Tackling non-linearities with the effective field theory of dark energy and modified gravity

We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly non-linear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, non-linear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding non-linear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the non-linear effective field theory framework by considering a general action in the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we proceed to map the beyond-Horndeski theory and low-energy Horava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the non-linear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly non-linear scales.Comment: 19 pages. Sec IV and Appendix B added. Matches JCAP versio

An Extended action for the effective field theory of dark energy: a stability analysis and a complete guide to the mapping at the basis of EFTCAMB

We present a generalization of the effective field theory (EFT) formalism for dark energy and modified gravity models to include operators with higher order spatial derivatives. This allows the extension of the EFT framework to a wider class of gravity theories such as Horava gravity. We present the corresponding extended action, both in the EFT and the Arnowitt-Deser-Misner (ADM) formalism, and proceed to work out a convenient mapping between the two, providing a self contained and general procedure to translate a given model of gravity into the EFT language at the basis of the Einstein-Boltzmann solver EFTCAMB. Putting this mapping at work, we illustrate, for several interesting models of dark energy and modified gravity, how to express them in the ADM notation and then map them into the EFT formalism. We also provide for the first time, the full mapping of GLPV models into the EFT framework. We next perform a thorough analysis of the physical stability of the generalized EFT action, in absence of matter components. We work out viability conditions that correspond to the absence of ghosts and modes that propagate with a negative speed of sound in the scalar and tensor sector, as well as the absence of tachyonic modes in the scalar sector. Finally, we extend and generalize the phenomenological basis in terms of $\alpha$-functions introduced to parametrize Horndeski models, to cover all theories with higher order spatial derivatives included in our extended action. We elaborate on the impact of the additional functions on physical quantities, such as the kinetic term and the speeds of propagation for scalar and tensor modes.Comment: 36 pages, matches published version, typos correcte

A de Sitter limit analysis for dark energy and modified gravity models

The effective field theory of dark energy and modified gravity is supposed to well describe, at low energies, the behaviour of the gravity modifications due to one extra scalar degree of freedom. The usual curvature perturbation is very useful when studying the conditions for the avoidance of ghost instabilities as well as the positivity of the squared speeds of propagation for both the scalar and tensor modes, or the St\"uckelberg field performs perfectly when investigating the evolution of linear perturbations. We show that the viable parameters space identified by requiring no-ghost instabilities and positive squared speeds of propagation does not change by performing a field redefinition, while the requirement of the avoidance of tachyonic instability might instead be different. Therefore, we find interesting to associate to the general modified gravity theory described in the effective field theory framework, a perturbation field which will inherit the whole properties of the theory. In the present paper we address the following questions: 1) how can we define such a field? and 2) what is the mass of such a field as the background approaches a final de Sitter state? We define a gauge invariant quantity which identifies the density of the dark energy perturbation field valid for any background. We derive the mass associated to the gauge invariant dark energy field on a de Sitter background, which we retain to be still a good approximation also at very low redshift ($z\simeq 0$). On this background we also investigate the value of the speed of propagation and we find that there exist classes of theories which admit a non-vanishing speed of propagation, even among the Horndeski model, for which in literature it has previously been found a zero speed. We finally apply our results to specific well known models.Comment: 22 page

The role of the tachyonic instability in Horndeski gravity

The tachyonic instability is associated with the unboundedness of the Hamiltonian from below and results in an unstable low-$k$ regime. In the cosmological exploration of modified gravity, it is seldom taken into account, with more focus given to the popular no-ghost and no-gradient conditions. The latter though are intrinsically high-$k$ statements. Here we combine all three conditions into a full set of requirements that we show to guarantee stability on the whole range of cosmological scales. We then explore the impact of the different conditions on the parameter space of scalar-tensor gravity, with particular emphasis on the no-tachyon one. We focus on Horndeski gravity and also consider separately the two subclasses of $f(R)$ and Generalized Brans Dicke theories. We identify several interesting features, for instance in the parameter space of designer $f(R)$ on a $w$CDM background, shedding light on previous findings. When looking at the phenomenological functions $\Sigma$ and $\mu$, associated to the weak lensing and clustering potential respectively, we find that in the case of Generalized Brans Dicke the no-tachyon condition clearly cuts models with $\mu\,,\,\Sigma>1$. This effect is less prevalent in the Horndeski case due to the larger amount of free functions in the theory.Comment: 9 pages, 4 figures - accepted version by JCA

Into the darkness : forging a stable path through the gravitational landscape

In this thesis we study the landscape of gravitational models which modify GR by introducing an additional scalar degree of freedom (d.o.f.) to source Cosmic Acceleration. In particular we answer the question "What is the complete set of theoretical conditions a gravitational model must satisfy, in order to give a theoretically viable cosmology?". In order to study the theoretical stability of extended models of gravity we emplout the E ective Field Theory of Dark Energy and Modied Gravity (EFToDE/MG). This is a unifying framework which allows us to study the landscape of gravitational models in a broad and model independent way. This will allow us to answer the research question in a model independent way. The D-ITP consortium, an initiative by the NWOTheoretical Physic

Prediction of chronic postsurgical pain in adults: A protocol for multivariable prediciton model development

INTRODUCTION: Chronic postsurgical pain (CPSP) is a condition that affects an estimated 10%–50% of adults, depending on the surgical procedure. CPSP often interferes with activities of daily living and may have a negative impact on quality of life, emotional and physical well-being. Clinical prediction models can help clinicians target preventive strategies towards patients at high-risk of CPSP. Therefore, the objective of this study is to develop a clinically applicable and generalisable prediction model for CPSP in adults. METHODS AND ANALYSIS: This research will be a prospective single-centre observational cohort study in Denmark spanning approximately 1 year or until a predefined number of patients are recruited (n=1526). Adult patients aged 18 years and older scheduled to undergo surgery will be recruited at Aarhus University Hospital. The primary outcome is CPSP 3 months after surgery defined as average pain intensity at rest or on movement ≥3 on numerical rating scale (NRS) within the past week, and/or average pain interference ≥3 on NRS among any of seven short-form Brief Pain Inventory items in the past week (general activity, mood, walking ability, normal work (including housework), relations with other people, sleep and enjoyment of life). Logistic regression will be used to conduct multivariate analysis. Predictive model performance will be evaluated by discrimination, calibration and model classification. ETHICS AND DISSEMINATION: This research has been approved by Central Region Denmark and will be conducted in accordance with the Danish Data Protection Act and Declaration of Helsinki. Study findings will be disseminated through conference presentations and peer-reviewed publication. A CPSP risk calculator (CPSP-RC) will be developed based on predictors retained in the final models. The CPSP-RC will be made available online and as a mobile application to be easily accessible for clinical use and future research including validation and clinical impact assessments. TRIAL REGISTRATION NUMBER: NCT04866147

On the stability conditions for theories of modified gravity in the presence of matter fields

Theoretical Physic

The posterior portion of the ilium as a sex indicator:A validation study

Establishing a biological profile of skeletal remains is a key task of forensic anthropologists. Sex estimation is essential in forensic examination, as other elements of the biological profile, such as age at death or stature, are sex dependent. Visual assessment is considered low-cost and quick, therefore it is a commonly applied method of sex estimation. The most reliable results can be obtained with the analysis of the anterior part of the pelvis, however, these skeletal elements are fragile and prone to destruction. In contrary, the more robust posterior portion of the pelvis is often recovered. Several features of the posterior pelvis have been explored in the context of sexual dimorphism. The aim of the present study was to test three previously published methods of sex assessment based on the analysis of the inferior shape of the auricular surface (Novotný, 1975), the greater sciatic notch shape (Walker, 2005 (revised)) and overall morphology, apex morphology and inflection of the auricular surface (Luna et al., 2017). The sample consisted of 194 individuals of Greek origin from a documented modern collection. Four features of the auricular surface and shape of the greater sciatic notch were examined. Logistic regression analysis was applied to produce a sex discriminatory formula. The method proposed by Luna et al. (2017) failed to produce satisfactory results with overall accuracies of 36%, 50% and 53% for overall morphology, apex morphology and inflection respectively. Slightly better results (64%) were obtained with the inferior shape morphology (Novotný, 1975). However, the highest accuracy rate of 81% was noted for the greater sciatic notch shape (Walker, 2005 (revised)). The formula produced in this study allowed correct classification of 83.2% of the sample. This study illustrates that in spite of the presence of sexual dimorphism in the posterior portion of ilium, features of the auricular surface proposed as sex indicators by Novotný (1975) and Luna et al. (2017) should not be used for sex estimation purposes in the Greek population. The formula produced in this study and the greater sciatic notch shape should only be used as additional methods in cases where neither the cranium nor the anterior portion of the pelvis is present