Spectrum from an Initially Anisotropic Universe
We revisit the issue on signatures of pre-inflationary background anisotropy by considering the quantization of a massless and minimally coupled scalar field in an axially symmetric Kasner background, mimicking cosmological perturbations. We show that the
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Abstract We revisit the issue on signatures of pre-inflationary background anisotropy by considering the quantization of a massless and minimally coupled scalar field in an axially symmetric Kasner background, mimicking cosmological perturbations. We show that the power spectrum of the scalar field fluctuation has a negligible difference from that in the standard inflation in the non-planar directions, but it has a sharp peak around the symmetry plane. This note is based on our recent paper (Kim and Minamitsuji, JCAP 1103:038, 2011).
1 Introduction Inflation has become one of the paradigms of modern cosmology. First of all, inflation elegantly solves many problems which are present in the standard Big-Bang model such as the horizon and flatness problems. Secondly, inflation accounts for the origin of the large scale structure of the universe in terms of the quantum fluctuations originated from the adiabatic vacuum structure in the early universe. Remarkably, the nature of the primordial fluctuations is understood in terms of symmetries of the de Sitter spacetime. In general, we need n-point correlation functions to characterize the statistical nature of the primordial fluctuations. However, these symmetries lead to the power spectrum with a scale invariant form. These predictions from symmetries are robust and universal in inflationary scenarios. In fact, the above predictions have been confirmed by H.-C. Kim School of Liberal Arts and Sciences, Korea National University of Transportation, Chungju 380-702, Korea e-mail: [email protected] M. Minamitsuji () Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan e-mail: [email protected] A. García-Parrado et al. (eds.), Progress in Mathematical Relativity, Gravitation and Cosmology, Springer Proceedings in Mathematics & Statistics 60, DOI 10.1007/978-3-642-40157-2__74, © Springer-Verlag Berlin Heidelberg 2014
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the measurements of the cosmic microwave background (CMB) [2, 3]. As the observational precision increases, we have to go beyond the power spectrum to look at the fine structures of the primordial fluctuations. Since in the realistic inflationary universe the symmetries of the de Sitter spacetime do not hold exactly, violation of them provides a measurable effect. A measurable effect may be induced by rotational symmetry breaking in the early universe [4]. Such cosmological models have been considered in e.g., [5, 6]. From the observational point of view, a lot of anomalies indicating the statistical anisotropy have been reported [7–9]. We work on the observational signatures from the preinflationary anisotropy [1]. We start from the discussion on the evolution of anisotropic universe in the Einstein gravity minimally coupled to a massive scalar field which plays the role of the inflation. Under the slow-roll approximations, the background metric can be well approximated by the Kasner de Sitter spacetime with a positive cosmological constant, .D 3Hi 2 /. Among the Kasner de Sitter solu
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