Degravitation of the Cosmological Constant and Graviton Width

TL;DR

The paper argues that degravitation of the cosmological constant can be realized only if gravity is described by a massive or resonance graviton, effectively filtering long-wavelength sources. It develops a Stückelberg-based framework to show how the extra polarizations render the full gravitational field physical and introduces the r_★ and t_★ scales that govern strong-coupling effects near spatial and temporal phase transitions. Non-linear Abelian and non-Abelian gravity models demonstrate that degravitation can occur via neutralization or filtering, but non-linearities can trigger BD ghost-type instabilities, complicating the construction of fully consistent theories. In cosmological settings, various filter types (massive-gravity-type, DGP-type, and general filters) lead to robust degravitating behavior, with early-time de Sitter-like phases transitioning to flat spaces or decaying curvature, offering a framework for testing large-distance gravity modifications.

Abstract

We study the possibility of decoupling gravity from the vacuum energy. This is effectively equivalent to promoting Newton's constant to a high-pass filter that degravitates sources of characteristic wavelength larger than a certain macroscopic (super) horizon scale L. We study the underlying physics and the consistency of this phenomenon. In particular, the absence of ghosts, already at the linear level, implies that in any such theory the graviton should either have a mass 1/L, or be a resonance of similar width. This has profound physical implications for the degravitation idea.

Figures (4)

• Figure 1: The weak coupling ($r>r_\star$) and strong coupling ($r<r_\star$) solution of (\ref{['red']}) for the Stückelberg-field in the case of a point charge at $r=0$. The change in the behavior at $r_\star$ is analogous to the gravity case.
• Figure 2: The effective potential for the metric function $f(t)$, as given by (\ref{['fpot']}).
• Figure 3: Conventions for the branch cut in the integrand for ${\cal I}$. This function has two poles, at $\omega_+$ and $\omega_-$, which lie in the upper and lower half plane, respectively. The pole in the lower half plane, however, lies on the second Riemann sheet and can be accessed by going under the branch cut.
• Figure 4: Choice of contour for ${\cal I}(t>0)$.