The so-called large angle anomalies of the cosmic microwave background (CMB) hint towards a possible violation of the Cosmological Principle. The land of cosmic variance, however, is a complicated one. To discern the possibility of genuine physical mechanisms causing them from the possibility of them being statistical flukes, due to systematic residuals or highly complex mask-induced couplings, it is important to move beyond the standard set of two-point statistics and characterise the CMB as completely as possible. In my work I have explored the hemispherical power asymmetry through the lens of Minkowski Functionals, using them to probe not only the local variance of the CMB temperature field, but also the variance of its gradients and deviations from Gaussian predictions. This provides a complementary view of large-scale anomalies and helps establish whether the observed asymmetries persist in the morphology of the field itself, rather than only in its power. More broadly, I am interested in developing robust statistical tools to disentangle genuine large-scale cosmological signatures from the effects of cosmic variance, foregrounds and observational systematics.

Related Publications:

• J. Carrón Duque, M.M.B., Joseba Martínez-Arrizabalaga. More Than Power: Revisiting the CMB Hemispherical Power Asymmetry with Morphological Descriptors. Submitted to Astronomy & Astrophysics (A&A). arXiv:2603.22449 (2026).

• Euclid Collaboration (incl. M.M.B.). Cosmic Dipole Measurement with the Euclid Mission. In preparation, expected June 2027.

I gave a talk about the HPA anomaly at DIPC that you can watch on YouTube

One of the most striking consequences of accepting General Relativity (GR) as the correct mathematical framework to describe the cosmos is that GR postulates that spacetime should be modeled as a manifold. Cosmologists have traditionally focused on learning what the metric on that manifold is, but not what the manifold itself is.

Under some philosophical assumptions, such as adopting the Cosmological Principle, we learn that the curvature of space dictates its local geometry: flat, open or closed. But curvature does not determine the global topology of the Universe. Space can, for example, be locally indistinguishable from Euclidean space while possessing a finite, multiply connected topology. This possibility makes cosmic topology a unique probe of the global structure of the Universe, with potentially observable signatures in the correlations of cosmological fields across the largest scales.

My work in cosmic topology has focused on understanding these signatures at a fundamental level and translating the geometry and topology of a spatial manifold into observable quantities. I have worked on the eigenmodes of the Laplacian, topology-dependent correlation matrices and the information content carried by both the CMB and the three-dimensional matter distribution. A particular interest of mine is the systematic treatment of non-trivial topologies beyond the simplest flat models, including spherical and lens-space geometries. This requires combining methods from cosmology with harmonic analysis, differential geometry and representation theory, and allows us to ask a fundamental question: how much can observations tell us about the global shape of the Universe?

Related Publications:

• D. P. Mihaylov, M. M. B. et al. Cosmic topology. Part Va. Information content of the observable Universe. Submitted to JCAP. arXiv:2608.25033 (2026)

• M.M.B. et al. (COMPACT Collaboration). Cosmic topology. Part IId. Eigenmodes and Correlation Matrices of Lens Spaces. Submitted to JCAP. arxiv:2610.12418 (2026)

We long ago entered the era of precision cosmology, and it has already been a while since the community entered the beyond 2-point era. Higher Order Statistics (HOS's) constitute a broad family of statistical tools that are sensitive to information that is lost when the matter distribution is compressed into its two-point function. This includes non-Gaussianity, phase correlations, environmental dependence and, more generally, the morphology and geometry of the cosmic web.

Throughout my PhD I have worked with marked fields and Minkowski Functionals as complementary ways of accessing this information. Marked statistics provide an efficient route to higher-order information by reweighting the density field according to its local environment, while Minkowski Functionals offer a direct description of the morphology of excursion sets. My recent work has focused on designing physically motivated marks that capture properties of the cosmic web beyond local density, such as tidal structure, isotropy and filamentarity, and on understanding how these observables can complement standard power-spectrum analyses. I am particularly interested in the connection between these statistical descriptors and perturbative descriptions of large-scale structure, with the aim of developing higher-order statistics that are both physically interpretable and useful for extracting cosmological information from upcoming galaxy surveys.

Related Publications:

• M.M.B., J. A. Cowell, D. Alonso, J. Carrón Duque, J. García-Bellido. Weighted Webs: Morphology-Informed Marked Fields. Submitted to JCAP. arXiv:2607.26021 (2026).

• J. Carrón Duque, M.M.B., Joseba Martínez-Arrizabalaga. More Than Power: Revisiting the CMB Hemispherical Power Asymmetry with Morphological Descriptors. Submitted to Astronomy & Astrophysics (A&A). arXiv:2603.22449 (2026).

• A. Samandar, M.M.B. et al. (COMPACT Collaboration) Beyond the Kullback--Leibler divergence: the likelihood-ratio distribution as a detectability measure. arxiv:2610.17186 (2026)

My training as a mathematician during my undergraduate studies has pushed me to pursue technically oriented problems at the interface between fundamental physics, geometry and cosmology. I am particularly interested in situations where the mathematical structure of a theory has direct consequences for observable physics, and where tools from differential geometry, harmonic analysis and representation theory can be brought to bear on cosmological questions.

One direction of my work concerns cosmology on non-trivial spatial manifolds. I have worked on harmonic analysis on curved and multiply connected spaces, the construction of eigenmodes of differential operators and the resulting topology-dependent correlation functions. In parallel, I am interested in more fundamental questions concerning quantum fields in curved spacetime, including particle production in cosmological backgrounds. My current work on cosmological gravitational particle production in the three-sphere provides a natural bridge between these areas, combining the geometry of a closed spatial universe with the quantum dynamics of fields evolving on it.

More broadly, I am interested in using the mathematical structure of cosmological models as a guide towards new physical observables and theoretical predictions. This includes understanding how curvature and topology affect field dynamics, how symmetry constrains the available degrees of freedom, and how these structures are ultimately encoded in cosmological observations. I see this interplay between mathematical physics and observational cosmology as a central part of my future research.

Related Publications:

• M.M.B. et al. (COMPACT collaboration). Cosmic topology. Part IId. Eigenmodes and Correlation Matrices of Lens Spaces. In preparation (Expected October 2026).

• M.M.B. et al. Cosmological Gravitational Particle Production in the Three-Sphere. In preparation (Expected November 2026).