AbstractConsistent frameworks of quantum gravity often predict the existence of large num-bers of ultralight pseudoscalar degrees of freedom, forming the phenomenologi-cal landscape of the String Axiverse. The complexity of the compactiﬁed extra-dimensional spacetime manifold and plethoric ensemble of possible vacuum solutions, indicate these ﬁelds could possess parameters ﬁxed to cosmologically signiﬁcant scales in the associated four-dimensional eﬀective ﬁeld theories, which may span many decades. In the framework of string/M- theory, a systematic construction of the spectrum of these free model variables, the axion decay constant, fa, and ﬁeld mass, ma, when studying explicit realisations of the string axiverse, is an arduous task to perform. The general approach to this problem requires extensive details of all instanton corrections to the model’s superpotential, along with a detailed knowledge of the full scalar potential, minimised in the supersymmetric theory. The diﬃculty of this task scales signiﬁcantly when considering realistic axion/moduli population numbers. These have often been shown to appear at the order of tens or even hundreds of axionic ﬁelds, realised from well deﬁned geometrical constructions and topological features of the model’s extra-dimensional manifold.
It is therefore of great interest to consider methods which can alleviate these issues, speciﬁcally through a randomised statistical approach, due to the lack of deﬁnitive information we can assert on the higher-dimensional complex space. The link be-tween free probability theory and the asymptotic nature of large random matrices has incorporated itself into various areas associated to multi-axion cosmology. These include models of inﬂation, quintessence and ensemble sampling of the superpotential Hessian in models of random supergravity. The complexities of these models can be reduced by considering a series of simple yet very powerful nomothetic principles applied to high-dimensional data structures. In this work we introduce a number of random matrix theory inspired models based loosely on axion ﬁeld alignment considerations for the eﬀective multi-ﬁeld Lagrangian, as well as a random matrix treatment of the explicit realisation of the string axiverse in M-theory. We detail the forms of their limiting spectral distributions, which take universal forms and provide traceable results based on both central limits theorems and classical ensemble random matrix theory, along with the relevant powerful statements stemming from the ﬁeld of free probability theory. Using these frameworks we investigate speciﬁc conﬁgurations of these models based on the initial basis we begin to sample our model, whilst providing simplistic ﬁts to the limiting spectra through considerations for the spectral moments. Such models can be used to test both the presence and viability of axion contributions to the cosmic history, using hierarchical Bayesian inference techniques, along with the possibility of performing an analysis of other phenomenological consequences which may signal the appearance of these ﬁelds in our four-dimensional spacetime.
To assess this, we discuss how astrophysical observations for stellar binary and super-massive black hole systems can be used to exclude the existence of axions spanning a large portion of the ultralight mass parameter space, via the superradiance phe-nomenon. We show how these measurements can be used to constrain properties of the deﬁned and introduced universal statistical distributions, associated to multiple bosonic ﬁeld theories, covering axion phenomenologies important to the dark sector of cosmological physics and grand uniﬁed theories. The presence of multiple ﬁelds can enhance the exclusion bounds on both solar and supermassive black holes in the so called Regge spin plane, as apposed to considering the case of a single ﬁeld. In this work, we explore for the ﬁrst time how these measurements can be used to constrain properties of statistical probability measure functions for the masses of multiple bosonic ﬁelds. We present an analysis of the statistical likelihoods for each of these models with recorded black hole data spin and mass measurements, in order to provide a picture of the signiﬁcance of the axion parameter space and its phenomenology in eﬀective theories. Quite generally, in the limit of weak self-interaction, our methodology excludes Nax ≥30 axion-like ﬁelds, associated to a range of mass distribution widths and central values, spanning many orders of mag-nitude. We demonstrate this for the speciﬁc example of axions motivated by string theory and M-theory in the random matrix theory axiverse, where the mass distri-butions in speciﬁc conﬁgurations takes universal forms over logarithmic scales.
Finally to conclude, we present an analysis of the background cosmological (quasi-)observables for a selection of the random matrix theory axiverse models, whilst incorporating axion ﬁeld population numbers, Nax∼O (10−100). This signiﬁcantly reduces the number of parameters from 2Nax to a small number of statistical hyper-parameters related to the matrix parameters which regulate the spectral moments of the parameter distributions. Once again our choice of models in this analysis rep-resents a selection of random matrix models, either motivated purely by statistical considerations, or the structure is speciﬁed according to a class of M-theory models and stochastic variables. If the axion masses and (eﬀective) decay constants, lie in speciﬁc ranges, then axions contribute to the cosmological dark matter and dark energy densities. We use these models to assess the chance of reproducing suitable dark matter or dark energy cosmologies. Our methodology incorporates the use of both random matrix theory sampling and Bayesian networks. Using Bayesian methods in a a hierarchical model we constrain the hyperparameters of the statistical axion distributions. In some cases the hyperparameters can be related to theoretical aspects of string theory, e.g. constraining the number ratio of axions to moduli, or the typical decay constant scales needed to provide the correct relic densities today.
|Date of Award
|1 May 2020
|Bobby Acharya (Supervisor)