arXiv subjects

Luca Bombelli

Publications and source records attributed to Luca Bombelli.

At least 19 recordsLinked to original sources

arXiv2020

A Tale of Two Actions: A Variational Principle for Two-Dimensional Causal Sets

In this paper we will explore two different proposals for the action for causal sets: the Benincasa-Dowker action and a modified version of the chain action. We propose a variational principle for two-dimensional causal sets and use it for both actions to determine which causal sets at least on average satisfy a discrete version of the Einstein equation. Specifically, we test this method on causal sets embedded in 2d Minkowski, de Sitter, and anti-de Sitter spacetimes and compare these results to the most prominent nonmanifoldlike causal sets, Kleitman-Rothschild causal sets.

gr-qc↗

arXiv2020

Hunting keV sterile neutrinos with KATRIN: building the first TRISTAN module

The KATRIN (Karlsruhe Tritium Neutrino) experiment investigates the energetic endpoint of the tritium beta-decay spectrum to determine the effective mass of the electron anti-neutrino. The collaboration has reported a first mass measurement result at this TAUP-2019 conference. The TRISTAN project aims at detecting a keV-sterile neutrino signature by measuring the entire tritium beta-decay spectrum with an upgraded KATRIN system. One of the greatest challenges is to handle the high signal rates generated by the strong activity of the KATRIN tritium source while maintaining a good energy resolution. Therefore, a novel multi-pixel silicon drift detector and read-out system are being designed to handle rates of about 100 Mcps with an energy resolution better than 300 eV (FWHM). This report presents succinctly the KATRIN experiment, the TRISTAN project, then the results of the first 7-pixels prototype measurement campaign and finally describes the construction of the first TRISTAN module composed of 166 SDD-pixels as well as its implementation in KATRIN experiment.

physics.ins-det↗

arXiv2019

Measurements with a TRISTAN prototype detector system at the "Troitsk nu-mass" experiment in integral and differential mode

Sterile neutrinos emerge in minimal extensions of the Standard Model which can solve a number of open questions in astroparticle physics. For example, sterile neutrinos in the keV-mass range are viable dark matter candidates. Their existence would lead to a kink-like distortion in the tritium $β$-decay spectrum. In this work we report about the instrumentation of the Troitsk nu-mass experiment with a 7-pixel TRISTAN prototype detector and measurements in both differential and integral mode. The combination of the two modes is a key requirement for a precise sterile neutrino search, as both methods are prone to largely different systematic uncertainties. Thanks to the excellent performance of the TRISTAN detector at high rates, a sterile neutrino search up to masses of about 6 keV could be performed, which enlarges the previous accessible mass range by a factor of 3. Upper limits on the neutrino mixing amplitude in the mass range < 5.6 keV (differential) and < 6.6 keV (integral) are presented. These results demonstrate the feasibility of a sterile neutrino search as planned in the upgrade of the KATRIN experiment with the final TRISTAN detector and read-out system.

physics.ins-det↗

arXiv2018

A novel detector system for KATRIN to search for keV-scale sterile neutrinos

Sterile neutrinos are a minimal extension of the Standard Model of Particle Physics. If their mass is in the kilo-electron-volt regime, they are viable dark matter candidates. One way to search for sterile neutrinos in a laboratory-based experiment is via tritium-beta decay, where the new neutrino mass eigenstate would manifest itself as a kink-like distortion of the $β$-decay spectrum. The objective of the TRISTAN project is to extend the KATRIN setup with a new multi-pixel silicon drift detector system to search for a keV-scale sterile neutrino signal. In this paper we describe the requirements of such a new detector, and present first characterization measurement results obtained with a 7-pixel prototype system.

physics.ins-det↗

arXiv2018

Path length distribution in two-dimensional causal sets

We study the distribution of maximal-chain lengths between two elements of a causal set and its relationship with the embeddability of the causal set in a region of flat spacetime. We start with causal sets obtained from uniformly distributed points in Minkowski space. After some general considerations we focus on the 2-dimensional case and derive a recursion relation for the expected number of maximal chains $n_k$ as a function of their length $k$ and the total number of points $N$ between the maximal and minimal elements. By studying these theoretical distributions as well as ones generated from simulated sprinklings in Minkowski space we identify two features, the most probable path length or peak of the distribution $k_0$ and its width $Δ$, which can be used both to provide a measure of the embeddability of the causal set as a uniform distribution of points in Minkowski space and to determine its dimensionality, if the causal set is manifoldlike in that sense. We end with a few simple examples of $n_k$ distributions for non-manifoldlike causal sets.

gr-qc↗

arXiv2018

Detector Development for a Sterile Neutrino Search with the KATRIN Experiment

The KATRIN (Karlsruhe Tritium Neutrino) experiment investigates the energetic endpoint of the tritium $β$-decay spectrum to determine the effective mass of the electron anti-neutrino with a precision of $200\,\mathrm{meV}$ ($90\,\%$ C.L.) after an effective data taking time of three years. The TRISTAN (tritium $β$-decay to search for sterile neutrinos) group aims to detect a sterile neutrino signature by measuring the entire tritium $β$-decay spectrum with an upgraded KATRIN system. One of the greatest challenges is to handle the high signal rates generated by the strong activity of the KATRIN tritium source. Therefore, a novel multi-pixel silicon drift detector is being designed, which is able to handle rates up to $10^{8}\,\mathrm{cps}$ with an excellent energy resolution of $<200\,\mathrm{eV}$ (FWHM) at $10\,\mathrm{keV}$. This work gives an overview of the ongoing detector development and test results of the first seven pixel prototype detectors.

physics.ins-det↗

arXiv2016

Effect of Accelerated Global Expansion on Bending of Light

In 2007 Rindler and Ishak showed that, contrary to previous claims, the value of the cosmological constant does have an effect on light deflection by a gravitating object in an expanding universe, modeled by a Schwarzschild-de~Sitter spacetime. In this paper we consider light bending in the more general situation of a gravitating object in a cosmological background with varying expansion rate $H(t)$. We calculate numerically the null geodesics representing light rays deflected by a black hole in an accelerating Friedmann-Lemaître-Robertson-Walker universe, modeled by a McVittie metric. Keeping the values of the distances from the observer to the lensing object and to the source fixed, we plot the dependence of the bending angle measured by two different sets of observers in this spacetime on the rate of change of $H(t)$.

gr-qc↗

arXiv2015

Testing General Relativity with Present and Future Astrophysical Observations

One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that general relativity should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of general relativity. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

gr-qc↗

arXiv2014

Link between quantum measurement and the iε term in the QFT propagator

Mensky has suggested to account for "continuous measurement" by attaching to a path integral a weight function centered around the classical path that the integral assigns a probability amplitude to. We show that in fact this weight function doesn't have to be viewed as an additional ingredient put in by hand. It can be derived instead from the conventional path integral if the infinitesimal term iε in the propagator is made finite; the "classical trajectory" is proportional to the current.

math-ph↗

arXiv2013

Lorentzian Manifolds and Causal Sets as Partially Ordered Measure Spaces

We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each Lorentzian metric. This places the structure normally used to describe spacetime in geometrical theories of gravity in a more general context, which includes the locally finite partially ordered sets of the causal set approach to quantum gravity. We then introduce a function characterizing the closeness between any two partially ordered measure spaces and show that, when restricted to compact spaces satisfying a simple separability condition, it is a distance. In particular, this provides a quantitative, covariant way of describing how close two manifolds with Lorentzian metrics are, or how manifoldlike a causal set is.

gr-qc↗

arXiv2011

Asymptotically anti de Sitter spacetimes in three dimensions

We revisit the asymptotically Anti de Sitter spacetimes in three dimensions. Using the conformal-completion technique, we formulate the boundary conditions in a covariant fashion and construct the global charges associated with the asymptotic symmetries. The charges so constructed are conserved for the asymptotic Killing vectors fields but are not conserved for the asymptotic conformal Killing vector fields. The quantity integrated to obtain the global charge is interpreted as the Brown-York boundary stress-energy tensor and it is found not to be traceless. The trace is interpreted as the trace anomaly and it turns out to be the same as the Brown-Henneaux central charge.

gr-qc↗

arXiv2009

Semiclassical Quantum Gravity: Obtaining Manifolds from Graphs

We address the "inverse problem" for discrete geometry, which consists in determining whether, given a discrete structure of a type that does not in general imply geometrical information or even a topology, one can associate with it a unique manifold in an appropriate sense, and constructing the manifold when it exists. This problem arises in a variety of approaches to quantum gravity that assume a discrete structure at the fundamental level; the present work is motivated by the semiclassical sector of loop quantum gravity, so we will take the discrete structure to be a graph and the manifold to be a spatial slice in spacetime. We identify a class of graphs, those whose vertices have a fixed valence, for which such a construction can be specified. We define a procedure designed to produce a cell complex from a graph and show that, for graphs with which it can be carried out to completion, the resulting cell complex is in fact a PL-manifold. Graphs of our class for which the procedure cannot be completed either do not arise as edge graphs of manifold cell decompositions, or can be seen as cell decompositions of manifolds with structure at small scales (in terms of the cell spacing). We also comment briefly on how one can extend our procedure to more general graphs.

gr-qc↗

arXiv2009

Dynamics for causal sets with matter fields: A Lagrangian-based approach

We present a framework for the dynamics of causal sets and coupled matter fields, which is a simplification and generalization of an approach we recently proposed. Given a set of fields including the gravitational one, the main step in implementing our proposal consists in writing their continuum-based action using as variables for the spacetime geometry the causal order and volume element. One then discretizes the resulting expression, with a procedure designed to maintain covariance. After a discussion of the general framework, we treat in detail the case of scalar fields, Yang-Mills gauge fields and the gravitational field.

gr-qc↗

arXiv2008

A Computation of the Expected Number of Posts in a Finite Random Graph Order

A random graph order is a partial order achieved by independently sprinkling relations on a vertex set (each with probability $p$) and adding relations to satisfy the requirement of transitivity. A \textit{post} is an element in a partially ordered set which is related to every other element. Alon et al.\ \cite{Alon} proved a result for the average number of posts among the elements $\{1,2,...,n\}$ in a random graph order on $\mathbb{Z}$. We refine this result by providing an expression for the average number of posts in a random graph order on $\{1,2,...,n\}$, thereby quantifying the edge effects associated with the elements $\mathbb{Z}\backslash\{1,2,...,n\}$. Specifically, we prove that the expected number of posts in a random graph order of size $n$ is asymptotically linear in $n$ with a positive $y$-intercept. The error associated with this approximation decreases monotonically and rapidly in $n$, permitting accurate computation of the expected number of posts for any $n$ and $p$. We also prove, as a lemma, a bound on the difference between the Euler function and its partial products that may be of interest in its own right.

math.CO↗

arXiv2008

Gravity and Matter in Causal Set Theory

The goal of this paper is to propose an approach to the formulation of dynamics for causal sets and coupled matter fields. We start from the continuum version of the action for a Klein-Gordon field coupled to gravity, and rewrite it first using quantities that have a direct correspondent in the case of a causal set, namely volumes, causal relations, and timelike lengths, as variables to describe the geometry. In this step, the local Lagrangian density $L(f;x)$ for a set of fields $f$ is recast into a quasilocal expression $L_0(f;p,q)$ that depends on pairs of causally related points $p \prec q$ and is a function of the values of $f$ in the Alexandrov set defined by those points, and whose limit as $p$ and $q$ approach a common point $x$ is $L(f;x)$. We then describe how to discretize $L_0(f;p,q)$, and use it to define a discrete action.

gr-qc↗

arXiv2006

Discreteness without symmetry breaking: a theorem

This paper concerns sprinklings into Minkowski space (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to ``Lorentz breaking'' effects like modified dispersion relations. Another consequence is that there is no way to associate a finite-valency graph to a sprinkling consistently with Lorentz invariance.

gr-qc↗

arXiv2005

Semiclassical States for Constrained Systems

The notion of semi-classical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is applied to kinematical coherent states to obtain physical semi-classical states. In the specific examples considered, the technique turns out to be surprisingly efficient, suggesting that it may well be possible to use kinematical structures to analyze the semi-classical behavior of physical states of an interesting class of constrained systems.

gr-qc↗

arXiv2004

Semiclassical Quantum Gravity: Statistics of Combinatorial Riemannian Geometries

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum scales" and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a "semiclassical" state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity.

gr-qc↗