It has recently been pointed out that Gaia is capable of detecting a stochastic gravitational wave background in the sensitivity band between the frequency of pulsar timing arrays and LISA. We argue that Gaia and Theia have great potential for early universe cosmology, since such a frequency range is ideal for probing phase transitions in asymmetric dark matter, SIMP and the cosmological QCD transition. Furthermore, there is the potential for detecting primordial black holes in the solar mass range produced during such an early universe transition and distinguish them from those expected from the QCD epoch. Finally, we discuss the potential for Gaia and Theia to probe topological defects and the ability of Gaia to potentially shed light on the recent NANOGrav results.

We propose a new out-of-equilibrium production mechanism of light dark matter: resonance scanning. If the dark matter mass evolved in the early Universe, resonant production may have occurred for a wide range of light dark matter masses today. We show that the dark matter relic abundance may be produced through the Higgs portal, in a manner consistent with current experimental constraints.

We prove that the expected number of braid moves in the commutation class of the reduced word $(s_1 s_2 \cdots s_{n-1})(s_1 s_2 \cdots s_{n-2}) \cdots (s_1 s_2)(s_1)$ for the long element in the symmetric group $\mathfrak{S}_n$ is one. This is a variant of a similar result by V. Reiner, who proved that the expected number of braid moves in a random reduced word for the long element is one. The proof is bijective and uses X. Viennot's theory of heaps and variants of the promotion operator. In addition, we provide a refinement of this result on orbits under the action of even and odd promotion operators. This gives an example of a homomesy for a nonabelian (dihedral) group that is not induced by an abelian subgroup. Our techniques extend to more general posets and to other statistics.

We present the possibility that the seesaw mechanism with thermal leptogenesis can be tested using the stochastic gravitational background. Achieving neutrino masses consistent with atmospheric and solar neutrino data, while avoiding nonperturbative couplings, requires right handed neutrinos lighter than the typical scale of grand unification. This scale separation suggests a symmetry protecting the right-handed neutrinos from getting a mass. Thermal leptogenesis would then require that such a symmetry be broken below the reheating temperature. We enumerate all such possible symmetries consistent with these minimal assumptions and their corresponding defects, finding that in many cases, gravitational waves from the network of cosmic strings should be detectable. Estimating the predicted gravitational wave background, we find that future space-borne missions could probe the entire range relevant for thermal leptogenesis.

The symmetry breaking of grand unified gauge groups in the early Universe often leaves behind relic topological defects such as cosmic strings, domain walls, or monopoles. For some symmetry breaking chains, hybrid defects can form where cosmic strings attach to domain walls or monopoles attach to strings. In general, such hybrid defects are unstable, with one defect "eating"the other via the conversion of its rest mass into the other's kinetic energy and, subsequently, decaying via gravitational waves. In this work, we determine the gravitational wave spectrum from 1) the destruction of a cosmic string network by the nucleation of monopoles which cut up and "eat"the strings, 2) the collapse and decay of a monopole-string network by strings that eat the monopoles, 3) the destruction of a domain wall network by the nucleation of string-bounded holes on the wall that expand and eat the wall, and 4) the collapse and decay of a string-bounded wall network by walls that eat the strings. We call the gravitational wave signals produced from the eating of one topological defect by another "gravitational wave gastronomy."We find that the four gravitational wave gastronomy signals considered yield unique spectra that can be used to narrow down the SO(10) symmetry breaking chain to the Standard Model and the scales of symmetry breaking associated with the consumed topological defects. Moreover, the systems we consider are unlikely to have a residual monopole or domain wall problem.