Modified Gravity and Cosmology

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

f(R) theories

Generalized Linear Models (2nd ed.)

The observable universe could be a 1 + 3-surface (the “brane”) embedded in a 1 + 3 + d-dimensional spacetime (the “bulk”), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the d extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak (∼ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1 + 10-dimensional M theory encompasses the known 1 + 9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. General relativity cannot describe gravity at high enough energies and must be replaced by a quantum gravity theory, picking up significant corrections as the fundamental energy scale is approached. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity “leaks” into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review discusses the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall-Sundrum models.

Brane-World Gravity

We update the constraints on the fraction of the Universe going into primordial black holes in the mass range ${10}^{9}--{10}^{17}\text{ }\text{ }\mathrm{g}$ associated with the effects of their evaporations on big bang nucleosynthesis and the extragalactic photon background. We include for the first time all the effects of quark and gluon emission by black holes on these constraints and account for the latest observational developments. We then discuss the other constraints in this mass range and show that these are weaker than the nucleosynthesis and photon background limits, apart from a small range ${10}^{13}--{10}^{14}\text{ }\text{ }\mathrm{g}$, where the damping of cosmic microwave background anisotropies dominates. Finally we review the gravitational and astrophysical effects of nonevaporating primordial black holes, updating constraints over the broader mass range $1--{10}^{50}\text{ }\text{ }\mathrm{g}$.

New cosmological constraints on primordial black holes

Background Reducing the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a global priority. Contact tracing identifies people who were recently in contact with an infected individual, in order to isolate them and reduce further transmission. Digital technology could be implemented to augment and accelerate manual contact tracing. Digital tools for contact tracing may be grouped into three areas: 1) outbreak response; 2) proximity tracing; and 3) symptom tracking. We conducted a rapid review on the effectiveness of digital solutions to contact tracing during infectious disease outbreaks. Objectives To assess the benefits, harms, and acceptability of personal digital contact tracing solutions for identifying contacts of an identified positive case of an infectious disease. Search methods An information specialist searched the literature from 1 January 2000 to 5 May 2020 in CENTRAL, MEDLINE, and Embase. Additionally, we screened the Cochrane COVID-19 Study Register. Selection criteria We included randomised controlled trials (RCTs), cluster-RCTs, quasi-RCTs, cohort studies, cross-sectional studies and modelling studies, in general populations. We preferentially included studies of contact tracing during infectious disease outbreaks (including COVID-19, Ebola, tuberculosis, severe acute respiratory syndrome virus, and Middle East respiratory syndrome) as direct evidence, but considered comparative studies of contact tracing outside an outbreak as indirect evidence. The digital solutions varied but typically included software (or firmware) for users to install on their devices or to be uploaded to devices provided by governments or third parties. Control measures included traditional or manual contact tracing, self-reported diaries and surveys, interviews, other standard methods for determining close contacts, and other technologies compared to digital solutions (e.g. electronic medical records). Data collection and analysis Two review authors independently screened records and all potentially relevant full-text publications. One review author extracted data for 50% of the included studies, another extracted data for the remaining 50%; the second review author checked all the extracted data. One review author assessed quality of included studies and a second checked the assessments. Our outcomes were identification of secondary cases and close contacts, time to complete contact tracing, acceptability and accessibility issues, privacy and safety concerns, and any other ethical issue identified. Though modelling studies will predict estimates of the effects of different contact tracing solutions on outcomes of interest, cohort studies provide empirically measured estimates of the effects of different contact tracing solutions on outcomes of interest. We used GRADE-CERQual to describe certainty of evidence from qualitative data and GRADE for modelling and cohort studies. Main results We identified six cohort studies reporting quantitative data and six modelling studies reporting simulations of digital solutions for contact tracing. Two cohort studies also provided qualitative data. Three cohort studies looked at contact tracing during an outbreak, whilst three emulated an outbreak in non-outbreak settings (schools). Of the six modelling studies, four evaluated digital solutions for contact tracing in simulated COVID-19 scenarios, while two simulated close contacts in non-specific outbreak settings. Modelling studies Two modelling studies provided low-certainty evidence of a reduction in secondary cases using digital contact tracing (measured as average number of secondary cases per index case - effective reproductive number (R eff)). One study estimated an 18% reduction in R eff with digital contact tracing compared to self-isolation alone, and a 35% reduction with manual contact-tracing. Another found a reduction in R eff for digital contact tracing compared to self-isolation alone (26% reduction) and a reduction in R eff for manual contact tracing compared to self-isolation alone (53% reduction). However, the certainty of evidence was reduced by unclear specifications of their models, and assumptions about the effectiveness of manual contact tracing (assumed 95% to 100% of contacts traced), and the proportion of the population who would have the app (53%). Cohort studies Two cohort studies provided very low-certainty evidence of a benefit of digital over manual contact tracing. During an Ebola outbreak, contact tracers using an app found twice as many close contacts per case on average than those using paper forms. Similarly, after a pertussis outbreak in a US hospital, researchers found that radio-frequency identification identified 45 close contacts but searches of electronic medical records found 13. The certainty of evidence was reduced by concerns about imprecision, and serious risk of bias due to the inability of contact tracing study designs to identify the true number of close contacts. One cohort study provided very low-certainty evidence that an app could reduce the time to complete a set of close contacts. The certainty of evidence for this outcome was affected by imprecision and serious risk of bias. Contact tracing teams reported that digital data entry and management systems were faster to use than paper systems and possibly less prone to data loss. Two studies from lower- or middle-income countries, reported that contact tracing teams found digital systems simpler to use and generally preferred them over paper systems; they saved personnel time, reportedly improved accuracy with large data sets, and were easier to transport compared with paper forms. However, personnel faced increased costs and internet access problems with digital compared to paper systems. Devices in the cohort studies appeared to have privacy from contacts regarding the exposed or diagnosed users. However, there were risks of privacy breaches from snoopers if linkage attacks occurred, particularly for wearable devices. Authors' conclusions The effectiveness of digital solutions is largely unproven as there are very few published data in real-world outbreak settings. Modelling studies provide low-certainty evidence of a reduction in secondary cases if digital contact tracing is used together with other public health measures such as self-isolation. Cohort studies provide very low-certainty evidence that digital contact tracing may produce more reliable counts of contacts and reduce time to complete contact tracing. Digital solutions may have equity implications for at-risk populations with poor internet access and poor access to digital technology. Stronger primary research on the effectiveness of contact tracing technologies is needed, including research into use of digital solutions in conjunction with manual systems, as digital solutions are unlikely to be used alone in real-world settings. Future studies should consider access to and acceptability of digital solutions, and the resultant impact on equity. Studies should also make acceptability and uptake a primary research question, as privacy concerns can prevent uptake and effectiveness of these technologies.

Digital contact tracing technologies in epidemics: a rapid review

Metasurfaces based on resonant nanophotonic structures have enabled novel types of flat-optics devices often outperforming the capabilities of bulk components, yet these advances remain largely unexplored for quantum applications. We show that non-classical multi-photon interferences can be achieved at the subwavelength scale in all-dielectric metasurfaces. We simultaneously image multiple projections of quantum states with a single metasurface, enabling a robust reconstruction of amplitude, phase, coherence, and entanglement of multi-photon polarization-encoded states. One- and two-photon states are reconstructed through nonlocal photon correlation measurements with polarization-insensitive click-detectors positioned after the metasurface, and the scalability to higher photon numbers is established theoretically. Our work illustrates the feasibility of ultra-thin quantum metadevices for the manipulation and measurement of multi-photon quantum states with applications in free-space quantum imaging and communications.

Quantum metasurface for multi-photon interference and state reconstruction

We investigate proper scoring rules for continuous distributions on the real line. It is known that the log score is the only such rule that depends on the quoted density only through its value at the outcome that materializes. Here we allow further dependence on a finite number $m$ of derivatives of the density at the outcome, and describe a large class of such $m$-local proper scoring rules: these exist for all even $m$ but no odd $m$. We further show that for $m\geq2$ all such $m$-local rules can be computed without knowledge of the normalizing constant of the distribution.

Proper local scoring rules

We investigate proper scoring rules for continuous distributions on the real line. It is known that the log score is the only such rule that depends on the quoted density only through its value at the outcome that materializes. Here we allow further dependence on a finite number m of derivatives of the density at the outcome, and describe a large class of such m-local proper scoring rules: these exist for all even m but no odd m. We further show that for m ≥ 2 all such m-local rules can be computed without knowledge of the normalizing constant of the distribution.

/pdf/proper-local-scoring-rules-3bsuajcc43.pdf

Matthew Parry

Papers

Digital contact tracing technologies in epidemics: a rapid review

Quantum metasurface for multi-photon interference and state reconstruction

Proper local scoring rules

Proper local scoring rules

Cosmological consequences of the brane/bulk interaction