Early Dark Energy in Type IIB String Theory

Published for SISSA by Springer Received: March 15, 2023 Accepted: May 20, 2023 Published: June 12, 2023 Early Dark Energy in Type IIB String Theory a Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna, Italy b INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy c Department of Physics, University of Winnipeg, Winnipeg MB, R3B 2E9, Canada d Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805, München, Germany E-mail: , , , , , Abstract: Early Dark Energy (EDE) is a promising model to resolve the Hubble Tension, that, informed by Cosmic Microwave Background data, features a generalization of the potential energy usually associated with axion-like particles. We develop realizations of EDE in type IIB string theory with the EDE field identified as either a C4 or C2 axion and with full closed string moduli stabilization within the framework of either KKLT or the Large Volume Scenario. We explain how to achieve a natural hierarchy between the EDE energy scale and that of the other fields within a controlled effective field theory. We argue that the data-driven EDE energy scale and decay constant can be achieved without any tuning of the microscopic parameters for EDE fields that violate the weak gravity conjecture, while for states that respect the conjecture it is necessary to introduce a fine-tuning. This singles out as the most promising EDE candidates, amongst several working models, the C2 axions in LVS with 3 non-perturbative corrections to the superpotential generated by gaugino condensation on D7-branes with non-zero world-volume fluxes. Keywords: Early Universe Particle Physics, String and Brane Phenomenology, Superstring Vacua ArXiv ePrint: 2303.03414 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP06(2023)052 JHEP06(2023)052 Michele Cicoli,a,b Matteo Licheri,a,b Ratul Mahanta,b Evan McDonough,c Francisco G. Pedroa,b and Marco Scalisid Contents 1 2 Early Dark Energy and the Hubble Tension 5 3 Moduli stabilization 3.1 KKLT 3.2 Large Volume Scenario 7 8 9 4 Odd axions and moduli stabilization 4.1 Axions in string theory 4.2 Odd axions in effective field theory 4.3 Odd axions and non-perturbative effects 4.3.1 ED3-instantons 4.3.2 Gaugino condensation on D7-branes 4.3.3 ED1-instantons and gaugino condensation on D5-branes 4.3.4 ED(-1)-instantons and gaugino condensation on D3-branes 4.4 Odd axions and D-terms 4.4.1 Fayet-Iliopoulos terms 4.4.2 B2 axion stabilization 11 11 12 14 14 16 17 18 19 19 20 5 EDE in KKLT 23 6 EDE in the Large Volume Scenario 6.1 EDE from C4 axions 6.2 EDE from C2 axions 6.2.1 Gaugino condensation on D7-branes 6.2.2 Gaugino condensation on D5-branes 26 26 30 30 34 7 Conclusions 36 A LVS Moduli Stabilization with Anti-brane Uplift 39 1 Introduction The Hubble constant H0 , as inferred from Planck 2018 Cosmic Microwave Background (CMB) data [1], is in 5σ disagreement with the SH0ES cosmic distance ladder measurement [2]. This ‘Hubble tension’ has spurred on an intense experimental effort and the development of new ways to measure H0 (see [3, 4] for reviews). The tension persists between varied early and late universe probes at the level of 4-6σ [4]. A commensurate effort has been made –1– JHEP06(2023)052 1 Introduction 1. Controlled de Sitter moduli stabilization: all string moduli should be stabilized in a dS vacuum where the effective field theory is under control. In particular the compactification volume should be large enough to trust the α0 expansion, the string coupling should be small enough to remain in the perturbative regime, and the instanton expansion should be well behaved. One of the main obstacles against achieving moduli stabilization with full control is the fact that the decay constant f of the EDE field has to be relatively close to the Planck scale. This can intuitively be seen as follows. Explicit string computations [37–39], as well as the weak gravity 1 See however [31] for cosmological applications. –2– JHEP06(2023)052 on the theory side, aimed at developing an alternative cosmological model to bring these measurements in agreement. Amongst the theory approaches, the modification of early universe physics holds particular promise (see [5]) by satisfying first and foremost the tight constraints that the CMB places on any new cosmological physics. A detailed review is provided in section 2 (see also the review section of [6]). Early Dark Energy (EDE) [7, 8] is an example of new physics in the early universe that resolves the Hubble tension by bringing the CMB inference into agreement with SH0ES, while leaving the former nearly indistinguishable from ΛCDM. The model proposed in [7] utilizes a scalar field with potential energy V (ϕ) = V0 [1 − cos (ϕ/f )]3 , featuring an exponent that distinguishes it from the conventional potential of an axion-like particle. This potential is motivated by data: it provides a significantly better fit to the data than a monomial V ∼ ϕ2n [9] or a cosine with a different exponent [7]. The vast majority of work on EDE (see e.g. [6, 10, 11]) has therefore focused on this form of the potential, though alternative EDE-like models abound [12–26]. This work has elucidated challenges to the model from data, in particular, tension with large scale structure (see e.g. [10, 11]), that has motivated extensions of the EDE model, see [24, 27–29], to include an additional ultralight axion dark matter component [28, 29]. Relatively little input has come from the formal theory community, with exception of ref. [6] and [30]. In this work, we seek to identify and address the challenges to building a phenomenologically viable EDE model within the context of string theory. The first steps have been already provided in [6], in the context of KKLT compactifications, with the EDE field identified as a C2 axion. Its potential is derived from non-perturbative corrections to the superpotential W generated by gaugino condensation on D5-branes. Besides the need to tune the prefactors of these non-perturbative effects to reproduce the correct EDE scale, it remains unclear if gaugino condensation on D5-branes can actually yield a non-zero contribution to the superpotential for cycles in the geometric regime 1 [32, 33]. Here we go beyond what achieved in [6] and perform a deeper analysis of EDE model building in type IIB string theory which is one of the most promising corners of string theory for moduli stabilization. We propose string embeddings of EDE in the moduli stabilization frameworks of KKLT [34] and the Large Volume Scenario (LVS) [35, 36]. Moreover, we identify different choices of axion as the EDE candidate. In particular, we try to realize the EDE potential V = V0 [1 − cos(ϕ/f )]3 with the phenomenologically relevant parameters V0 ∼ eV4 and f ' 0.2 MP , while satisfying the following conditions: conjecture applied to axions [40–43], give f S ' λMP (...truncated)