Late-time cosmological evolution in degenerate higher-order scalar-tensor models

Boumaza, Hamza; Langlois, David; Noui, Karim

doi:10.1103/physrevd.102.024018

Cited by 11 publications

(10 citation statements)

References 26 publications

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“…Interestingly, this action is a qDHOST of class 2 N -I/Ia [61,62], as first noticed in [27]. The cosmological perturbations of such qDHOST theories were done in [62,63,64], which here we also follow.…”

Section: Analysis In Riemann Framesupporting

confidence: 55%

Cosmological Perturbations in Palatini Formalism

Kubota,

Oda,

Shimada

et al. 2020

Preprint

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We investigate cosmological perturbations of scalar-tensor theories in Palatini formalism. First we introduce an action where the Ricci scalar is conformally coupled to a function of a scalar field and its kinetic term and there is also a k-essence term consisting of the scalar and its kinetic term. This action has three frames that are equivalent to one another: the original Jordan frame, the Einstein frame where the metric is redefined, and the Riemann frame where the connection is redefined. For the first time in the literature, we calculate the quadratic action and the sound speed of scalar and tensor perturbations in three different frames and show explicitly that they coincide. Furthermore, we show that for such action the sound speed of gravitational waves is unity. Thus, this model serves as dark energy as well as an inflaton even though the presence of the dependence of the kinetic term of a scalar field in the non-minimal coupling, different from the case in metric formalism. We then proceed to construct the L3 action called Galileon terms in Palatini formalism and compute its perturbations. We found that there are essentially 10 different (inequivalent) definitions in Palatini formalism for a given Galileon term in metric formalism. We also see that, in general, the L3 terms have a ghost due to Ostrogradsky instability and the sound speed of gravitational waves could potentially deviate from unity, in sharp contrast with the case of metric formalism. Interestingly, once we eliminate such a ghost, the sound speed of gravitational waves also becomes unity. Thus, the ghost-free L3 terms in Palatini formalism can still serve as dark energy as well as an inflaton, like the case in metric formalism.

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Section: Analysis In Riemann Framesupporting

confidence: 55%

Cosmological Perturbations in Palatini Formalism

Kubota,

Oda,

Shimada

et al. 2020

Preprint

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show abstract

“…However, since the LIGO-Virgo measurements probe wavelengths many orders of magnitude smaller than cosmological scales, these constraints do not necessarily apply on cosmological scales (see e.g. [31]), leaving the other DHOST theories still relevant for cosmology [32].…”

Section: A Dhost Theories In Class Imentioning

confidence: 99%

Quadratic DHOST theories revisited

Langlois,

Noui,

Roussille

2020

Preprint

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We present a novel and remarkably simple formulation of degenerate higher-order scalartensor (DHOST) theories whose Lagrangian is quadratic in second derivatives of some scalar field. Using disformal transformations of the metric, we identify a special "frame" (or metric) for which the Lagrangian of quadratic DHOST theories reduces to the usual Einstein-Hilbert term plus a few terms that depend on simple geometric quantities characterizing the uniform scalar field hypersurfaces. In particular, for quadratic DHOST theories in the physically interesting class Ia, the Lagrangian simply consists of the Einstein-Hilbert term plus a term proportional to the three-dimensional scalar curvature of the uniform scalar field hypersurfaces. The classification of all quadratic DHOST theories becomes particularly transparent in this geometric reformulation, which also applies to scalar-tensor theories that are degenerate only in the unitary gauge.

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“…They encompass Horndeski theories, beyond Horndeski and also arbitrary disformal transformations of Horndeski theories, but their Euler-Lagrange equations are no longer second order in general. DHOST theories have been used intensively in the context of cosmology and astrophysics (see [32][33][34][35][36] for instance and the reviews [22,37]). Most of the literature has recently concentrated on DHOST theories where the speed of gravitational waves coincides with that of light [38][39][40][41][42][43][44].…”

Section: Discussionmentioning

confidence: 99%

Reconsidering the Ostrogradsky theorem: Higher-derivatives Lagrangians, Ghosts and Degeneracy

Ganz¹,

Noui²

2020

Preprint

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We review the fate of the Ostrogradsky ghost in higher-order theories. We start by recalling the original Ostrogradsky theorem and illustrate, in the context of classical mechanics, how higher-derivatives Lagrangians lead to unbounded Hamiltonians and then lead to (classical and quantum) instabilities. Then, we extend the Ostrogradsky theorem to higher-derivatives theories of several dynamical variables and show the possibility to evade the Ostrogradsky instability when the Lagrangian is "degenerate", still in the context of classical mechanics. In particular, we explain why higher-derivatives Lagrangians and/or higher-derivatives Euler-Lagrange equations do not necessarily lead to the propagation of an Ostrogradsky ghost. We also study some quantum aspects and illustrate how the Ostrogradsky instability shows up at the quantum level. Finally, we generalize our analysis to the case of higher order covariant theories where, as the Hamiltonian is vanishing and thus bounded, the question of Ostrogradsky instabilities is subtler.

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Late-time cosmological evolution in degenerate higher-order scalar-tensor models

Cited by 11 publications

References 26 publications

Cosmological Perturbations in Palatini Formalism

Cosmological Perturbations in Palatini Formalism

Quadratic DHOST theories revisited

Reconsidering the Ostrogradsky theorem: Higher-derivatives Lagrangians, Ghosts and Degeneracy

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