The inheritance of energy conditions: Revisiting no-go theorems in string compactifications

Abstract

One of the fundamental challenges in string theory is to derive realistic four-dimensional cosmological backgrounds from it and it has been recently shown that there are strict consistency conditions which must be satisfied in string compactifications, thus constraining its possible lowenergy backgrounds. In this work, we focus on energy conditions as covariant and background independent consistency requirements in order to classify possible backgrounds coming from low-energy string theory in two steps. Firstly, we show how supergravity actions typically obey many relevant energy conditions, under some reasonable assumptions. Remarkably, we find that the energy conditions are satisfied even in the presence of objects which individually violate them due to the tadpole cancellation condition. Thereafter, we list a set of conditions for a higher-dimensional energy condition to imply the corresponding lower-dimensional one, thereby categorizing the allowed low-energy solutions. As for any no-go theorem, our aim is to highlight the assumptions which must be circumvented for deriving four-dimensional spacetimes that necessarily violate these energy conditions, with emphasis on cosmological backgrounds.

Stringy running vacuum model and current tensions in cosmology

“…Having said that, though, we also remark that our string inspired cosmology at late epochs, which has been the focus of our work in this article, has its origin in supergravity theories which describe low-energy effective string theories at early times. In [137], it has been argued that higher-dimensional string-compatible supergravity actions, corresponding to the standard content of the massless string spectrum, as in our case in this article, do satisfy all the energy conditions, provided quantum corrections are ignored. Such higher-dimensional energy conditions might induce the preservation of the four-dimensional energy conditions, so we might expect this to characterize our models.…”

A bouncing cosmology from VECROs

“…A key open issue is a clear derivation of VECROs in cosmology from superstring theory. At a superficial level, our proposed gas of VECROs is in tension with energy conditions for an effective four space-time dimensional theory derived from string theory [48,49], where it is shown that the Null Energy Condition (NEC) must be obeyed. While our total energy density obeys the NEC, the gas of VECROs does not since it has negative energy density.…”

“…While our total energy density obeys the NEC, the gas of VECROs does not since it has negative energy density. The assumptions made in [48,49] on the continuity properties of the scale factor are obeyed in our model, our VECROs are quantum objects, and hence the analysis of [48,49] does not directly apply. Nevertheless, this issue requires further study.…”

Universal accelerating cosmologies from 10d supergravity

“…Such transient acceleration is in fact generic in flux compactifications, see [11] for a review, although de Sitter space is still ruled out by the SEC, if the time-independence of the 4d Newton's constant is obeyed in a conventional way [12]. If instead the time-independence of the 4d Newton's constant is obeyed in an averaged way, even de Sitter space is not ruled out by the SEC, although the so-called dominant energy condition does rule out non-singular de Sitter compactifications [13] (see also [14,15] for a recent discussion on energy conditions).…”