Lensing corrections to features in the angular two-point correlation function and power spectrum

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theory of axion field arising from Type IIB string theory compacted to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For a massless axion field, in all three formalisms, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.

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Weak lensing cosmology with convolutional neural networks on noisy data

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2610 ◽

2019 ◽

Vol 490 (2) ◽

pp. 1843-1860 ◽

Cited By ~ 8

Author(s):

Dezső Ribli ◽

Bálint Ármin Pataki ◽

José Manuel Zorrilla Matilla ◽

Daniel Hsu ◽

Zoltán Haiman ◽

...

Keyword(s):

Neural Networks ◽

Correlation Function ◽

Power Spectrum ◽

Convolutional Neural Networks ◽

Higher Order ◽

Weak Lensing ◽

Noise Levels ◽

Point Correlation ◽

Point Correlation Function ◽

Non Gaussian

ABSTRACT Weak gravitational lensing is one of the most promising cosmological probes of the late universe. Several large ongoing (DES, KiDS, HSC) and planned (LSST, Euclid, WFIRST) astronomical surveys attempt to collect even deeper and larger scale data on weak lensing. Due to gravitational collapse, the distribution of dark matter is non-Gaussian on small scales. However, observations are typically evaluated through the two-point correlation function of galaxy shear, which does not capture non-Gaussian features of the lensing maps. Previous studies attempted to extract non-Gaussian information from weak lensing observations through several higher order statistics such as the three-point correlation function, peak counts, or Minkowski functionals. Deep convolutional neural networks (CNN) emerged in the field of computer vision with tremendous success, and they offer a new and very promising framework to extract information from 2D or 3D astronomical data sets, confirmed by recent studies on weak lensing. We show that a CNN is able to yield significantly stricter constraints of (σ8, Ωm) cosmological parameters than the power spectrum using convergence maps generated by full N-body simulations and ray-tracing, at angular scales and shape noise levels relevant for future observations. In a scenario mimicking LSST or Euclid, the CNN yields 2.4–2.8 times smaller credible contours than the power spectrum, and 3.5–4.2 times smaller at noise levels corresponding to a deep space survey such as WFIRST. We also show that at shape noise levels achievable in future space surveys the CNN yields 1.4–2.1 times smaller contours than peak counts, a higher order statistic capable of extracting non-Gaussian information from weak lensing maps.

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The Power Spectrum, Bias Evolution, and the Spatial Three‐Point Correlation Function

The Astrophysical Journal ◽

10.1086/307531 ◽

1999 ◽

Vol 521 (1) ◽

pp. 1-16 ◽

Cited By ~ 12

Author(s):

Ari Buchalter ◽

Marc Kamionkowski

Keyword(s):

Correlation Function ◽

Power Spectrum ◽

Point Correlation ◽

Point Correlation Function

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Two-point Correlation Function and Power Spectrum at Very Large Scales

Symposium - International Astronomical Union ◽

10.1017/s0074180900216616 ◽

2005 ◽

Vol 201 ◽

pp. 449-450

Author(s):

Z.-G. Deng ◽

X.-Y. Xia

Keyword(s):

Correlation Function ◽

Power Spectrum ◽

Correlation Functions ◽

Large Scale ◽

Wave Number ◽

Scale Fluctuation ◽

Point Correlation ◽

Point Correlation Function ◽

Redshift Survey ◽

Large Scale Fluctuation

Subsamples of galaxies with different morphological types have been sorted out from Stromlo-APM redshift survey. Two-point correlation function for each subsample has been calculated. The two-point correlation functions for all subsamples show very large scale fluctuation. We show that the two-point correlation function with fluctuation could be fitted by a modified power spectrum with power excess at wave number comparable to the scale of the fluctuation.

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The matter fluctuation amplitude inferred from the weak lensing power spectrum and correlation function in CFHTLenS data

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2931 ◽

2019 ◽

Vol 490 (4) ◽

pp. 5033-5042

Author(s):

Tianhuan Lu ◽

Zoltán Haiman

Keyword(s):

Correlation Function ◽

Power Spectrum ◽

Systematic Errors ◽

Small Scale ◽

Microwave Background ◽

Planck Data ◽

Point Correlation ◽

Point Correlation Function ◽

Fluctuation Amplitude ◽

Excess Power

ABSTRACT Based on the cosmic shear data from the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS), Kilbinger et al. obtained a constraint on the amplitude of matter fluctuations of σ8(Ωm/0.27)0.6 = 0.79 ± 0.03 from the two-point correlation function (2PCF). This is ≈3σ lower than the value 0.89 ± 0.01 derived from Planck data on cosmic microwave background (CMB) anisotropies. On the other hand, based on the same CFHTLenS data, but using the power spectrum, and performing a different analysis, Liu et al. obtained the higher value of $\sigma _8(\Omega _\mathrm{m}/0.27)^{0.64}=0.87^{+0.05}_{-0.06}$. We here investigate the origin of this difference, by performing a fair side-by-side comparison of the 2PCF and power spectrum analyses on CFHTLenS data. We find that these two statistics indeed deliver different results, even when applied to the same data in an otherwise identical procedure. We identify excess power in the data on small scales (ℓ > 5000) driving the larger values inferred from the power spectrum. We speculate on the possible origin of this excess small-scale power. More generally, our results highlight the utility of analysing the 2PCF and the power spectrum in tandem, to discover (and to help control) systematic errors.

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Fast Edge-corrected Measurement of the Two-Point Correlation Function and the Power Spectrum

The Astrophysical Journal ◽

10.1086/496971 ◽

2005 ◽

Vol 631 (1) ◽

pp. L1-L4 ◽

Cited By ~ 21

Author(s):

István Szapudi ◽

Jun Pan ◽

Simon Prunet ◽

Tamás Budavári

Keyword(s):

Correlation Function ◽

Power Spectrum ◽

Point Correlation ◽

Point Correlation Function

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Generalization of the Kaiser Rocket effect in general relativity in the wide-angle galaxy 2-point correlation function

International Journal of Modern Physics D ◽

10.1142/s0218271820500856 ◽

2020 ◽

Vol 29 (12) ◽

pp. 2050085

Author(s):

Daniele Bertacca

Keyword(s):

General Relativity ◽

Correlation Function ◽

Power Spectrum ◽

Relativistic Effects ◽

Wide Angle ◽

The Galaxy ◽

Point Correlation ◽

Point Correlation Function ◽

General Relativistic ◽

Rocket Effect

We study wide-angle correlations in the galaxy power spectrum in redshift space, including all general relativistic effects and the Kaiser Rocket effect in general relativity. We find that the Kaiser Rocket effect becomes important on large scales and at high redshifts, and leads to new contributions in wide-angle correlations. We believe this effect might be very important for future large volume surveys.

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From correlation functions to event shapes in QCD

Journal of High Energy Physics ◽

10.1007/jhep02(2021)053 ◽

2021 ◽

Vol 2021 (2) ◽

Cited By ~ 2

Author(s):

D. Chicherin ◽

J. M. Henn ◽

E. Sokatchev ◽

K. Yan

Keyword(s):

Correlation Function ◽

Correlation Functions ◽

Event Shape ◽

Proof Of Concept ◽

Yang Mills ◽

Point Correlation ◽

Point Correlation Function ◽

Event Shapes ◽

A Charge ◽

Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

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