The effective field theory of inflation/dark energy and the Horndeski theory

Abstract

The effective field theory (EFT) of cosmological perturbations is a useful framework to deal with the low-energy degrees of freedom present for inflation and dark energy. We review the EFT for modified gravitational theories by starting from the most general action in unitary gauge that involves the lapse function and the three-dimensional geometric scalar quantities appearing in the Arnowitt-Deser-Misner (ADM) formalism. Expanding the action up to quadratic order in the perturbations and imposing conditions for the elimination of spatial derivatives higher than second order, we obtain the Lagrangian of curvature perturbations and gravitational waves with a single scalar degree of freedom. The resulting second-order Lagrangian is exploited for computing the scalar and tensor power spectra generated during inflation. We also show that the most general scalar-tensor theory with second-order equations of motion-Horndeski theory-belongs to the action of our general EFT framework and that the background equations of motion in Horndeski theory can be conveniently expressed in terms of three EFT parameters. Finally we study the equations of matter density perturbations and the effective gravitational coupling for dark energy models based on Horndeski theory, to confront the models with the observations of large-scale structures and weak lensing.

39 pages, no figures, lecture note for the 7th Aegean Summer School, Paros, 23-28 September, 2013

References in corpus (29)

• Dynamics of dark energy
• Cosmology and the Fate of Dilatation Symmetry
• The Standard Model Higgs boson as the inflaton
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• The Effective Field Theory of Inflation
• Covariant Galileon
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• Imperfect Dark Energy from Kinetic Gravity Braiding
• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• A Parameterized Post-Friedmann Framework for Modified Gravity
• Measuring the dark side (with weak lensing)
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• The Effective Theory of Quintessence: the w<-1 Side Unveiled
• Weak Lensing Probes of Modified Gravity
• Constraints on scalar-tensor models of dark energy from observational and local gravity tests
• Cosmological Constraints on f(R) Acceleration Models
• Large-Scale Tests of the DGP Model
• UV-Protected Inflation
• Matter perturbations in Galileon cosmology
• The dispersion of growth of matter perturbations in f(R) gravity
• Primordial non-Gaussianities in general modified gravitational models of inflation
• Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Trispectrum
• Effective field theory of modified gravity with two scalar fields: dark energy and dark matter
• The effect of modified gravity on weak lensing
• Chameleon dark energy models with characteristic signatures
• Cosmological Implications of the Effective Field Theory of Cosmic Acceleration

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• Exploring gravitational theories beyond Horndeski
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• Anisotropic stress as signature of non-standard propagation of gravitational waves
• Selected topics in scalar-tensor theories and beyond
• Hamiltonian structure of scalar-tensor theories beyond Horndeski
• Generalised tensor fluctuations and inflation
• Effective field theory approach to modified gravity including Horndeski theory and Hořava-Lifshitz gravity
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Modified gravity realizations of quintom dark energy after DESI DR2
• Weakening Gravity on Redshift-Survey Scales with Kinetic Matter Mixing
• A parametrisation of modified gravity on nonlinear cosmological scales
• Observational signatures of the theories beyond Horndeski
• Gravitational wave propagation in $f(R)$ models: New parametrizations and observational constraints
• Comparison of different approaches to the quasi-static approximation in Horndeski models
• General Effective Field Theory of Teleparallel Gravity
• Inflation with non-canonical scalar fields revisited
• Higher derivative scalar-tensor theory from the spatially covariant gravity: a linear algebraic analysis
• Positivity bounds on reconstructed Horndeski models
• Chaotic Inflation and Reheating in Generalized Scalar-Tensor Gravity
• Inflation from a generalized exponential plateau: towards extra suppressed tensor-to-scalar ratios
• Testing No slip model with pulsar timing arrays: NANOGrav and IPTA