Naturalness in cosmological initial conditions

We propose a novel approach to the problem of constraining cosmological initial conditions. Within the framework of effective field theory, we classify initial conditions in terms of boundary terms added to the effective action describing the cosmological evolution below Planckian energies. These boundary terms can be thought of as spacelike branes which may support extra instantaneous degrees of freedom and extra operators. Interactions and renormalization of these boundary terms allow us to apply to the boundary terms the field-theoretical requirement of naturalness, i.e. stability under radiative corrections. We apply this requirement to slow-roll inflation with nonadiabatic initial conditions, and to cyclic cosmology. This allows us to define in a precise sense when some of these models are fine-tuned. We also describe how to parametrize in a model-independent way non-Gaussian initial conditions; we show that in some cases they are both potentially observable and pass our naturalness requirement.

Figure 1

A schematic view of the EFT description of a cyclic cosmology. It plots the scale factor vs time. The Planckian era around the bounce is replaced by an effective spacelike brane ($S$-brane).

Figure 2

On the left, a schematic view of our brane, its position is represented by the vertical lines. By changing the operators on the brane and/or its position, we can change the initial conditions for the flow, hence the flow itself. On the left, the holographic brane of Ref. 19. Its boundary operators are constrained by requiring that the flow remains the same when its position is changed.

Figure 3

Self-energy correction to the ${\zeta }^2$ boundary mass terms. $\zeta$’s are denoted by solid lines and $\chi$’s by broken lines.

Figure 4

Effective boundary two-point vertex induced at one loop by the field redefinition $\zeta \to \zeta +f(\zeta )$. The quartic interaction is proportional to $\gamma f{\partial }^{2}f$.

Figure 5

The one-loop, UV finite diagram giving rise to the effective action in Eq. (88). The solid line denotes $\phi$, whereas dashed lines denote $\varphi$.

Figure 6

The one-loop diagram giving rise to the effective action in Eq. (91). Dashed lines represent $\psi$, whereas dashed-dotted lines represent $\phi$.

Figure 7

The one-loop diagram giving rise to the effective action in Eq. (91). Dashed lines represent $\psi$ and the solid line represents $\zeta$.

Figure 8

A mixed bulk-boundary interaction may generate a boundary mass term. The black square denotes the bulk interaction $\mu v\partial v\partial v$, the black circle denotes the boundary interaction $\lambda v^3$.