Axion-like particles (ALPs) are a candidate for dark matter, the elusive ‘missing mass’ of the universe, inferred by it’s gravitational presence in galaxies, clusters and cosmological structure formation. As a dark matter candidate, ALPs are preferred by theorists since they are a model independent generalisation of the standard model of particle physics, and are predicted by many beyond standard model extensions such as string theory. ALPs are preferred by experimentalists since data have not yet ruled them out (in a way that historical candidates such MACHOs and increasingly WIMPS have been in recent years).

ALPs have characteristic properties, such as their mass, lifetime and possibly nonzero interaction rate with matter. This state-of-the-art analysis considers a class of ALPs which can have the capacity to occasionally decay into photons. This is interesting cosmologically, since for certain ranges of mass and lifetimes these would have effects on the expansion rate, element formation and large-scale structure evolution of the universe. Observations of the cosmos can therefore be combined with terrestrial experiments to rule out or confirm classes of ALP with (non-)detections informing our theories of fundamental physics and dark matter.

We find a lower bound on the ALP mass (>300keV) a little lower than around that of the electron (MeV), which can only be evaded if ALPs are stable on cosmological timescales. In order to achieve these strongest constraints, the team had to combine state-of-the-art calculations of the irreducible ALP freeze-in abundance, primordial element abundances (including photodisintegration through ALP decays), CMB spectral distortions and anisotropies, and constraints from supernovae and stellar cooling. In addition to these theoretical and observational innovations, the analysis also makes use of the global fitting framework GAMBIT, using state-of-the-art frequentist and Bayesian analyses. Future observations of CMB spectral distortions with a PIXIE-like mission are expected to improve this bound by two orders of magnitude, moving toward ruling out ALPs with masses of the proton and neutron (GeV).

The complexity of these calculations and the power of the data means that scouring the ALP parameter space requires high-performance computing, enabled by our DiRAC allocation. This analysis showcases the diversity of the datasets and sophistication tools the GAMBIT team has developed over the past decade, which we will continue to deploy over the next five years.

## Finite inflation in curved space

The shape of the universe is one of the fundamental questions in cosmology. From their first lecture on Einstein’s theory applied to our Universe, students learn that the extended copernican principle demands the universe must come in one of three forms: closed, flat, or open (hyperspherical, Euclidean or saddle shaped), depending on the sign and degree of spatial curvature.

Since the release of Planck cosmic microwave background satellite data, there has been a debate in the literature as to the degree to which the current cosmological observations prefer closed, flat or open universes. Planck data alone has an moderate preference for closed universes (with betting odds of over 100:1). Alternative datasets, such as CMB lensing, Baryon acoustic oscillations and supernovae generally prefer flat universes. This discrepancy is termed ‘curvature tension’. Flat universers maintain that the Planck preference for closed universes is consistent with a statistical fluctuation, whilst proponents of the spherical Universe counter that the data analysis of all other datasets currently must assume a flat Universe. Future observations and more advanced data analyses will one day close this question, but in the meantime it is interesting to examine the impact that a closed universe has on other theories.

The standard model of the universe includes a primordial epoch of hyperinflation, where the universe begins in a rapidly accelerating phase. The theory of inflation explains the apparently acausal homogeneity of the CMB, the patterns of the microscopic anisotropies, and why the universe we see today is flat. An observation of spatial curvature today therefore has significant impact on many of the standard results in inflationary theory.

This paper represents a magnum opus lead by Lukas Hergt’s phd work. It’s careful and deep analysis, filled with informative and artistic figures represents the state-of-the-art in the theory and data analysis curved inflating Universes. Many results quantitatively shift when moving from flat to curved universes, as this figure shows. We can see that from an a priorir (grey) agnostic curvature prior Planck and BICEP data select for closed universes over flat ones, and in doing so prefer a higher value of the primordial inflationary parameter ns. Curvature therefore has non-trivial impact on other cosmological predictions. The paper considers a variety of inflationary and reheating models, and their non-trivial interaction with the shape of the universe.