The correlation function for density perturbations in an expanding universe. II - Nonlinear theory

1977 ◽  
Vol 217 ◽  
pp. 331 ◽  
Author(s):  
J. McClelland ◽  
J. Silk
Keyword(s):  
Correlation Function ◽  
Nonlinear Theory ◽  
Expanding Universe ◽  
Density Perturbations

scholarly journals The Spectrum of Density Perturbations in an Expanding Universe

1974 ◽  
Vol 63 ◽  
pp. 175-193
Author(s):  
Joseph Silk
Keyword(s):  
Large Scale ◽  
Background Radiation ◽  
Large Scale Structure ◽  
Challenging Problem ◽  
Expanding Universe ◽  
Related Matter ◽  
Widespread Acceptance ◽  
Density Perturbations ◽  
Density Inhomogeneities ◽  
The Universe

Perhaps the most challenging problem confronting a cosmologist is to reconcile the observed large-scale structure of the Universe with the Friedmann-Lemaître cosmological models that have gained such widespread acceptance in recent years (cf. however the alternative viewpoint, as exemplified in this Symposium by Arp and others). In this review, I shall look anew at the spectrum of density inhomogeneities that survive decoupling of matter and radiation at z ~ 1000 and provide the primordial fluctuations that can eventually generate galaxies. A closely related matter, that of the associated fluctuations in the background radiation, is discussed elsewhere in this volume by Doroshkevich, Sunyaev and Zel'dovich.

TYPICAL SCALES IN THE CLUSTERING OF THE UNIVERSE

1995 ◽  
Vol 04 (04) ◽  
pp. 417-428
Author(s):  
LI-ZHI FANG ◽  
ZU-GAN DENG ◽  
XIAO-YANG XIA
Keyword(s):  
Correlation Function ◽  
Clusters Of Galaxies ◽  
High Confidence ◽  
Scale Free ◽  
Density Perturbations ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Periodic Components ◽  
The Universe ◽  
Characteristic Scales

The cosmic density perturbations are not completely scale-free, i.e. preferential scales should exist in the clustering of the universe. Observations do show the existence of the typical scales, namely, the distribution of various objects cannot be described by a simple fractal law. However, the standard two-point correlation function statistic is ineffective in detecting the typical scales. A better method based on identifying the periodic components in two-point correlation functions was developed. Using this method, the typical scales have been systematically searched for in samples of galaxies, clusters of galaxies, quasars and absorption lines of quasars. It showed the existence of typical scales in the range of 20–130 h−1 Mpc with high confidence. In particular, two typical scales, 60−1 Mpc and 130−1 Mpc, have been detected in all the samples being analysed. Such “universal” scales are probably the characteristic scales in the primordial fluctuations of the universe. Other theoretical implications of the detected typical scales have also been reviewed.

scholarly journals Trans-Planckian quantum corrections and inflationary vacuum fluctuations of non-minimally coupled scalar fields

2019 ◽  
Vol 34 (33) ◽  
pp. 1950275
Author(s):  
Hiroki Matsui
Keyword(s):  
Correlation Function ◽  
Effective Potential ◽  
Density Perturbation ◽  
Scalar Fields ◽  
New Physics ◽  
Quantum Corrections ◽  
Vacuum Fluctuations ◽  
Density Perturbations ◽  
Point Correlation ◽  
Point Correlation Function

In this paper, we discuss how trans-Planckian physics affects inflationary vacuum fluctuations and primordial density perturbations. The trans-Planckian problem during inflation has been widely discussed in the literature, but it is still under debate. We reconsider this problem by using the two-point correlation function of the non-minimally coupled scalar fields and constructing the effective potential with the adiabatic (WKB) regularization or approximation. First, we clearly show that the cut-off divergence of the quantum fluctuations does not drastically change during inflation under reasonable assumptions and the corrections can be embedded in standard effective potential. Thus, the UV effects on the primordial density perturbation are well translated into the effective potential. Then, we find out the modified effective potential from the inflationary fluctuations and show how the trans-Planckian or UV corrections change the potential during inflation. We clearly show that the new physics strongly affects the inflation potential during inflation and we obtain an inflationary constraint [Formula: see text], where [Formula: see text] is the interaction coupling at the UV scale [Formula: see text].

scholarly journals Exploring suppressed long-distance correlations as the cause of suppressed large-angle correlations

2019 ◽  
Vol 490 (4) ◽  
pp. 5174-5181
Author(s):  
Craig J Copi ◽  
James Gurian ◽  
Arthur Kosowsky ◽  
Glenn D Starkman ◽  
Hezi Zhang
Keyword(s):  
Correlation Function ◽  
Large Angle ◽  
Real Space ◽  
Harmonic Space ◽  
Microwave Background ◽  
Long Distance ◽  
Cosmic Microwave Background Temperature ◽  
Angular Correlation Function ◽  
Density Perturbations ◽  
Background Temperature

ABSTRACT The absence of large-angle correlations in the map of cosmic microwave background temperature fluctuations is among the well-established anomalies identified in full-sky and cut-sky maps over the past three decades. Suppressed large-angle correlations are rare statistical flukes in standard inflationary cosmological models. One natural explanation could be that the underlying primordial density perturbations lack correlations on large distance scales. To test this idea, we replace Fourier modes by a wavelet basis with compact spatial support. While the angular correlation function of perturbations can readily be suppressed, the observed monopole- and dipole-subtracted correlation function is not generally suppressed. This suggests that suppression of large-angle temperature correlations requires a mechanism that has both real-space and harmonic-space effects.

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