Abstracts Gravity 2023

We consider quantum field theory with self-interactions in various patches of Minkowski and de Sitter spacetimes. Namely, in Minkowski spacetime we consider separately the right (left) Rindler wedge, past wedge, and future wedge. In de Sitter spacetime we consider expanding the Poincaré patch, the static patch, the contracting Poincaré patch, and the global de Sitter itself. In all cases we restrict our considerations to the isometry invariant states leading to maximally analytic propagators. We prove that loop corrections in the right (left) Rindler wedge, in the past wedge (of Minkowski spacetime), in the static patch and in the expanding Poincaré patch (of de Sitter spacetime) respect the isometries of the corresponding symmetric spacetimes. All these facts are related to the causality and analyticity properties of the propagators for the states that we consider. At the same time in the future wedge, in the contracting Poincaré patch and in the global de Sitter spacetime infrared effects violate the isometries.

It is suggested that the late time exponential expansion of our Universe is caused by the universe being bombarded by baby universes. This leads to a modified Friedmann equation that is in agreement with late-time cosmological observations without invoking a cosmological constant.

It is well known that the limit eigenvalue distribution of the scaled standard Wigner matrix is the semi-circular distribution whose $2k$th moment equals the number of non-crossing pair-partitions of $\{1,2,\ldots ,2k\}$. There are several extensions of this result in the literature, including the sparse case. We discuss extension of these results by relaxing significantly the i.i.d. assumption.
The limiting spectral distribution then involve a larger class of partitions. In the process we show how some new sets of partitions gain importance. Several existing and new results for their band and sparse versions, as well as for matrices with continuous and discretevariance profile follow as special cases.
Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have also been studied quite extensively. Under the assumption that the entries are taken from an i.i.d. sequence with finite variance, the LSD are tied together by a common thread \textemdash{}the $2k$th moment of the limit equals a weighted sum over different types of pair-partitions of the set $\{1,2,\ldots ,2k\}$ and are universal. Some results are also known for the sparse case. Time permitting we show suitable extension of these results also, along the lines of the Wigner matrix

To be communicated.

Phantom fields have been widely invoked as a source of dark energy in cosmology, but rarely taken seriously as quantum theories. The vacuum is automatically unstable to production of negative energy ghost particles plus ordinary particles, requiring such theories to be effective only, below some UV cutoff. I will present recent cosmological constraints arising from the vacuum instability, both at the level of the homogeneous background, and the density perturbations.