Abstract
We study the dual 3d Euclidean RG flow of single-field slow-roll Inflation using the postulates of the dS/CFT correspondence. For that purpose we solve for the inflationary fluctuation at all times using a matching procedure between two approximate solutions which are separately valid at different regions of the space of parameters but together cover all of it. The two modes of the full solution mix such that each of the modes at late times is a superposition of the modes in the quasi-de Sitter region. We find that the dual theory admits two phases of explicit and spontaneous breaking of conformal symmetry. We also find that the mixing effect between the two modes in the bulk implies that slow-roll inflation does not guarantee, but rather generically generates, a nearly scale invariant power spectrum, except in fine-tuned situations. We suggest that the mixing effect can have a unique signature on other cosmological observables such as the bispectrum.
Highlights
We find that the mixing effect between the two modes in the bulk implies that slowroll inflation does not guarantee, but rather generically generates, a nearly scale invariant power spectrum, except in fine-tuned situations
We study the dual 3d Euclidean renormalization group (RG) flow of single-field slow-roll Inflation using the postulates of the dS/CFT correspondence
We find that the dual theory admits two phases of explicit and spontaneous breaking of conformal symmetry
Summary
It is possible to study the asymptotic forms of the solution near the fixed points. Let us start by looking exactly at a fixed point of the potential, where its derivative is zero. At this point the potential takes a constant value. The value of the potential at each of the fixed points is different and the potential interpolates between two de Sitter spaces with different Hubble constants. Near a fixed point the potential can be expanded as follows d(d − 1) H2 + 2 Plugging this into (2.4), and defining δφ ≡ φ − φ0, we find the following equation for the scalar δφ + dHδφ + m2δφ = 0. Note that the value of m2 is different in each fixed point (and, in particular, is negative for a maximum of the potential)
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