Of pNGB QuiN tessence

We review the pNGB quintessence models, and point out that the reason why the large decay constants fa > ∼ O(1)MP l are really needed is to tame a tachyonic instability present for a wide range of initial vevs. Starting very close to potential maxima does not help because quantum fluctuations during early inflation at a scale HI perturb the quintessence vev, displacing it from the maxima. This issue is quite interesting for pNGB dark energy in light of the recently discussed difficulties with embedding models with fa > MP l in fundamental theory. A possible way around is provided by models with several ultralight pNGBs, which can drive a short burst of very late inflation together even if all of their decay constants obey fa < MP l. Starting with their vev ∼ fa, the pNGBs will hold each other up on the potential for a longer time period. Their effective dynamics is captured by a collective mode, containing admixtures of all of the rolling pNGBs, which behaves as an ultralight field with feff > MP l. We point out that there may be potentially observable large scale disturbances in the sea of dark energy in such models. PACS: 98.80.Cq, 98.80.-k, 98.80.Es, 14.80.Mz [email protected] [email protected] “The time has come,” the Walrus said, “To talk of many things: Of shoes–and ships–and sealing-wax– Of cabbages–and kings– And why the sea is boiling hot– And whether pigs have wings.” (Lewis Carroll) There is mounting evidence that our universe may be accelerating [1, 2]. If gravity obeys Einstein’s General Relativity (GR), this means that the universe is currently dominated by a dark energy component, contributing about ∼ 70% to the critical energy density. To fuel cosmic acceleration dark energy ought to have negative pressure, satisfying roughly w = p/ρ < ∼ −2/3 to fit the observations [3, 4], if it is the only agent responsible for supernovae dimming. Because dark energy would control both the present state of the universe and the course of its future evolution, it is extremely interesting and important to try to elucidate the microscopic nature of dark energy. The first step in this quest is to devise benchmark models which are useful to compare with observations. Dark energy is usually modelled as a cosmological constant or as a timedependent quintessence field [7, 8, 9, 10]. Each must be finely tuned to fit the observations [11]. Even if we leave aside the mystery of tuning the vacuum energy to nearly zero, and assume that the current acceleration is due to a quintessence field, it is hard to build realistic models. Quintessence requires more fine tunings, over and above the scale of dark energy density: a tiny mass mQ smaller than the current Hubble parameter H0 ∼ 10eV as well as sub-gravitational couplings to normal matter, to satisfy the Solar system gravity bounds [12]. This leaves but a few models which appear natural from the point of view of 4D effective field theory, in the sense that their masses and their couplings to the visible matter remain small in spite of the corrections arising in the loop expansion of quantum field theory. In these models quintessence is a pseudo-Nambu-Goldstone boson (pNGB) [13, 14, 15, 16], which in perturbation theory has only naturally weak, derivative couplings to visible matter, protected by a shift symmetry φ → φ + C. Its potential, V = μ [1 − cos(φ/fa)] + . . ., and specifically the mass term mQ ≃ μ/fa are generated by non-perturbative effects breaking the shift symmetry to a discrete subgroup, and hence are radiatively stable [13, 14, 15, 16]. It is often quoted that to serve as quintessence, the pNGB models need a large decay constant fa > MP l [13, 14]. The idea is that the dynamics of quintessence should be akin to chaotic inflation [17, 18, 19, 20] where a dynamical field impersonates dark energy if the potential admits a slow roll regime. However, for models where fa > ∼ O(1)MP l there will generically be higher order corrections to the pNGB potential, coming as higher harmonics in the expansion over the instanton contributions, which typically spoil the flatness of the potential [20, 21]. Although one may invent models where such large values of fa appear and the potential remains flat [20, 22, 23], it has been questioned whether they can come from fundamental theory, e.g string theory [21]. Even though higher order corrections might still allow an e-fold or few of acceleration to unravel, which could be enough to account for observations, this poses some challenges for model building. See [5, 6] for a recent analysis of the observational status of some alternatives.