Towards Early Dark Energy in String Theory

Early Dark Energy (EDE) is a prominent model to resolve the Hubble tension, which employs a dynamical axion with a periodic potential. In this work, we take first steps towards the embedding of this model into stable compactifications of string theory. First, we provide a pedagogical review of the EDE scenario and its main challenges. Second, we construct a simple supergravity toy model using only minimal ingredients. Already at this level, we can understand the origin of the harmonics of the EDE scalar potential in terms of a delicate balance of the leading terms from separate non-perturbative effects. Third and final, we embed the model into a KKLT-type compactification, with the EDE scalar field realized by a two-form axion. We find that a successful embedding, with all moduli stabilized, requires restrictive assumptions both on the Pfaffians and on the exponents of the non-perturbative terms responsible for the EDE dynamics. We point out that such non-generic conditions reflect well known challenges of the EDE model and further investigation might guide us towards a conclusive resolution.