Nonlocality of quantum matter corrections and cosmological constant running

Abstract

Semiclassical loop corrections to the gravitational action include various terms with zero, two, and four derivatives of the metric as well as nonlocal form factors for these terms. Contributions to some of these terms could be confused with others on a specific metric background or for a particular gauge fixing. We present a critical analysis of the recent works where the tensor structure and the number of derivatives in the action of gravity were not properly taken into account. Taking these relevant aspects into account, we show that although some contributions owing to the quantum fluctuations of massive or massless scalar as well as fermion and vector fields may be attributed to the “running” of the cosmological constant, in reality they correspond to the fourth derivative terms of the action.

Effective approach to the Antoniadis-Mottola model: quantum decoupling of the higher derivative terms

“…Recently, similar observations were done, e.g., in [26,56,57]). This situation confirms the general expectation that there cannot be physical running of the cosmological constant term, detectable by means of flat-space calculations, as discussed in [2] and more recently in [44]. Let us stress that this does not mean that the cosmological constant running is impossible in general, it just cannot be detected in the flat-space calculations [3].…”

“…In particular, this issue was described in detail, exactly as a reaction to the attribution of the part of the gravitational form factor to the cosmological constant in [45]. It reality, the corresponding terms appear as part of the expansion of the nonlocal form factors of the R µν R µν and R 2 terms and have no direct relation to the cosmological constant term [44].…”

Resummed heat-kernel and form factors for surface contributions: Dirichlet semitransparent boundary conditions

“…In this subsection we will use a more physical scheme, in spirit similar to the discussions in [79,[81][82][83][84][85][86][87], noting that the functions C…”