We revisit constraints on decaying very heavy dark matter (VHDM) using the latest ultrahigh-energy cosmic-ray (UHECR; E >1e18 eV) data and ultrahigh-energy (UHE) gamma-ray flux upper limits, measured by the Pierre Auger Observatory. We present updated limits on the VHDM lifetime for masses up to ∼ 1e15 GeV, considering decay into quarks, leptons, and massive bosons. In particular, we consider not only the UHECR spectrum but their composition data that favors heavier nuclei. Such a combined analysis improves the limits at <1e12 GeV because VHDM decay does not produce UHECR nuclei.

Aspects of non-resonant high scale leptogenesis (LG) associated with type I seesaw mechanism  will be discussed.
The questions of
i) how low can be the LG scale in the case of three right-handed neutrinos,
ii) how low/high can be the LG scale when the  CP violation is provided by the Dirac or Majorana phases in the PMNS neutrino mixing matrix,
iii)   how the transitions between the different flavour regimes take place, and

I will derive new classes of soft theorems for theories in which time symmetries (i.e., symmetries that involve the transformation of time, an example of which are Lorentz boosts) are spontaneously broken. The soft theorems involve unequal-time correlation functions with the insertion of a soft Goldstone in the far past. I will discuss explicit examples, which include the effective theory of a relativistic superfluid and inflationary cosmology.

False vacuum decay (FVD) plays a vital role in many models of the early Universe, with important implications for inflation, the multiverse, and gravitational waves. However, we still lack a satisfying theoretical understanding of this process, with existing approaches working only in imaginary (Euclidean) time, and relying on numerous assumptions that have yet to be empirically tested. An exciting route forward is to use laboratory experiments which undergo transitions analogous to FVD, allowing nature to simulate all of the non-perturbative quantum effects for us.