Primeval Corrections to the CMB Anisotropies

We show that deviations of the quantum state of the inflaton from the thermal vacuum of inflation may leave an imprint in the CMB anisotropies. The quantum dynamics of the inflaton in such a state produces corrections to the inflationary fluctuations, which may be observable. Because these effects originate from IR physics below the Planck scale, they will dominate over any trans-Planckian imprints in any theory which obeys decoupling. Inflation sweeps away these initial deviations and forces its quantum state closer to the thermal vacuum. We view this as the quantum version of the cosmic no-hair theorem. Such imprints in the CMB may be a useful, independent test of the duration of inflation, or of significant features in the inflaton potential about 60 e-folds before inflation ended, instead of an unlikely discovery of the signatures of quantum gravity. The absence of any such substructure would suggest that inflation lasted uninterrupted much longer than O(100) e-folds. [email protected] [email protected] Generic models of inflation produce a lot of accelerated expansion. They far surpass the minimum needed to solve the horizon and flatness problems, of the order of N ' 60. For example in the case of chaotic inflation driven by a power-law potential λφ/n, one finds that typically N > ∼ 10 O(100). This yields perhaps the most robust of all inflationary predictions, that the universe should be spatially flat, with Ωmatter+ΩDE = 1 [1]. More generally, this is usually taken to mean that inflation acts as a powerful amnesia tonic, efficiently relieving the universe of the memory of its initial state. Having fewer e-folds, or producing significant changes in the inflaton sector mid-way through inflation, requires fine-tunings of the initial conditions and/or the inflaton sector beyond those which are deemed acceptable by the current lore [2]. A more optimistic stance could be that any signs of short inflation or new dynamics during it is an indication of some as yet unknown new physics, which the inflaton is sensitive to. Although such phenomena may appear like fine-tuning by the current lore, one could hope to identify the underlying physics with better understanding of inflation. Hence either short inflation or changes of the inflaton dynamics ∼ 60 e-folds before the exit at this point cannot be taken as a robust prediction but as an indication of something special about inflationary dynamics and/or the initial conditions. On the other hand, we can take a bottom-up approach to conceptual cosmology, and simply ask if we can measure for how long the final stage of inflation went on uninterrupted. For example, the current cosmological observations are indirectly sensitive to short inflation, because it could leave nonvanishing spatial curvature of the universe. At present the observations limit the spatial curvature to be at most a few percent of the total Ω, and the bounds are a little bit weaker if the curvature is positive [3, 4, 5]. The bounds will be improved some in the future [6]. Thus it would be interesting to consider alternative probes of the length of inflation, or of significant features in the inflaton dynamics. In this note we show that substructure in the CMB anisotropies could provide us with another probe of inflation some ∼ 60 e-folds before the end. If inflation was interrupted ∼ 60 e-folds before the exit by environmental conditions, induced either by a non-inflationary stage, or by a change of slow roll parameters, the quantum state of the inflaton during the generation of the inflationary fluctuations was not the usual thermal vacuum, but included some deviations from it. These effects may resemble classical inhomogeneities, in that they can be viewed as lumps of energy on top of the ground state, and can be represented as coherent state excitations of the thermal vacuum. They may also be intrinsically quantum, encoding initial phase correlations arranged by quantum effects before inflation, or by the dynamics which may have intervened at the onset of the last 60 e-folds. The latter effects can be represented as squeezed states, which have been prepared by primordial quantum effects preceding inflation. We will demonstrate explicitly how such a squeezed state arises from the kinks in the inflaton slow roll parameters. During the onset of the final stage of inflation the frequencies of the inflaton eigenmodes change in time slightly non-adiabatically. This induces a Bogoliubov transformation between the modes before and after the transition, and therefore between their corresponding annihilation and creation operators. We will take the initial inflaton state to be Possibly excepting anthropic arguments, about which we are agnostic at the moment. We thank J.D. Bjorken for a very useful discussion of this issue.