoustic Oscillations ◽  
Microwave Background ◽  
Linear Evolution ◽  
James Webb Space Telescope ◽  
Non Linear

ABSTRACT Cold Dark Matter with cosmological constant (ΛCDM) cosmological models with early dark energy (EDE) have been proposed to resolve tensions between the Hubble constant $H_0=100\, h$ km ṡ−1Ṁpc−1 measured locally, giving h ≈ 0.73, and H0 deduced from Planck cosmic microwave background (CMB) and other early-Universe measurements plus ΛCDM, giving h ≈ 0.67. EDE models do this by adding a scalar field that temporarily adds dark energy equal to about 10 per cent of the cosmological energy density at the end of the radiation-dominated era at redshift z ∼ 3500. Here, we compare linear and non-linear predictions of a Planck-normalized ΛCDM model including EDE giving h = 0.728 with those of standard Planck-normalized ΛCDM with h = 0.678. We find that non-linear evolution reduces the differences between power spectra of fluctuations at low redshifts. As a result, at z = 0 the halo mass functions on galactic scales are nearly the same, with differences only 1–2 per cent. However, the differences dramatically increase at high redshifts. The EDE model predicts 50 per cent more massive clusters at z = 1 and twice more galaxy-mass haloes at z = 4. Even greater increases in abundances of galaxy-mass haloes at higher redshifts may make it easier to reionize the universe with EDE. Predicted galaxy abundances and clustering will soon be tested by the James Webb Space Telescope (JWST) observations. Positions of baryonic acoustic oscillations (BAOs) and correlation functions differ by about 2 per cent between the models – an effect that is not washed out by non-linearities. Both standard ΛCDM and the EDE model studied here agree well with presently available acoustic-scale observations, but the Dark Energy Spectroscopic Instrument and Euclid measurements will provide stringent new tests.

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