Abstract
Calculating the quantum evolution of a de Sitter universe on superhorizon scales is notoriously difficult. To address this challenge, we introduce the Soft de Sitter Effective Theory (SdSET). This framework holds for superhorizon modes whose comoving momentum is far below the UV scale, which is set by the inverse comoving horizon. The SdSET is formulated using the same approach that yields the Heavy Quark Effective Theory. The degrees of freedom that capture the long wavelength dynamics are identified with the growing and decaying solutions to the equations of motion. The operator expansion is organized using a power counting scheme, and loops can be regulated while respecting the low energy symmetries. For massive quantum fields in a fixed de Sitter background, power counting implies that all interactions beyond the horizon are irrelevant. Alternatively, if the fields are very light, the leading interactions are at most marginal, and resumming the associated logarithms using (dynamical) renormalization group techniques yields the evolution equation for canonical stochastic inflation. The SdSET is also applicable to models where gravity is dynamical, including inflation. In this case, diffeomorphism invariance ensures that all interactions are irrelevant, trivially implying the all-orders conservation of adiabatic density fluctuations and gravitational waves. We briefly touch on the application to slow-roll eternal inflation by identifying novel relevant operators. This work serves to demystify many aspects of perturbation theory outside the horizon, and has a variety of applications to problems of cosmological interest.
Highlights
Beyond issues of theoretical curiosity, there is a pragmatic application of de Sitter (dS) quantum field theory that is critical to the success of the inflation
Unlike conventional Effective Field Theory (EFT), where the power counting λ 1 is typically determined by a ratio of physical scales, the Soft de Sitter Effective Theory (SdSET) is formulated as an expansion in terms of the physical wavenumber in Hubble units, λ ∼ k /[a(t)H]
We will encounter situations where potentially large logarithms appear, which will we show how to resum using the techniques of the Dynamical Renormalization Group (DRG)
Summary
In order to setup up an EFT, we must first specify the low energy degrees of freedom and the symmetries that emerge in the IR. The fact that these soft and hard fields only have support for a limited range of momenta might naively seem to introduce a hard cutoff, in the Wilsonian EFT sense This is not the case because we will formulate the theory such that divergent integrals will be regulated using dim reg and variants thereof. The non-trivial fact that scaleless integrals vanish in dim reg allows us to treat both the ΦH and φS fields as being defined for the full range of momenta (and times), since the regions of loop momentum that have been integrated out will make scaleless contributions to the EFT.5 This is how continuum EFT allows one to decouple heavy physics without using an explicit cutoff, which in turn allows integrals to be regulated such that the low energy symmetries are preserved. While this is perhaps less intuitive than a Wilsonian approach that relies on a hard cutoff, there are tremendous computational and conceptual benefits to the continuum EFT formulation, as we will see in what follows
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
