The cosmological vacuum ambiguity, effective actions, and transplanckian effects in inflation

TL;DR

The paper reframes the cosmological vacuum ambiguity as a boundary action problem within a Wilsonian effective field theory, showing that RG flow generically induces leading irrelevant boundary operators that encode transplanckian physics in inflation. By computing the resulting corrections to the inflationary power spectrum, it demonstrates that the dominant high-energy effects enter at order $H/M$ and are controlled by a finite set of boundary couplings, with the Bunch-Davies vacuum emerging as a natural, but not unique, boundary choice. The framework preserves decoupling, makes the $H/M$ dependence explicit, and provides a route to potentially observable signatures in the CMB. It also clarifies the relationship between BD, adiabatic vacua, and α-states, arguing that while α-states can be accommodated as particular boundary-content, they do not threaten the EFT’s predictivity. Overall, the boundary EFT approach offers a coherent, testable connection between Planck-scale physics and cosmological observables.

Abstract

We provide a prescription for parametrizing the vacuum choice ambiguity in cosmological settings. We introduce an arbitrary boundary action representing the initial conditions. A Lagrangian description is moreover the natural setting to study decoupling of high-energy physics. RG flow affects the boundary interactions. As a consequence the boundary conditions are sensitive to high-energy physics through irrelevant terms in the boundary action. Using scalar field theory as an example, we derive the leading dimension four irrelevant boundary operators. We discuss how the known vacuum choices, e.g. the Bunch-Davies vacuum, appear in the Lagrangian description and square with decoupling. For all choices of boundary conditions encoded by relevant boundary operators, of which the known ones are a subset, backreaction is under control. All, moreover, will generically feel the influence of high-energy physics through irrelevant (dimension four) boundary corrections. Having established a coherent effective field theory framework including the vacuum choice ambiguity, we derive an explicit expression for the power spectrum of inflationary density perturbations including the leading high energy corrections. In accordance with the dimensionality of the leading irrelevant operators, the effect of high energy physics is linearly proportional to the Hubble radius H and the scale of new physics l = 1/M. Effects of such strength are potentially observable in future measurements of the cosmic microwave background.

Figures (1)

• Figure 1: The left panel shows the change in the (amplitude of the) power spectrum due to the presence of the leading order irrelevant operator $\frac{\beta}{M} (\partial_i\phi)^2$ as a function of the physical momentum in units of the size of the horizon at the 'earliest time'. (Only for one specific choice is the full oscillatory Bessel function behaviour plotted.) This graph should be read as follows. Given the scale of new physics $M$ and the Hubble constant $H$ during inflation (or more precisely at the time when the highest mode $k_{max}$ of interest exits the horizon) the earliest time up to which we can trust the effective action is when $y_{0,max}\equiv k_{max}/a_{0,min}H =M/H$ (see subsection). Anything to the right of $y_{0,max}$ should be discarded as untrustworty. Precisely at $y_{0,max}$ the change in the power spectrum is linearly dependent on the value of $\beta$. The values of $M/H$ and $\beta$ corresponding to the various curves can thus be read of from the intersection of the plumblines to the upper and right axis. The right panel shows an exclusion plot for $\beta$ as a function of $H/M$. The $45^o$ lines (black) correspond to the backreaction bounds (\ref{['eq:260a']})- (\ref{['eq:12c']}) (continuous for zeroth order in slow roll, dashed for first order in slow roll, dotted for second order in slow roll). The $60^o$ lines (green) correspond to the order of magnitude estimate made in Porrati:2004gz. The upper horizontal line is an order of magnitude estimation of the current error to which we have a nearly scale invariant spectrum Bennett:2003bz. The lower horizontal line is an order of magnitude estimate of the cosmic variance limitations of resolution. Finally the vertical line denotes a maximal value of $H/M$ consistent with observation. $H/M_{Planck}$ is extracted from the observed amplitude of the power spectrum and we have set $M \equiv 10^{16}$ GeV. This leaves the shaded region as the window of opportunity to observe transplanckian physics in the CMB.