The Cosmic Microwave Background is our primary source of information for understanding the very early stages of the evolution of the Universe [3,4] . Although highly homogeneous and isotropic, minute fluctuations in temperature from different directions in space point to an early era of accelerated expansion, inflation. In this picture of primordial inflation, the fluctuations are the amplification of quantum field fluctuations, through rapid expansion, particle creation and gravitational collapse into under- and overdense regions in space.

Two distinct phenomena are observed, whose origin may be the evolution of fundamental (scalar) quantum fields. One is the accelerated expansion, inflation, which can arise from a state dominated by “vacuum” or potential energy. This is typically modelled by a scalar field in overdamped rolling in some field potential. The other is the seeding of fluctuations, due to a light quantum (scalar) field present during inflation.

The first scalar field is referred to as the inflaton [1,2], the second, the curvaton [5,6], and in traditional models of inflation, they are one and the same. The appeal of this identification is that it is simple, and the requirements on the field potential to fit with observational signatures of both these phenomena are fairly strict.

But a priori, there is no reason why the inflaton and curvaton could not be distinct scalar degrees of freedom.

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In the CMB, we measure a temperature fluctuation spectrum consistent with an almost scale-independent primordial spectrum. This means that after we back-track observations through 13 billion years of astrophysics, the amplitude of fluctuations on the length scales represented on the sky is almost independent of the scale. We represent it by a power law:

k0 is a reference scale which for WMAP is 0.05/Mpc, for Planck 0.002/Mpc. Scale independence corresponds to n=1. Recent observations by Planck fix n = 0.96+/-0.01.

A second important observable is the spectrum of tensor modes (gravitational waves), and the ratio between the power in tensor and scalar modes, r. Tensor modes have sofar not been observed, and this puts an upper limit on the energy scale of inflation (10^16 GeV), and on the types of models allowed.

These constraints only apply if the inflaton also plays the role of the curvaton.

Traditionally, inflation model-building has relied on classical or effectively free quantum field dynamics. Current and future high precision Cosmological observation open up for exploring truly quantum interacting fields. These are best described in terms of quantum effective actions, which however need to be recast in the context of expanding metrics, and ideally coupled to quantized gravitational degrees of freedom.

References (biased selection):

[1] Starobinsky: Phys. Lett. B91 (1980) 99-102; Phys. Lett. B117 (1982) 175-178.

[2] Linde: Phys. Lett B108 (1982) 389-393; Phys. Lett. B129 (1983) 177-181.

[3] Planck Mission: 1303.5082; 1303.5976.

[4] WMAP Mission: Astrophysical Journal Suppl. 192 (2011) 18.

[5] Sloth, Enqvist: Nucl. Phys. B626 (2002) 395-409.

[6] Lyth, Wands: Phys. Lett. B524 (2002) 5-14.

[7] Markkanen, Tranberg: JCAP 1211 (2012) 027.

[8] Enqvist, Lerner, Taanila, Tranberg: JCAP 1210 (2012) 052.

[9] van Tent, Smit, Tranberg: JCAP 0407 (2004) 003.