The modern theory of ghost-free massive gravity hinges upon the notion of a square root of a matrix. This is non-trivial and not unique. It makes the standard perturbation theory in terms of matrices problematic, and in some cases even impossible. I will describe the mathematics behind these issues, and also discuss a method of dealing with perturbation theory around a given solution in terms...
What is the maximum possible strength of a first-order electroweak phase transition and the resulting gravitational wave signal? While naively one might expect that supercooling could increase the strength of the transition to very high values, for strong supercooling the Universe is no longer radiation-dominated and the vacuum energy of the unstable minimum of the potential dominates the...
The information loss problem in black hole physics is a very important but unresolved problem. I will review the issue including the recent discussion with the firewall controversy. Instead of the firewall conjecture or other candidates of resolutions, I will suggest that the Euclidean path integral sheds some lights to the problem.
I will review the problem of the acceleration of the expansion of the universe at late times and discuss how models of modifications of gravity can provide an alternative mechanism to the cosmological constant. I will discuss the space of models, how to best think about the generic effects these models have on structure formation and therefore how they can be constrained through observations....