Primordial non-Gaussianity from the 21 cm power spectrum during the epoch of reionization

Primordial non-Gaussianity is a crucial test of inflationary cosmology. We consider the impact of non-Gaussianity on the ionization power spectrum from 21 cm emission at the epoch of reionization. We focus on the power spectrum on large scales at redshifts of 7 to 8 and explore the expected constraint on the local non-Gaussianity parameter f(NL) for current and next-generation 21 cm experiments. We show that experiments such as SKA and MWA could measure f(NL) values of order 10. This can be improved by an order of magnitude with a fast-Fourier transform telescope like Omniscope.     

Frequency Spectra and Probability Distributions for Quantum Fluctuations

This paper discusses two distinct, but related issues in quantum fluctuation effects. The first is the frequency spectrum which can be assigned to one loop quantum processes. The formal spectrum is a flat one, but the finite quantum effects can be associated with a rapidly oscillating spectrum, as in the case of the Casimir effect. The leads to the speculation that one might be able to dramatically change the final answer by upsetting the delicate cancellation which usually occurs. The second issue is the probability distribution for quantum fluctuations. It is well known that quantities which are linear in a free quantum field have a Gaussian distribution. Here it will be argued that quadratic quantities, such as the quantum stress tensor, must have a skewed distribution. Some possible implications of this result for inflationary cosmology will be discussed. In particular, this might be a source for non-Gaussianity.     

Non-stationary regimes of surface gravity wave turbulence

We present experimental results about rising and decaying gravity wave turbulence in a large laboratory flume. We consider the time evolution of the wave energy spectral components in ω- and k-domains and demonstrate that emerging wave turbulence can be characterized by two time scales—a short dynamical scale due to nonlinear wave interactions and a longer kinetic time scale characterizing formation of a stationary wave energy spectrum. In the decay regime we observed the maximum of the wave energy spectrum decreasing in time initially as the power law, ∝t ^?1/2, as predicted by the weak turbulence theory, and then exponentially due to viscous friction.     

Dissipative or conservative cosmology with dark energy?

All evolutional paths for all admissible initial conditions of FRW cosmological models with dissipative dust fluid (described by dark matter, baryonic matter and dark energy) are analyzed using dynamical system approach. With that approach, one is able to see how generic the class of solutions leading to the desired property—acceleration—is. The theory of dynamical systems also offers a possibility of investigating all possible solutions and their stability with tools of Newtonian mechanics of a particle moving in a one-dimensional potential which is parameterized by the cosmological scale factor. We demonstrate that flat cosmology with bulk viscosity can be treated as a conservative system with a potential function of the Chaplygin gas type. We characterize the class of dark energy models that admit late time de Sitter attractor solution in terms of the potential function of corresponding conservative system. We argue that inclusion of dissipation effects makes the model more realistic because of its structural stability. We also confront viscous models with SNIa observations. The best fitted models are obtained by minimizing the χ² function which is illustrated by residuals and χ² levels in the space of model independent parameters. The general conclusion is that SNIa data supports the viscous model without the cosmological constant. The obtained values of χ² statistic are comparable for both the viscous model and ΛCDM model. The Bayesian information criteria are used to compare the models with different power-law parameterization of viscous effects. Our result of this analysis shows that SNIa data supports viscous cosmology more than the ΛCDM model if the coefficient in viscosity parameterization is fixed. The Bayes factor is also used to obtain the posterior probability of the model.     

Casimir Effect Near the Future Singularity in Kaluza Klein Viscous Cosmology

In this paper we investigate the analytical properties of the scalar expansion θ in the cosmic fluid close to the future singularity, when the fluid possesses a constant bulk viscosity ζ in the framework of Kaluza-Klein theory of gravitation. In addition, we assume the viscous cosmology theories in the sense that the Casimir contributions to the energy density and pressure are both proportional to 1/a ⁴, where a being scale factor. We also worked out the series expansion for the scalar expansion θ under the condition that the Casimir influence is small. However, near to the big rip singularity the Casimir term has to fade away and we obtain the same singularity behavior for the scalar expansion θ, energy density ρ, the scale factor a as in the Casimir-free viscous case.     

Inflation with multiple sound speeds: A model of multiple DBI type actions and non-Gaussianities

In this Letter we study adiabatic and isocurvature perturbations in the frame of inflation with multiple sound speeds involved. We suggest this scenario can be realized by a number of generalized scalar fields with arbitrary kinetic forms. These scalars have their own sound speeds respectively, so the propagations of field fluctuations are individual. Specifically, we study a model constructed by two DBI type actions. We find that the critical length scale for the freezing of perturbations corresponds to the maximum sound horizon. Moreover, if the mass term of one field is much lighter than that of the other, the entropy perturbation could be quite large and so may give rise to a growth outside sound horizon. At cubic order, we find that the non-Gaussianity of local type is possibly large when entropy perturbations are able to convert into curvature perturbations. We also calculate the non-Gaussianity of equilateral type approximately.     

贝叶斯频率估计中频率的先验分布对有色噪声作用的影响

在贝叶斯参数估计理论框架下,研究了被测参数的先验分布对有色噪声的抑制作用.选择一个受1/f~α型谱密度有色噪声影响的自旋1/2量子比特作为量子探测系统来估计一个磁场强度的大小,利用贝叶斯代价函数的动力学演化来评判估计的精度,重点研究先验概率分布对噪声非高斯性的限制作用.研究发现:当先验概率的不确定度比较大时,有色噪声的非高斯性对频率估计精度的影响比较小;当先验概率的不确定度比较小时,有色噪声的非高斯性对频率估计精度的影响比较大.     

Frequency modulation of waveguides in acoustic band-gap materials consisting of solid cylinders in viscous liquid

We investigated waveguides in acoustic band-gap materials consisting of steel cylinders in a liquid with viscous damping. Numerical results show that when the viscous penetration depth is comparable to the structural length scale, linear defect states fall in complete acoustic band gaps forming waveguides. It is also found that the magnitude of the viscosity in the liquid has an influence on the frequency of waveguides, that large viscous damping can make the defect modes ascend. An expected frequency of waveguides can be obtained by modulating the viscous damping parameter θ.     

Dissipative Model of the Universe

In the present study a trial is carried out to generalize the non-relativistic-dynamic model of cosmology put forward by O. Heckmann. The generalization is performed under the framework of the Gyarmati principle of irreversible thermodynamics for anisotropic inhomogeneous and viscous case. The equation of motion of the dissipative Universe will be a Navier-Stokes tensor equation leading to a Riccatian differential equation general in one dimension. The equations of the Heckmann model compatible with standard cosmology can be obtained from this by means of further simplifying assumption.     

Bouncing cosmology inspired by regular black holes

In this article, we present a bouncing cosmology inspired by a family of regular black holes. This scale-dependent cosmology deviates from the cosmological principle by means of a scale factor which depends on the time and the radial coordinate as well. The model is isotropic but not perfectly homogeneous. That is, this cosmology describes a universe almost homogeneous only for large scales, such as our observable universe.     

Diagnosis and impacts of non-Gaussianity of innovations in data assimilation

Most of the atmospheric and oceanic data assimilation (DA) schemes rely on the Best Linear Unbiased Estimator (BLUE), which is sub-optimal if errors of assimilated data are non-Gaussian, thus calling for a full Bayesian data assimilation. This paper contributes to the study of the non-Gaussianity of errors in the observational space. Possible sources of non-Gaussianity range from the inherent statistical skewness and positiveness of some physical observables (e.g. moisture, chemical species), the nonlinearity, both of the data assimilation models and of the observation operators among others. Deviations from Gaussianity can be justified from a priori hypotheses or inferred from statistical diagnostics of innovations (observation minus background), leading to consistency relationships between the error statistics. From samples of observations and backgrounds as well as their specified error variances, we evaluate some measures of the innovation non-Gaussianity, such as the skewness, kurtosis and negentropy. Under the assumption of additive errors and by relating statistical moments from both data errors and innovations, we identify potential sources of the innovation non-Gaussianity. These sources range from: (1) univariate error non-Gaussianity, (2), nonlinear correlations between errors, (3) spatio-temporal variability of error variances (heteroscedasticity) and (4) multiplicative noise. Observational and background errors are often assumed independent. This leads to variance-dependent bounds for the skewness and the kurtosis of errors. From innovation statistics, we assess the potential DA impact of some scenarios of non-Gaussian errors. This impact is measured through the mean square difference between the BLUE and the Minimum Variance Unbiased Estimator (MVUE), obtained with univariate observations and background estimates. In order to accomplish this, we compute maximum entropy probability density functions (pdfs) of the errors, constrained by the first four order moments. These pdfs are then used to compute the Bayesian posterior pdf and the MVUE. The referred impact is studied for a large range of statistical moments, being higher for skewed innovations and growing in average with the skewness of data errors, specially if the skewnesses have the same sign. An application has been performed to the quality-accepted ECMWF innovations of brightness temperatures of a set of High Resolution Infrared Sounder (HIRS) channels. In this context, the MVUE has led in some extreme cases to a potential reduction of 20%-60% of the posterior error variance as compared to the BLUE, specially for extreme values of the innovations.     

What can we learn from the tension between PLANCK and BICEP2 data?

Recently BICEP2 collaboration has announced the detection of the primordial gravitational waves at high confidence level.In light of the results of B-modes power spectrum from BICEP2 and using the basedΛCDM,a constraint on the tensor-to-scalar ratio r=0.20+0.07-0.05(68%C.L.)can be obtained,however,this result is in apparent tension with the limit on standard inflation models from the recent PLANCK measurement,r0.11(95%C.L.).Herein we review the recent progress on the cosmological studies after BICEP2 and discuss on different ways of reconciling the tension between PLANCK and BICEP2 data.We will discuss possible modifications on the standard cosmological model,such as including the running of scalar spectral index or other cosmological parameters correlated with inflationary cosmological parameters,or tilting the primordial power spectrum at large scales by introducing a cut off which can be predicted by bouncing cosmology.We will also comment on another possibility of generating extra B-modes of CMB polarization,namely by a non-zero polarization rotation angle during its transferring from the last scattering surface.     

Coupled Criticality Analysis of Inflation and Unemployment

In this paper, we focus on the critical periods in the economy that are characterized by unusual and large fluctuations in macroeconomic indicators, like those measuring inflation and unemployment. We analyze U.S. data for 70 years from 1948 until 2018. To capture their fluctuation essence, we concentrate on the non-Gaussianity of their distributions. We investigate how the non-Gaussianity of these variables affects the coupling structure of them. We distinguish “regular” from “rare” events, in calculating the correlation coefficient, emphasizing that both cases might lead to a different response of the economy. Through the “multifractal random wall” model, one can see that the non-Gaussianity depends on time scales. The non-Gaussianity of unemployment is noticeable only for periods shorter than one year; for longer periods, the fluctuation distribution tends to a Gaussian behavior. In contrast, the non-Gaussianities of inflation fluctuations persist for all time scales. We observe through the “bivariate multifractal random walk” that despite the inflation features, the non-Gaussianity of the coupled structure is finite for scales less than one year, drops for periods larger than one year, and becomes small for scales greater than two years. This means that the footprint of the monetary policies intentionally influencing the inflation and unemployment couple is observed only for time horizons smaller than two years. Finally, to improve some understanding of the effect of rare events, we calculate high moments of the variables’ increments for various q orders and various time scales. The results show that coupling with high moments sharply increases during crises.     

G-Curvaton

In this Letter, we study a curvaton model where the curvaton is acted by Galileon field. We calculate the power spectrum of fluctuation of G-Curvaton during inflation and discuss how it converts to the curvature perturbation after the end of inflation. We estimate the bispectrum of curvature perturbation induced, and show the dependence of non-Gaussianity on the parameters of model. It is found that our model can have sizable local and equilateral non-Gaussianities to up to O(¹⁰²), which is illustrated by an explicit example.     

O(d,d) symmetry in quantum cosmology

We analyze the quantum cosmology of one-loop string effective models which exhibit an O(d, d) symmetry. It is shown that due to the large symmetry of these models the Wheeler-de Witt equation can completely be solved. As a result, we find a basis of solutions with well-defined transformation properties under O(d, d) and under scale factor duality in particular. The general results are explicitly applied to 2-dimensional target spaces while some aspects of higher dimensional cases are also discussed. Moreover, a semiclassical wave function for the 2-dimensional black hole is constructed as a superposition of our basis.     

Quantum gravitational contributions to the cosmic microwave background anisotropy spectrum

We derive the primordial power spectrum of density fluctuations in the framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer approximation to the Wheeler-DeWitt equation for an inflationary universe with a scalar field. In this way, we first recover the scale-invariant power spectrum that is found as an approximation in the simplest inflationary models. We then obtain quantum gravitational corrections to this spectrum and discuss whether they lead to measurable signatures in the cosmic microwave background anisotropy spectrum. The nonobservation so far of such corrections translates into an upper bound on the energy scale of inflation.     

Explicit cosmological coarse graining via spatial averaging

The present matter density of the Universe, while highly inhomogeneous on small scales, displays approximate homogeneity on large scales. We propose that whereas it is justified to use the Friedmann–Lemaître–Robertson–Walker (FLRW) line element (which describes an exactly homogeneous and isotropic universe) as a template to construct luminosity distances in order to compare observations with theory, the evolution of the scale factor in such a construction must be governed not by the standard Einstein equations for the FLRW metric, but by the modified Friedmann equations derived by Buchert (Gen Relat Gravit 32:105, 2000; 33:1381, 2001) in the context of spatial averaging in Cosmology. Furthermore, we argue that this scale factor, defined in the spatially averaged cosmology, will correspond to the effective FLRW metric provided the size of the averaging domain coincides with the scale at which cosmological homogeneity arises. This allows us, in principle, to compare predictions of a spatially averaged cosmology with observations, in the standard manner, for instance by computing the luminosity distance versus red-shift relation. The predictions of the spatially averaged cosmology would in general differ from standard FLRW cosmology, because the scale-factor now obeys the modified FLRW equations. This could help determine, by comparing with observations, whether or not cosmological inhomogeneities are an alternative explanation for the observed cosmic acceleration.     

On the possibility of dark energy from corrections to the Wheeler–DeWitt equation

We present a method for approximating the effective consequence of generic quantum gravity corrections to the Wheeler–DeWitt equation. We show that in many cases these corrections can produce departures from classical physics at large scales and that this behaviour can be interpreted as additional matter components. This opens up the possibility that dark energy (and possible dark matter) could be large scale manifestations of quantum gravity corrections to classical general relativity. As a specific example we examine the first order corrections to the Wheeler–DeWitt equation arising from loop quantum cosmology in the absence of lattice refinement and show how the ultimate breakdown in large scale physics occurs.     

Geometrical Detection of Weak Non-Gaussianity upon Coarse-Graining

Measures of the non-Gaussianity of a random field depend on how accurately one is able to measure the field. If a signal measured at a certain point is to be averaged with its surroundings, or coarse-grained, the magnitude of its non-Gaussian component can vary. In this article, we investigate the variation of the “apparent” non-Gaussianity, as a function of the coarse-graining length, when we measure non-Gaussianity using the statistics of extrema in the field. We derive how the relative difference between maxima and minima—which is a geometrical measure of the field’s non-Gaussianity—behaves as the field is coarse-grained over increasingly larger length scales. Measuring this function can give extra information about the non-Gaussian statistics and facilitate its detection.     

Tensor modes from a primordial Hagedorn phase of string cosmology

It has recently been shown that a Hagedorn phase of string gas cosmology can provide a causal mechanism for generating a nearly scale-invariant spectrum of scalar metric fluctuations, without the need for an intervening period of de Sitter expansion. In this Letter, we compute the spectrum of tensor metric fluctuations (gravitational waves) in this scenario and show that it is also nearly scale invariant. However, whereas the spectrum of scalar modes has a small red tilt, the spectrum of tensor modes has a small blue tilt, unlike what occurs in slow-roll inflation. This provides a possible observational way to distinguish between our cosmological scenario and conventional slow-roll inflation.