The Universe at extreme magnification

Extreme magnifications of distant objects by factors of several thousand have recently become a reality. Small very luminous compact objects, such as supernovae (SNe), giant stars at z=1-2, Pop III stars at z>7 and even gravitational waves from merging binary black holes near caustics of gravitational lenses can be magnified to many thousands or even tens of thousands thanks to their small size. We explore the probability of such extreme magnifications in a cosmological context including also the effect of microlenses near critical curves. We show how a natural limit to the maximum magnification appears due to the presence of microlenses near critical curves. We use a combination of state of the art halo mass functions, high-resolution analytical models for the density profiles and inverse ray tracing to estimate the probability of magnification near caustics. We estimate the rate of highly-magnified events in the case of SNe, GW and very luminous stars including Pop III stars. Our findings reveal that future observations will increase the number of events at extreme magnifications opening the door not only to study individual sources at cosmic distances but also to constrain compact dark matter candidates.Comment: 22 pages and 11 figures. Matches accepted versiion in A&

The hybrid SZ power spectrum: Combining cluster counts and SZ fluctuations to probe gas physics

Sunyaev-Zeldovich (SZ) effect from a cosmological distribution of clusters carry information on the underlying cosmology as well as the cluster gas physics. In order to study either cosmology or clusters one needs to break the degeneracies between the two. We present a toy model showing how complementary informations from SZ power spectrum and the SZ flux counts, both obtained from upcoming SZ cluster surveys, can be used to mitigate the strong cosmological influence (especially that of sigma_8) on the SZ fluctuations. Once the strong dependence of the cluster SZ power spectrum on sigma_8 is diluted, the cluster power spectrum can be used as a tool in studying cluster gas structure and evolution. The method relies on the ability to write the Poisson contribution to the SZ power spectrum in terms the observed SZ flux counts. We test the toy model by applying the idea to simulations of SZ surveys.Comment: 12 pages. 11 plots. MNRAS submitte

Chiral Scale and Conformal Invariance in 2D Quantum Field Theory

It is well known that a local, unitary Poincare-invariant 2D QFT with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this paper we consider a chiral situation beginning with only a left global scaling symmetry and do not assume Lorentz invariance. We find that a left conformal symmetry is still implied, while right translations are enhanced either to a right conformal symmetry or a left U(1) Kac-Moody symmetry.Comment: 6 pages, no figures. v2: reference added, minor typos correcte

Reasoning about Data Repetitions with Counter Systems

We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or past. We demonstrate correspondences between satisfiability problems for logics and reachability-like decision problems for counter systems. We show that allowing/disallowing atomic formulas expressing repetitions of values in the past corresponds to the reachability/coverability problem in Petri nets. This gives us 2EXPSPACE upper bounds for several satisfiability problems. We prove matching lower bounds by reduction from a reachability problem for a newly introduced class of counter systems. This new class is a succinct version of vector addition systems with states in which counters are accessed via pointers, a potentially useful feature in other contexts. We strengthen further the correspondences between data logics and counter systems by characterizing the complexity of fragments, extensions and variants of the logic. For instance, we precisely characterize the relationship between the number of attributes allowed in the logic and the number of counters needed in the counter system.Comment: 54 page