TY - JOUR

T1 - The effective field theory of inflation/dark energy and the Horndeski theory

AU - Tsujikawa, Shinji

N1 - Funding Information:
The author is grateful to the organizers of the 7th Aegean Summer School for wonderful hospitality. The author thanks Antonio De Felice, Laszlo Arpad Gergely, and Federico Piazza for useful discussions. This work was supported by Grant-in-Aid for Scientific Research Fund of the JSPS (No. 30318802) and Grant-in-Aid for Scientific Research on Innovative Areas (No. 21111006).
Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - 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 scalartensor 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.

AB - 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 scalartensor 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.

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U2 - 10.1007/978-3-319-10070-8__4

DO - 10.1007/978-3-319-10070-8__4

M3 - Article

AN - SCOPUS:84921634385

SN - 0075-8450

VL - 892

SP - 97

EP - 136

JO - Lecture Notes in Physics

JF - Lecture Notes in Physics

ER -