Precision Calculation of Inflation Correlators at One Loop

Abstract

We initiate a systematic study of precision calculation of the inflation correlators at the 1-loop level, starting in this paper with bosonic 1-loop bispectrum with chemical-potential enhancement. Such 1-loop processes could lead to important cosmological collider observables but are notoriously difficult to compute due to the lack of symmetries. We attack the problem from a direct numerical approach based on the real-time Schwinger-Keldysh formalism and show full numerical results for arbitrary kinematics containing both the oscillatory "signals" and the "backgrounds". Our results show that, while the non-oscillatory part can be one to two orders of magnitude larger, the oscillatory signal can be separated out by applying appropriate high-pass filters. We have also compared the result with analytic estimates typically adopted in the literature. While the amplitude is comparable, there is a non-negligible deviation in the frequency of the oscillatory part away from the extreme squeezed limit.

Cutting Rule for Cosmological Collider Signals: A Bulk Evolution Perspective

“…The upper panels show the full 4-point function while the lower panels show the CC signals alone. In order to extract oscillatory signals from the total numerical result, we have evoked high-pass filters to eliminate the low-frequency EFT background [43]. As we can see from the plots, the numerical results (red dashed lines) match our analytical cut results (blue line) very well, especially for the signal part.…”

Soft limits of the wavefunction in exceptional scalar theories

“…The second type of boundary term does not contain normal derivatives, and we will refer to such terms as contact terms. 55 We will argue that there is a natural way to fix nonlocal boundary terms, and that contact terms may be precluded by derivative counting.…”

“…The general recursion formula is given in equation (4.14), and is obtained by deforming the kinematics that the wavefunction depends on into the complex plane. The recursion relations as a sort of cosmological collider [23,34,35,[46][47][48][49][50][51][52][53][54][55][56][57]. 2 Scattering amplitudes can also satisfy soft theorems when there are cubic vertices present that are compatible with the nonlinearly realized symmetries, for example in the conformal dilaton [61], or in non-relativistic cases [62] (see also [63] for another relativistic example).…”

On Holography in General Background and the Boundary Effective Action from AdS to dS

“…The one-loop boundary effective action, through the heat kernel coefficients, contains much more information on the (bulk and boundary) divergences and on the long-distance EFT. Boundary correlators in dS : There has been a lot of activity about computing cosmological correlators and understanding their structure in terms of conformal symmetry and singularities [69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85]. 2 A bootstrap program analogous to flat space amplitudes techniques has also been developed, often at the level of the dS wavefunction coefficients, with e.g.…”