The large-scale angular correlations in CMB temperature maps

Abstract

Observations show that the Cosmic Microwave Background (CMB) contains tiny variations at the 10 −5 level around its black-body equilibrium temperature. The detection of these temperature fluctuations provides to modern Cosmology evidence for the existence of primordial density perturbations that seeded all the structures presently observed. The vast majority of the cosmological information is contained in the 2-point temperature function, which measures the angular correlation of these temperature fluctuations distributed on the celestial sphere. Here we study such angular correlations using a recently introduced statistic-geometrical method. Moreover, we use Monte Carlo simulated CMB temperature maps to show the equivalence of this method with the 2-point temperature function (best known as the 2-Point Angular Correlation Function). We also investigate here the robustness of this new method under possible divisions of the original catalog-data in sub-catalogs. Finally, we show some applications of this new method to simple cases.

On the cosmic microwave background large-scale angular correlations

“…1, where we plotted the difference of such expected function minus each one of the MPASH-minus-EPASH functions from the six CMB maps. What is revealed in these difference plots is that the ACS lacking in CMB data at large-angular scales correspond to a quadrupolelike angular correlation signature (see, e.g., Bernui 2005). To assess this, we plotted the angular correlation function of a quadrupole (corrected for the Kp2 mask) with moment C 2 670 µK 2 .…”

“…Finally, one plots the MPASH-minus-EPASH function. It can be shown (see Bernui 2005) that the MPASH-minus-EPASH function is independent of the number of sub-maps K − ≥ 1 and K + ≥ 1 in which the original CMB map is divided.…”

Spatial correlation functions for the collective degrees of freedom of many trapped ions

“…m is an entry of B, which defines the spatial mode functions of the normal mode. 1 We can define a unitless version of this local displacement oeprator, as well:…”

“…In a cosmological setting, spatial correlations in the temperature distribution of the cosmic microwave background provide direct access to the fluctuations of a primordial quantum field during inflation. Details of these spatial correlations provide direct and detailed tests of inflationary cosmological models [1]. For example, Grishchuk [2] has suggested a model in which anisotropies reflect the underlying statistics of squeezed vacuum states.…”

“…The scheme has two components: (1) external lasers weakly couple the motion of two distinct ions to their local displacement from equilibrium; subsequently, (2) external readout lasers are used to probe the electronic state of all the ions. In the second stage, some ions will "light up" (made more precise below), while others remain dark.…”