Search

Black holes binaries coming from a distribution of primordial black holes might exhibit a large merger rate up to large redshifts. Using a phenomenological model for the merger rate, we show that changes in its slope, up to redshifts $z\sim 4$, are constrained by current limits on the amplitude of the stochastic gravitational wave background from LIGO/Virgo O3 run. This shows that the stochastic background constrains the merger rate for redshifts larger than the single event horizon of detection ($z\simeq 1$ for the same detector). Moreover, we show that for steep merger rates the shape of the stochastic gravitational wave signal at intermediate frequencies differs from the usual $2/3$ IR scaling. We discuss the implications of our model for future experiments in a wide range of frequencies, as the design LIGO/Virgo array, Einstein Telescope, LISA and PTA. Additionally, we show that i) the stochastic background and the present merger rate provide equally constraining bounds on the abundance of PBHs arising from a Gaussian distribution of inhomogeneities and ii) Degeneracies at the level of the stochastic background (i.e. different merger histories leading to a similar stochastic background) can be broken by considering the complementary direct observation of the merger rate from number counts by future detectors such as the Einstein Telescope., Comment: 29 pages, 7 figures

We give an explanation for the signal detected by NANOGrav as the stochastic gravitational wave background from binary mergers of primordial "Stupendously Large Black Holes" (SLABs) of mass $M\sim(10^{11}-10^{12})M_{\odot}$, and corresponding to roughly $0.1\%$ of the dark matter. We show that the stringent bounds coming from $\mu$ distortions of the CMB can be surpassed if the perturbations resulting in these BHs arise from the non-Gaussian distribution of fluctuations expected in single field models of inflation generating a spike in the power spectrum. While the tail of the stochastic background coming from binaries with $M\lesssim 10^{11}M_{\odot}$ could both fit NANOGrav and respect $\mu$ distortions limits, they become excluded from large scale structure constraints., Comment: 6 pages, 2 figures

We discuss the effect of clustering for the determination of the merger rate of binary black holes in the LIGO mass range. While for a Poissonian initial distribution, and assuming isolated binaries, the allowed fraction of Primordial Black Holes (PBHs) to dark matter (DM) is a few percent, we show that this bound can be relaxed if PBHs are clustered. More precisely we show that for large clustering the merger rate can drop with increasing fraction of PBHs, introducing a degeneracy in the parameters of the theory consistent with a given present merger rate, and allowing all the DM to be in the form of stellar mass PBHs. This degeneracy can however be broken by looking at the evolution of the merger rate with redshift. For a simple clustering model that we consider, we show that the LIGO projected sensitivity can disentangle, through the observation of a stochastic background of gravitational waves, different clustered distributions having the same present merger rate., Comment: 23 pages, 6 figures. v2: refs added, small changes. v3: Fig. 6 corrected, conclusions unchanged

The rate of merger events observed by LIGO/Virgo can be used in order to probe the fraction $f$ of dark mater in the form of Primordial Black Holes. Here, we consider the merger rate of PBH binaries, accounting for the effect of cosmological perturbations on their initial eccentricity $e$. The torque on the binaries receives significant contributions from a wide range of scales, that goes from the size of the horizon at the time when the binary forms, down to the co-moving size of the binary. In scenarios where PBH are formed from adiabatic perturbations, it is natural to expect an enhancement of the power spectrum $P_\Phi$ at small scales, where it is poorly constrained observationally. The effect can then be quite significant. For instance, a nearly flat spectrum with amplitude $P_\Phi \gtrsim 10^{-7}$ on scales smaller than $\sim 10 Mpc^{-1}$ gives a contribution $\langle j^2 \rangle \sim 10^3 P_\Phi$, where $j= (1-e^2)^{1/2}$ is the dimensionless angular momentum parameter of the binaries. This contribution can dominate over tidal torques from neighboring PBHs for any value of $f$. Current constraints allow for a power spectrum as large as $P_\Phi \sim 10^{-5}$ at the intermediate scales $10^3-10^5 Mpc^{-1}$, comparable to the co-moving size of the binaries at the time of formation. In particular, this can relax current bounds on the PBH abundance based on the observed LIGO/Virgo merger rate, allowing for a fraction $f\sim 10\%$ of dark matter in PBH of mass $\sim 30 M_\odot$. We investigate the differential merger rate $\Delta\Gamma(m_1,m_2)$, as a function of the masses of the binary components, and the corresponding ``universality" coefficient $\alpha = -(m_1+m_2)^2 \partial^2 \ln \Delta\Gamma/\partial m_1\partial m_2$, concluding that merger rates may provide valuable information on the spectrum of primordial cosmological perturbations at currently uncharted lengthscales., Comment: 38 pages, 12 figures

Design by Constract (DBC) has influenced the development of formal specification languages that allow the mix of specification and implementation code, like Eiffel, the Java Modeling Language (JML) and Spec#. Meanwhile algebraic specification languages have been developing independently and offer full support for specification and verification of design for large and complex systems in a mathematical rigorous way. However there is no guarantee that the final implementation will comply to the specification. In this paper we proposed the use of the latter for the specification and verification of the systems design and then by presenting a translation between the two, the use of the former to ensure that the implementation respects the specification and thus enjoy the verified properties.

Digital Right Management (DRM) Systems have been created to meet the need for digital content protection and distribution. In this paper we present some of the directions of our ongoing research to apply algebraic specification techniques on mobile DRM systems., Comment: 6 pages

We present a formal specification of the Semantic Web, as an extension of the World Wide Web using the well known algebraic specification language CafeOBJ. Our approach allows the description of the key elements of the Semantic Web technologies, in order to give a better understanding of the system, without getting involved with their implementation details that might not yet be standardized. This specification is part of our work in progress concerning the modeling the Social Semantic Web., Comment: 6 pages

With the help of the Internet, social networks have grown rapidly. This has increased security requirements. We present a formalization of social networks as composite behavioral objects, defined using the Observational Transition System (OTS) approach. Our definition is then translated to the OTS/CafeOBJ algebraic specification methodology. This translation allows the formal verification of safety properties for social networks via the Proof Score method. Finally, using this methodology we formally verify some security properties., Comment: 8 apges, 1 figure, 5 tables

We claim that the Open Mobile Alliance (OMA) License Choice Algorithm, implemented in mobile DRM agents as specified by OMA suffers from a bug. More precisely there exist some cases that the user, may end up losing some rights without even to exercise them. We redesign this algorithm and claim that our approach eliminates this bug., Comment: 10 pages, 2 tables, 1 figure