Strongly coupled quintessence
Guido D'Amico, Nemanja Kaloper, Albion Lawrence
2019
Physical Review D
We present a family of consistent quantum field theories of monodromy quintessence in strong coupling, which can serve as benchmarks in modeling dark energy different from the cosmological constant. These theories have discrete gauge symmetries that can protect them from quantum field theory and quantum gravity corrections, both perturbative and nonperturbative. The strong coupling effects, at scales ≳mm −1 , flatten the potential and activate operators with higher powers of derivatives. The
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... dicted equation of state is close to, but not exactly equal to, −1. Thus testing the model may be within reach of the (near) future programs to explore the nature of dark energy. Roughly three quarters of the invisible world is dark energy, whose dynamics is not understood. It may be a cosmological constant, but explaining how it would be as small as needed is a well-known challenge: one needs some reason to ignore or almost completely cancel the large quantum vacuum energy contributions [1-3]. The alternatives that treat dark energy as a dynamical field, also known as quintessence, are even more challenging: one needs both the magnitude and the slope of the potential to be exquisitely small compared to the Planck scale or any fundamental scales of the standard model. That being said, quintessence is a simple concept, and future observations of the expansion history of the Universe will probe a large and interesting range of parameters. It is important to better understand whether a microscopic theory of quintessence can be made consistent and, to any degree possible, natural (in the sense of Wilson and 't Hooft). In this letter we discuss these issues and provide a class of models that are natural and appear to consistently couple to quantum gravity. Regardless of whether quintessence is realized in nature, a discussion of these issues and their resolution turns out to be interesting in its own right. For a canonically normalized quintessence field with scalar potential VðϕÞ, such that Vð0Þ ¼ 0, we must satisfy two constraints. First, the vacuum energy at the present epoch must be consistent with the present Hubble constant, that is, V ∼ ð2 × 10 −30 m pl Þ 4 , where m pl is the reduced Planck mass. Secondly, the equation of state parameter w, defined by p ¼ wρ, is related to the slope of the potential by Observations indicate 1 that −1 ≤ w ≤ −0.95 [5], or 0 ≤ ϵ ≤ 0.075. During the observable epoch, the quintessence field should traverse a distance δϕ ∼ _ ϕH −1 0 ∼ ffiffi ffi ϵ p m pl , where we have used the slow-roll equations. Writing down models that satisfy these constraints requires some care when we take quantum gravity into account. The simplest potentials, including ones that are technically natural from a QFT point of view, require that ϕ is at a distance Δϕ > m Pl from the minimum [6] [7] [8] [9] [10] [11] [12] . When coupled to quantum gravity, fairly basic arguments render such field ranges inaccessible to a single, simple effective field theory (EFT). This is a slightly different problem than the one large-field inflation faces [13]: in single field models the inflaton must traverse super-Planckian distances during inflation, and physics over those field ranges would be imprinted in the observable sky. In contrast, as we see, the quintessence scalar need only traverse sub-to near-Planckian distances during the observable epoch. Whether it really needs to change by a Planckian scale is a question of model-building and eschatology.
doi:10.1103/physrevd.100.103504
fatcat:6lyvmvextfdxnfysb4iffwgq7q