Lorentz violating kinematics: Threshold theorems

Recent tentative experimental indications, and the subsequent theoretical speculations, regarding possible violations of Lorentz invariance have attracted a vast amount of attention. An important technical issue that considerably complicates detailed calculations in any such scenario, is that once one violates Lorentz invariance the analysis of thresholds in both scattering and decay processes becomes extremely subtle, with many new and naively unexpected effects. In the current article we develop several extremely general threshold theorems that depend only on the existence of some energy momentum relation E(p), eschewing even assumptions of isotropy or monotonicity. We shall argue that there are physically interesting situations where such a level of generality is called for, and that existing (partial) results in the literature make unnecessary technical assumptions. Even in this most general of settings, we show that at threshold all final state particles move with the same 3-velocity, while initial state particles must have 3-velocities parallel/anti-parallel to the final state particles. In contrast the various 3-momenta can behave in a complicated and counter-intuitive manner.Comment: V1: 32 pages, 6 figures, 3 tables. V2: 5 references adde

Doubly Special Relativity and de Sitter space

In this paper we recall the construction of Doubly Special Relativity (DSR) as a theory with energy-momentum space being the four dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate systems on this space. We investigate the emerging geometrical picture of Doubly Special Relativity by presenting the basis independent features of DSR that include the non-commutative structure of space-time and the phase space algebra. Next we investigate the relation between our geometric formulation and the one based on quantum $\kappa$-deformations of the Poincar\'e algebra. Finally we re-derive the five-dimensional differential calculus using the geometric method, and use it to write down the deformed Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde

Quantum symmetry, the cosmological constant and Planck scale phenomenology

We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory invariant, not under the Poincare group, but under a deformation of it parameterized by a dimensional parameter proportional to the Planck mass. Such deformations, called kappa-Poincare algebras, imply modified energy-momentum relations of a type that may be observable in near future experiments. Our argument applies in both 2+1 and 3+1 dimensions and assumes only 1) that the low energy limit of a quantum theory of gravity must involve also a limit in which the cosmological constant is taken very small with respect to the Planck scale and 2) that in 3+1 dimensions the physical energy and momenta of physical elementary particles is related to symmetries of the full quantum gravity theory by appropriate renormalization depending on Lambda l^2_{Planck}. The argument makes use of the fact that the cosmological constant results in the symmetry algebra of quantum gravity being quantum deformed, as a consequence when the limit \Lambda l^2_{Planck} -> 0 is taken one finds a deformed Poincare invariance. We are also able to isolate what information must be provided by the quantum theory in order to determine which presentation of the kappa-Poincare algebra is relevant for the physical symmetry generators and, hence, the exact form of the modified energy-momentum relations. These arguments imply that Lorentz invariance is modified as in proposals for doubly special relativity, rather than broken, in theories of quantum gravity, so long as those theories behave smoothly in the limit the cosmological constant is taken to be small.Comment: LaTex, 19 page

Comparison of relativity theories with observer-independent scales of both velocity and length/mass

We consider the two most studied proposals of relativity theories with observer-independent scales of both velocity and length/mass: the one discussed by Amelino-Camelia as illustrative example for the original proposal (gr-qc/0012051) of theories with two relativistic invariants, and an alternative more recently proposed by Magueijo and Smolin (hep-th/0112090). We show that these two relativistic theories are much more closely connected than it would appear on the basis of a naive analysis of their original formulations. In particular, in spite of adopting a rather different formal description of the deformed boost generators, they end up assigning the same dependence of momentum on rapidity, which can be described as the core feature of these relativistic theories. We show that this observation can be used to clarify the concepts of particle mass, particle velocity, and energy-momentum-conservation rules in these theories with two relativistic invariants.Comment: 21 pages, LaTex. v2: Andrea Procaccini (contributing some results from hia Laurea thesis) is added to the list of authors and the paper provides further elements of comparison between DSR1 and DSR2, including the observation that both lead to the same formula for the dependence of momentum on rapidit

New varying speed of light theories

We review recent work on the possibility of a varying speed of light (VSL). We start by discussing the physical meaning of a varying $c$, dispelling the myth that the constancy of $c$ is a matter of logical consistency. We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a color dependent speed of light; varying $c$ induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation. We show how VSL scenarios may solve the cosmological problems usually tackled by inflation, and also how they may produce a scale-invariant spectrum of Gaussian fluctuations, capable of explaining the WMAP data. We then review the connection between VSL and theories of quantum gravity, showing how ``doubly special'' relativity has emerged as a VSL effective model of quantum space-time, with observational implications for ultra high energy cosmic rays and gamma ray bursts. Some recent work on the physics of ``black'' holes and other compact objects in VSL theories is also described, highlighting phenomena associated with spatial (as opposed to temporal) variations in $c$. Finally we describe the observational status of the theory. The evidence is currently slim -- redshift dependence in the atomic fine structure, anomalies with ultra high energy cosmic rays, and (to a much lesser extent) the acceleration of the universe and the WMAP data. The constraints (e.g. those arising from nucleosynthesis or geological bounds) are tight, but not insurmountable. We conclude with the observational predictions of the theory, and the prospects for its refutation or vindication.Comment: Final versio

Prevalence Estimates of Amyloid Abnormality Across the Alzheimer Disease Clinical Spectrum

Importance: One characteristic histopathological event in Alzheimer disease (AD) is cerebral amyloid aggregation, which can be detected by biomarkers in cerebrospinal fluid (CSF) and on positron emission tomography (PET) scans. Prevalence estimates of amyloid pathology are important for health care planning and clinical trial design. Objective: To estimate the prevalence of amyloid abnormality in persons with normal cognition, subjective cognitive decline, mild cognitive impairment, or clinical AD dementia and to examine the potential implications of cutoff methods, biomarker modality (CSF or PET), age, sex, APOE genotype, educational level, geographical region, and dementia severity for these estimates. Design, Setting, and Participants: This cross-sectional, individual-participant pooled study included participants from 85 Amyloid Biomarker Study cohorts. Data collection was performed from January 1, 2013, to December 31, 2020. Participants had normal cognition, subjective cognitive decline, mild cognitive impairment, or clinical AD dementia. Normal cognition and subjective cognitive decline were defined by normal scores on cognitive tests, with the presence of cognitive complaints defining subjective cognitive decline. Mild cognitive impairment and clinical AD dementia were diagnosed according to published criteria. Exposures: Alzheimer disease biomarkers detected on PET or in CSF. Main Outcomes and Measures: Amyloid measurements were dichotomized as normal or abnormal using cohort-provided cutoffs for CSF or PET or by visual reading for PET. Adjusted data-driven cutoffs for abnormal amyloid were calculated using gaussian mixture modeling. Prevalence of amyloid abnormality was estimated according to age, sex, cognitive status, biomarker modality, APOE carrier status, educational level, geographical location, and dementia severity using generalized estimating equations. Results: Among the 19 097 participants (mean [SD] age, 69.1 [9.8] years; 10 148 women [53.1%]) included, 10 139 (53.1%) underwent an amyloid PET scan and 8958 (46.9%) had an amyloid CSF measurement. Using cohort-provided cutoffs, amyloid abnormality prevalences were similar to 2015 estimates for individuals without dementia and were similar across PET- and CSF-based estimates (24%; 95% CI, 21%-28%) in participants with normal cognition, 27% (95% CI, 21%-33%) in participants with subjective cognitive decline, and 51% (95% CI, 46%-56%) in participants with mild cognitive impairment, whereas for clinical AD dementia the estimates were higher for PET than CSF (87% vs 79%; mean difference, 8%; 95% CI, 0%-16%; P = .04). Gaussian mixture modeling-based cutoffs for amyloid measures on PET scans were similar to cohort-provided cutoffs and were not adjusted. Adjusted CSF cutoffs resulted in a 10% higher amyloid abnormality prevalence than PET-based estimates in persons with normal cognition (mean difference, 9%; 95% CI, 3%-15%; P = .004), subjective cognitive decline (9%; 95% CI, 3%-15%; P = .005), and mild cognitive impairment (10%; 95% CI, 3%-17%; P = .004), whereas the estimates were comparable in persons with clinical AD dementia (mean difference, 4%; 95% CI, -2% to 9%; P = .18). Conclusions and Relevance: This study found that CSF-based estimates using adjusted data-driven cutoffs were up to 10% higher than PET-based estimates in people without dementia, whereas the results were similar among people with dementia. This finding suggests that preclinical and prodromal AD may be more prevalent than previously estimated, which has important implications for clinical trial recruitment strategies and health care planning policies

Prevalence Estimates of Amyloid Abnormality Across the Alzheimer Disease Clinical Spectrum

Importance: One characteristic histopathological event in Alzheimer disease (AD) is cerebral amyloid aggregation, which can be detected by biomarkers in cerebrospinal fluid (CSF) and on positron emission tomography (PET) scans. Prevalence estimates of amyloid pathology are important for health care planning and clinical trial design. Objective: To estimate the prevalence of amyloid abnormality in persons with normal cognition, subjective cognitive decline, mild cognitive impairment, or clinical AD dementia and to examine the potential implications of cutoff methods, biomarker modality (CSF or PET), age, sex, APOE genotype, educational level, geographical region, and dementia severity for these estimates. Design, Setting, and Participants: This cross-sectional, individual-participant pooled study included participants from 85 Amyloid Biomarker Study cohorts. Data collection was performed from January 1, 2013, to December 31, 2020. Participants had normal cognition, subjective cognitive decline, mild cognitive impairment, or clinical AD dementia. Normal cognition and subjective cognitive decline were defined by normal scores on cognitive tests, with the presence of cognitive complaints defining subjective cognitive decline. Mild cognitive impairment and clinical AD dementia were diagnosed according to published criteria. Exposures: Alzheimer disease biomarkers detected on PET or in CSF. Main Outcomes and Measures: Amyloid measurements were dichotomized as normal or abnormal using cohort-provided cutoffs for CSF or PET or by visual reading for PET. Adjusted data-driven cutoffs for abnormal amyloid were calculated using gaussian mixture modeling. Prevalence of amyloid abnormality was estimated according to age, sex, cognitive status, biomarker modality, APOE carrier status, educational level, geographical location, and dementia severity using generalized estimating equations. Results: Among the 19 097 participants (mean [SD] age, 69.1 [9.8] years; 10 148 women [53.1%]) included, 10 139 (53.1%) underwent an amyloid PET scan and 8958 (46.9%) had an amyloid CSF measurement. Using cohort-provided cutoffs, amyloid abnormality prevalences were similar to 2015 estimates for individuals without dementia and were similar across PET- and CSF-based estimates (24%; 95% CI, 21%-28%) in participants with normal cognition, 27% (95% CI, 21%-33%) in participants with subjective cognitive decline, and 51% (95% CI, 46%-56%) in participants with mild cognitive impairment, whereas for clinical AD dementia the estimates were higher for PET than CSF (87% vs 79%; mean difference, 8%; 95% CI, 0%-16%; P = .04). Gaussian mixture modeling-based cutoffs for amyloid measures on PET scans were similar to cohort-provided cutoffs and were not adjusted. Adjusted CSF cutoffs resulted in a 10% higher amyloid abnormality prevalence than PET-based estimates in persons with normal cognition (mean difference, 9%; 95% CI, 3%-15%; P = .004), subjective cognitive decline (9%; 95% CI, 3%-15%; P = .005), and mild cognitive impairment (10%; 95% CI, 3%-17%; P = .004), whereas the estimates were comparable in persons with clinical AD dementia (mean difference, 4%; 95% CI, -2% to 9%; P = .18). Conclusions and Relevance: This study found that CSF-based estimates using adjusted data-driven cutoffs were up to 10% higher than PET-based estimates in people without dementia, whereas the results were similar among people with dementia. This finding suggests that preclinical and prodromal AD may be more prevalent than previously estimated, which has important implications for clinical trial recruitment strategies and health care planning policies

Prevalence Estimates of Amyloid Abnormality Across the Alzheimer Disease Clinical Spectrum

Importance: One characteristic histopathological event in Alzheimer disease (AD) is cerebral amyloid aggregation, which can be detected by biomarkers in cerebrospinal fluid (CSF) and on positron emission tomography (PET) scans. Prevalence estimates of amyloid pathology are important for health care planning and clinical trial design. Objective: To estimate the prevalence of amyloid abnormality in persons with normal cognition, subjective cognitive decline, mild cognitive impairment, or clinical AD dementia and to examine the potential implications of cutoff methods, biomarker modality (CSF or PET), age, sex, APOE genotype, educational level, geographical region, and dementia severity for these estimates. Design, Setting, and Participants: This cross-sectional, individual-participant pooled study included participants from 85 Amyloid Biomarker Study cohorts. Data collection was performed from January 1, 2013, to December 31, 2020. Participants had normal cognition, subjective cognitive decline, mild cognitive impairment, or clinical AD dementia. Normal cognition and subjective cognitive decline were defined by normal scores on cognitive tests, with the presence of cognitive complaints defining subjective cognitive decline. Mild cognitive impairment and clinical AD dementia were diagnosed according to published criteria. Exposures: Alzheimer disease biomarkers detected on PET or in CSF. Main Outcomes and Measures: Amyloid measurements were dichotomized as normal or abnormal using cohort-provided cutoffs for CSF or PET or by visual reading for PET. Adjusted data-driven cutoffs for abnormal amyloid were calculated using gaussian mixture modeling. Prevalence of amyloid abnormality was estimated according to age, sex, cognitive status, biomarker modality, APOE carrier status, educational level, geographical location, and dementia severity using generalized estimating equations. Results: Among the 19097 participants (mean [SD] age, 69.1 [9.8] years; 10148 women [53.1%]) included, 10139 (53.1%) underwent an amyloid PET scan and 8958 (46.9%) had an amyloid CSF measurement. Using cohort-provided cutoffs, amyloid abnormality prevalences were similar to 2015 estimates for individuals without dementia and were similar across PET- and CSF-based estimates (24%; 95% CI, 21%-28%) in participants with normal cognition, 27% (95% CI, 21%-33%) in participants with subjective cognitive decline, and 51% (95% CI, 46%-56%) in participants with mild cognitive impairment, whereas for clinical AD dementia the estimates were higher for PET than CSF (87% vs 79%; mean difference, 8%; 95% CI, 0%-16%; P =.04). Gaussian mixture modeling-based cutoffs for amyloid measures on PET scans were similar to cohort-provided cutoffs and were not adjusted. Adjusted CSF cutoffs resulted in a 10% higher amyloid abnormality prevalence than PET-based estimates in persons with normal cognition (mean difference, 9%; 95% CI, 3%-15%; P =.004), subjective cognitive decline (9%; 95% CI, 3%-15%; P =.005), and mild cognitive impairment (10%; 95% CI, 3%-17%; P =.004), whereas the estimates were comparable in persons with clinical AD dementia (mean difference, 4%; 95% CI, -2% to 9%; P =.18). Conclusions and Relevance: This study found that CSF-based estimates using adjusted data-driven cutoffs were up to 10% higher than PET-based estimates in people without dementia, whereas the results were similar among people with dementia. This finding suggests that preclinical and prodromal AD may be more prevalent than previously estimated, which has important implications for clinical trial recruitment strategies and health care planning policies