Letters to the Editor

A weakly random Universe?

¹ Yerevan Physics Institute and Yerevan State University, Yerevan, Armenia
² School of Mathematical Sciences, Monash University, Clayton, Australia
³ Dipartimento di Fisica “E.R. Caianiello”, Universita’ degli Studi di Salerno, Fisciano, Italy
⁴ Institute of Theoretical Physics, University of Zurich, Zurich, Switzerland
⁵ Salento University and INFN, Sezione di Lecce, Lecce, Italy

Received: 27 October 2010
Accepted: 16 November 2010

Abstract

Cosmic microwave background (CMB) radiation is characterized by well-established scales, the 2.7 K temperature of the Planckian spectrum and the 10^-5 amplitude of the temperature anisotropy. These features were instrumental in indicating the hot and equilibrium phases of the early history of the Universe and its large-scale isotropy, respectively. We now reveal one more intrinsic scale in CMB properties. We introduce a method developed originally by Kolmogorov, which quantifies a degree of randomness (chaos) in a set of numbers, such as measurements of the CMB temperature in a given region. Considering CMB as a composition of random and regular signals, we solve the inverse problem of recovering of their mutual fractions from the temperature sky maps. Deriving the empirical Kolmogorov’s function in the Wilkinson Microwave Anisotropy Probe’s maps, we obtain the fraction of the random signal to be about 20 per cent; i.e., the cosmological sky is a weakly random one. The paper is dedicated to the memory of Vladimir Arnold (1937–2010).