Essential Building Blocks of Dark Energy

By J. Gleyzes, D. Langlois, F. Piazza, F. Vernizzi. 2013

353 citations recorded by the source corpus.

We propose a minimal description of single field dark energy/modified gravity within the effective field theory formalism for cosmological perturbations, which encompasses most existing models. We start from a generic Lagrangian given as an arbitrary function of the lapse and of the extrinsic and intrinsic curvature tensors of the time hypersurfaces in unitary gauge, i.e. choosing as time slicing the uniform scalar field hypersurfaces. Focusing on linear perturbations, we identify seven Lagrangian operators that lead to equations of motion containing at most two (space or time) derivatives, the background evolution being determined by the time dependent coefficients of only three of these operators. We then establish a dictionary that translates any existing or future model whose Lagrangian can be written in the above form into our parametrized framework. As an illustration, we study Horndeski's-or generalized Galileon-theories and show that they can be described, up to linear order, by only six of the seven operators mentioned above. This implies, remarkably, that the dynamics of linear perturbations can be more general than that of Horndeski while remaining second order. Finally, in order to make the link with observations, we provide the entire set of linear perturbation equations in Newtonian gauge, the effective Newton constant in the quasi-static approximation and the ratio of the two gravitational potentials, in terms of the time-dependent coefficients of our Lagrangian.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f235375b74efea4f546f654cb81a41004ea5db18

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Citations in the corpus

Effective field theory of cosmological perturbations (2013, methodology): “Similar analysis in the unitary gauge can be found in [6, 33, 65, 66].”
Gravitational wave decay into dark energy (2018, methodology): “owed. For other works studying the damping of gravitational waves see e.g. [12,13,14,15,16,17]. We will study the decay of gravitons in the framework of the Eective Field Theory (EFT) of Dark Energy [18,19,20,21,22]. We review the formalism in Sec.2and specify it to the subset of theories with GWs t”
Horndeski theory and beyond: a review (2019, methodology): “essions cannot be used for f(R) and chameleon models of dark energy, because we dropped the mass term for simplicity. See Refs. [151, 152, 153] for the limits of the quasi-static assumption and Refs. [150, 154, 155] for the complete expression of the equations (without using the quasi-static approxi”
Effective description of higher-order scalar-tensor theories (2017, methodology): “The above quadratic action extends the one derived in [4] and written in terms of the dimensionless time-dependent functions αA (introduced in [16] and [17]) in [7], with the addition of four new functions of time: the parameter αL, and the three parameters βA that characterize the terms containing ”
Exploring gravitational theories beyond Horndeski (2014, methodology): “[11] we explicitly separated the operators affecting the perturbations from those fixed by the background evolution, writing the action as”
Cosmological tests of modified gravity (2015, background): “Another approach is to build the effective action [231, 232, 233, 234, 235, 236, 237, 238] following the effective field theory approach developed for inflationary models [239, 240].”
The VIMOS Public Extragalactic Redshift Survey (VIPERS): The growth of structure at $0.5 < z < 1.2$ from redshift-space distortions in the clustering of the PDR-2 final sample (2016, background): “…prior, while allowing room for deviations from GR, we base our choice on the E ﬀ ective Field Theory of Gubitosi et al. 2013; Bloomﬁeld et al. 2013; Gleyzes et al. 2013), which allows a description of various kinds of dark energy models and modiﬁcations of gravity to be expressed in a…”
The Effective Field Theory of nonsingular cosmology (2016, methodology): “As matter of fact, by mapping the cubic Galileon to the EFT [41], eq.”
Dark Energy in Light of Multi-Messenger Gravitational-Wave Astronomy (2018, background): “Different versions of the linear EFT-DE approach has been implemented in numerical codes able to obtain predictions based on linear perturbation theory.”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “Using the language of effective description of dark energy [233, 234, 235] in terms of lapse, shift and the extrinsic curvature, the quadratic action for DHOST can be written as [236]”
Extended scalar-tensor theories of gravity (2016, background): “These operators have not been considered so far in the so-called effective field theory of dark energy [17, 18], which starts from a general Lagrangian in the unitary gauge [22]:”