A Note on Infinities in Eternal Inflation

In some well-known scenarios of open-universe eternal inflation, developed by Vilenkin and co-workers, a large number of universes nucleate and thermalize within the eternally inflating mega-universe. According to the proposal, each universe nucleates at a point, and therefore the boundary of the nucleated universe is a space-like surface nearly coincident with the future light cone emanating from the point of nucleation, all points of which have the same proper-time. This leads the authors to conclude that at the proper-time t = t_{nuc} at which any such nucleation occurs, an infinite open universe comes into existence. We point out that this is due entirely to the supposition of the nucleation occurring at a single point, which in light of quantum cosmology seems difficult to support. Even an infinitesimal space-like length at the moment of nucleation gives a rather different result -- the boundary of the nucleating universe evolves in proper-time and becomes infinite only in an infinite time. The alleged infinity is never attained at any finite time.Comment: 13 pages and 6 figure

A Hamilton-Jacobi approach to non-slow-roll inflation

I describe a general approach to characterizing cosmological inflation outside the standard slow-roll approximation, based on the Hamilton-Jacobi formulation of scalar field dynamics. The basic idea is to view the equation of state of the scalar field matter as the fundamental dynamical variable, as opposed to the field value or the expansion rate. I discuss how to formulate the equations of motion for scalar and tensor fluctuations in situations where the assumption of slow roll is not valid. I apply the general results to the simple case of inflation from an ``inverted'' polynomial potential, and to the more complicated case of hybrid inflation.Comment: 21 pages, RevTeX (minor revisions to match published version

Imprints of Short Distance Physics On Inflationary Cosmology

We analyze the impact of certain modifications to short distance physics on the inflationary perturbation spectrum. For the specific case of power-law inflation, we find distinctive -- and possibly observable -- effects on the spectrum of density perturbations.Comment: Revtex 4, 3 eps figs, 4 page

Inflation: flow, fixed points and observables to arbitrary order in slow roll

I generalize the inflationary flow equations of Hoffman and Turner to arbitrary order in slow roll. This makes it possible to study the predictions of slow roll inflation in the full observable parameter space of tensor/scalar ratio $r$, spectral index $n$, and running $d n / d \ln k$. It also becomes possible to identify exact fixed points in the parameter flow. I numerically evaluate the flow equations to fifth order in slow roll for a set of randomly chosen initial conditions and find that the models cluster strongly in the observable parameter space, indicating a ``generic'' set of predictions for slow roll inflation. I comment briefly on the the interesting proposed correspondence between flow in inflationary parameter space and renormalization group flow in a boundary conformal field theory.Comment: 16 pages, 7 figures. LaTeX. V4: Fixed important error in numerical constant in the second-order slow roll expressions for the observables r, n, and dn/dlog(k). See footnote after Eq. (48). New figures, minor changes to conclusions. Supersedes version published in Phys. Rev.

The ATLAS inner detector trigger performance in pp collisions at 13 TeV during LHC Run 2

The design and performance of the inner detector trigger for the high level trigger of the ATLAS experiment at the Large Hadron Collider during the 2016-18 data taking period is discussed. In 2016, 2017, and 2018 the ATLAS detector recorded 35.6 fb$^{-1}$, 46.9 fb$^{-1}$, and 60.6 fb$^{-1}$ respectively of proton-proton collision data at a centre-of-mass energy of 13 TeV. In order to deal with the very high interaction multiplicities per bunch crossing expected with the 13 TeV collisions the inner detector trigger was redesigned during the long shutdown of the Large Hadron Collider from 2013 until 2015. An overview of these developments is provided and the performance of the tracking in the trigger for the muon, electron, tau and $b$-jet signatures is discussed. The high performance of the inner detector trigger with these extreme interaction multiplicities demonstrates how the inner detector tracking continues to lie at the heart of the trigger performance and is essential in enabling the ATLAS physics programme

The ATLAS inner detector trigger performance in pp collisions at 13 TeV during LHC Run 2

The design and performance of the inner detector trigger for the high level trigger of the ATLAS experiment at the Large Hadron Collider during the 2016-18 data taking period is discussed. In 2016, 2017, and 2018 the ATLAS detector recorded 35.6 fb$^{-1}$, 46.9 fb$^{-1}$, and 60.6 fb$^{-1}$ respectively of proton-proton collision data at a centre-of-mass energy of 13 TeV. In order to deal with the very high interaction multiplicities per bunch crossing expected with the 13 TeV collisions the inner detector trigger was redesigned during the long shutdown of the Large Hadron Collider from 2013 until 2015. An overview of these developments is provided and the performance of the tracking in the trigger for the muon, electron, tau and $b$-jet signatures is discussed. The high performance of the inner detector trigger with these extreme interaction multiplicities demonstrates how the inner detector tracking continues to lie at the heart of the trigger performance and is essential in enabling the ATLAS physics programme

Observation of electroweak production of two jets in association with an isolated photon and missing transverse momentum, and search for a Higgs boson decaying into invisible particles at 13 TeV with the ATLAS detector

This paper presents the measurement of the electroweak production of two jets in association with a $Z\gamma$ pair with the $Z$ boson decaying into two neutrinos. It also presents the search for invisible or partially invisible decays of a Higgs boson with a mass of 125 GeV produced through vector-boson fusion with a photon in the final state. These results use data from LHC proton-proton collisions at $\sqrt{s}$ = 13 TeV collected with the ATLAS detector corresponding to an integrated luminosity of 139 fb$^{-1}$. The event signature, shared by all benchmark processes considered for measurements and searches, is characterized by a significant amount of unbalanced transverse momentum and a photon in the final state, in addition to a pair of forward jets. For electroweak production of $Z\gamma$ in association with two jets, the background-only hypothesis is rejected with an observed (expected) significance of 5.2 (5.1) standard deviations. The measured fiducial cross-section for this process is 1.31$\pm$0.29 fb. Observed (expected) upper limit of 0.37 (0.34) at 95% confidence level is set on the branching ratio of a 125 GeV Higgs boson to invisible particles, assuming the Standard Model production cross-section. The signature is also interpreted in the context of decays of a Higgs boson to a photon and a dark photon. An observed (expected) 95% CL upper limit on the branching ratio for this decay is set at 0.018 (0.017), assuming the 125 GeV Standard Model Higgs boson production cross-section

Developing new avenues for growth: Challenges presented by five trends in the global environment

This paper documents five major trends in the global environment, and examines the impact of each on the corporate strategies of multinational firms striving for higher rates of growth in corporate earnings. The five trends documented are: 1. shifts in economic activity and growth between and within regions of the world; 2. increasing demand for goods and services among the very poor in emerging markets; 3. a faster pace and wider locus of technological innovation; 4. Increasingly global labor markets; and 5. increasingly ubiquitous and inexpensive access to information and knowledge. Each of these trends presents multinational firms with a potentially new avenue for growth, or an avenue down which they should consider moving further and/or faster. These potentially new avenues for growth are encouraging managers of multinational firms to challenge the current corporate strategies of their firms, and examine the need to reorient or renew them. The paper discusses the strategic challenges associated with these new avenues for growth, and the need for more research on the concept of country risk, on the concepts of the transnational strategy and organizational structure, and on the challenges of very limited sustainable capacity to consume among the very poor.Corporate strategy Strategic reorientation Strategic renewal New avenues for growth Firm geographic scope Very poor customers Technological innovation Outsourcing Offshoring Surplus labor markets Transnational organization structure Ambiguous knowledge