Abstract
The string/$M$ theory Axiverse -- a plethora of very light Axion Like Particles (ALPs) with a vast range of masses -- is arguably a generic prediction of string/$M$ theory. String/$M$ theory also tends to predict that the early Universe is dominated by moduli fields. When the heavy moduli decay, before nucleosynthesis, they produce dark radiation in the form of relativistic ALPs. Generically one estimates that the number of relativistic species grows with the number of axions in the Axiverse, in contradiction to the observations that $N_{eff} \leq 4$. We explain this problem in detail and suggest some possible solutions to it. The simplest solution requires that the lightest modulus decays only into its own axion superpartner plus Standard Model particles and this severely constrains the moduli Kahler potential and mass matrix.
Highlights
This number is a topological invariant of the extra dimensions, so if the extra dimensions have a suitably rich topology there will be a large number of axions present in the spectrum
The topology is relatively simple and, equivalently, the axions you would expect based on the couplings argument have obtained a large mass through a direct breaking of the axion shift symmetries by the background geometry
Since the corresponding contribution to the energy density will dilute like matter, even if the Universe was radiation dominated prior to this point, a modulus field will quickly dominate the Universe since its energy density is comparable to radiation at the onset of the oscillations
Summary
In Calabi-Yau compactifications of superstring theories to four dimensions, The moduli and axion kinetic terms in the Lagrangian are derived from a function of the moduli fields called the Kahler potential, K, which, up to a coefficient is given by. From the above discussions, one can suppress dark radiation from moduli decays when the Kahler metric for the moduli fields is approximately diagonal. This will be the case when the Volume function is dominated by just one term only. Though non-generic, this occurs when there is a relation between the moduli mass matrix and the eigenvalues of the Kahler metric: KiDi ∝ Uij (3.21) Under these very special circumstances, dark radiation can be suppressed by the number of axions on average. This is merely a curious observation rather than a realistic case
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