Abstract
We examine the late time behavior of the Bunch-Davies wavefunction for interacting light fields in a de Sitter background. We use perturbative techniques developed in the framework of AdS/CFT, and analytically continue to compute tree and loop level contributions to the Bunch-Davies wavefunction. We consider self-interacting scalars of general mass, but focus especially on the massless and conformally coupled cases. We show that certain contributions grow logarithmically in conformal time both at tree and loop level. We also consider gauge fields and gravitons. The four-dimensional Fefferman-Graham expansion of classical asymptotically de Sitter solutions is used to show that the wavefunction contains no logarithmic growth in the pure graviton sector at tree level. Finally, assuming a holographic relation between the wavefunction and the partition function of a conformal field theory, we interpret the logarithmic growths in the language of conformal field theory.
Highlights
Computing field correlations at a fixed time
There is one particular solution of the Schrodinger equation in a fixed de Sitter background which exhibits a simplifying structure. This solution is the BunchDavies/Hartle-Hawking wavefunction ΨBD [8,9,10,11], and its form strongly resembles that of the partition function in a Euclidean AdS background upon analytic continuation of the de Sitter length and conformal time
Known as the dS/CFT correspondence, is true,3 infrared effects in de Sitter spacetime should be related to quantities in the putative conformal field theory itself
Summary
The main emphasis of this section is to show that our method perturbatively solves the functional Schrodinger equation for a scalar field in the Bunch-Davies state. For simplicity we consider a self-interacting scalar but analogous equations will hold for other types of fields. We specify the potential later, but we envisage the structure of a mass term plus φn interactions. Upon defining the canonical momenta πk = −iδ/δφk conjugate to φk, we can write the Schrodinger equation governing wavefunctions Ψ[φk, η] in a fixed dSd+1 background: k∈Rd. The variable φk is the momentum mode φk evaluated at the time η where Ψ is evaluated. The potential V (φk) is the Fourier transform of the original V (φ(η, x)); it has the structure of a convolution in k-space
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
