William Giarè, Ph.D. 

Research Associate in Theoretical Cosmology 

School of Mathematics & Statistics, The University of Sheffield

Get in touch:  E-mail | Skype | Twitter 

 Scientific Interests

Numerical Cosmology

Theoretical Cosmology

Cosmo/Particle Physics


In recent decades, our understanding of the Universe has experienced a revolutionary level of advancement. With the measurements of the Cosmic Microwave Background radiation and the detailed mapping of the Universe's large-scale structure, we have entered an era of precision cosmology. Thanks to these experimental efforts, we can now predict the matter and energy content of our Universe down to the sub-percent level of accuracy. Furthermore, we can also trace the evolution of the Universe back to its earliest moments, shedding light on its history from the Big Bang singularity to the present day. 

Although the ΛCDM model of structure formation has proven to be incredibly successful in explaining several observations at different cosmic epochs and scales, it is important to note that our comprehension of the Universe remains incomplete and far from exhaustive. There are still fundamental questions regarding its origins, composition, and evolution that require clear answers, and numerous open problems that must be fully explored and understood. 

The standard ΛCDM model is based on three major unknown ingredients that, even if absolutely necessary to explain observations, are not well understood neither theoretically nor experimentally:

In addition, in recent years, more accurate cosmological and astrophysical measurements are providing several convincing evidence for tensions between independent observations from early and late time Universe, undermining the solidity of the scenario developed over the past century and motivating the possibility to testing new physics with increasing precision.  

The Aim of My Work

My ultimate goal is to progress in the knowledge of several open problems in cosmology, such as the underlying physics of the early and late-time accelerated expansions of the Universe, the nature of fundamental intersections among particles and the identity of the dark sector.  

For this reason, my research activity is very diversified and covers different interesting topics; ranging from theoretical and observational cosmology to astroparticle physics and gravitational waves

Working at the interface between theory and data, I aim to identify and characterize possible hints for new physics that could be unveiled by cosmological and astrophysical observations in the near future.  This back-and-forth interplay between existing data, future experiments and theories/models, represents maybe the main characteristic of my research activity.

My Research Topics

Among all the possible extensions to ΛCDM that may be considered, probably the most interesting are those connected with fundamental interactions, namely the Einstein's theory of General Relativity for the geometrical description of gravity and the Standard Model of elementary particles for the fundamental interactions of matter and radiation.  Cosmology provides an elegant and powerful way for testing them

Currently, I'm working on the following research topics in cosmology, gravitation and (cosmo/astro)particle physics.

Dark Interactions in the Cosmic Microwave Background

The validity of the standard ΛCDM model of cosmology has been called into question due to recent tensions and anomalies which suggest that there may be missing components or interactions in the theory.

Some Interesting theoretical extensions that I am currently extensively studying involve interactions in the dark components of the cosmological model, such as interactions between Dark Matter and Dark Energy as well as interactions between Dark Matter and Neutrinos. 

What makes these models particularly intriguing is that several independent observations of the cosmic microwave background seem to indicate a preference for an interacting dark sector, which could also help to address part of the observed discrepancies among independent probes. 

These "dark interactions" can be accurately tested by small-scale CMB observations, which can uncover unique signatures that would otherwise be very challenging to detect on larger scales.

Small-scale effects of Neutrino-Dark Matter interactions in the CMB anisotropies
Cosmological Constraints on QCD thermal axions

Axions, Neutrinos and Hot Dark Matter

Cosmology is a powerful tool for testing extensions of the Standard Model (SM) of elementary particles such as axions. 

Axions are bosons postulated by R. Peccei and H. Quinn to solve the so-called strong CP problem in Quantum Chromodynamics (QCD). If these elusive particles actually exist, they can be copiously produced in the early Universe, both via thermal and non-thermal channels, leaving characteristic signatures in different cosmological observables. For instance, thermal relics, behaving as hot dark matter, can modify the CMB temperature power spectrum and the abundances of light elements predicted by the Big Bang Nucleosynthesis (BBN). 

Exploiting current and future (forecasted) cosmological and astrophysical observations, I study what kind of constraints one can derive on realistic mixed dark matter scenarios that consider axions and massive neutrinos as additional thermal species. 

Constraints on the Inflationary parameters from different CMB experiments

Cosmological Inflation and Primordial Perturbations

In the very Early Universe a phase of almost de Sitter spacetime expansion known as cosmological inflation is supposed to set the appropriate initial conditions for the subsequent Hot Big Bang theory evolution, driving the Universe towards homogeneity and flatness. 

In the framework of single-field inflation with Einstein's gravity, primordial inflationary perturbations are expected to be (nearly) Gaussian and hence they can be described in terms of their two-point correlation function (or primordial spectrum). However, the standard slow-roll inflationary predictions can be violated by many different physical mechanisms, from multi-field models to modified gravity theories. 

From the theoretical side, I study the way non-standard high-energy physics on the inflationary scales can be encoded in the primordial spectrum of density perturbations and how we can test it.  From the data analysis side,  I study the best way to combine different cosmological and astrophysical measurements to increase the data constraining power, interpreting the results in light of the different models proposed in the literature. 

Hunting Primordial Gravitational Waves

The quantum fluctuations of the Inflaton field, becoming classical on large scales, can induce energy-density fluctuations, sourcing both rotational invariant scalar modes and, if the energy scale of inflation is sufficiently high, a satiable background of primordial gravitational waves. As a matter of fact, the detection of inflationary gravitational waves would provide direct evidence for inflation, opening at the same time an inestimable observational window on fundamental physics. 

I am studying what kind of information we can derive from a future (missing) detection of the cosmic background of inflationary gravitational waves, focusing on the implications for fundamental physics, such as modified gravity theories and/or models of the early Universe.  From the data analysis side, I am working to characterize the phenomenology testable by current and future cosmic observers. I analyze the detectable imprints that Primordial Gravitational Waves may have left in the different cosmological observables and towards different cosmic epochs and scales, including their effects before recombination, the current and future perspectives for B-mode polarization in the Cosmic Microwave Background and the implications for direct gravitational wave detection. 

A reliable calculation of relic radiation from primordial gravitational waves

Tension between Planck and Atacama Cosmology Telescopoe in extended models of cosmology.

Cosmological Tensions and Anomalies

In recent years, as the experimental sensitivity increased and the error-bars on cosmological parameters started to narrow, several intriguing tensions and anomalies emerged between independent cosmological and astrophysical observations. These disagreements represent a new challenge for cosmology, revealing either the presence of important observational systematics in the experiments or the need for a major theoretical breakthrough in the field. Either way, it is becoming particularly relevant to shed light on the nature of such tensions, above all if we are aiming to test fundamental physics with cosmology. 

Recently, I am extensively working on statistical methods able to quantify inconsistencies between different experiments as well as on theoretical extensions to the standard model of cosmology (possibly involving non-flat spatial geometries, modified gravity theories, new physics beyond the SM and/or dynamical and non-dynamical parameterizations of the dark sector) that may reconcile or at least alleviate the increasing tensions between cosmological and astrophysical observations. 

Cosmology with Machine Learning

Although the standard ΛCDM model of cosmology successfully describes observations from widely different epochs of the Universe, its three major unknown ingredients (Inflation, Dark Matter and Dark Energy), still lack solid theoretical interpretations and direct experimental evidence. In this sense, the model resembles a phenomenological data-driven approximation to a more accurate scenario that has yet to be fully explored (or even understood) on a more fundamental level. 

I am aimed to perform consistency checks of the first principle of modern cosmology and to robustly test early and/or late time new physics beyond ΛCDM by analyzing cosmological and astrophysical measurements in light of modern machine-learning techniques such as Artificial Neural Networks and Gaussian Process where the impact of model-dependent assumptions are typically removed or strongly reduced. 

A test of cosmological models based on the Distance Duality Relation

For more information, you can read my publications on all these topics