Potential-driven inflation with disformal coupling to gravity

Qiu, Taotao; Xiao, Zehua; Shi, Jiaming; Aljaf, Muhsin

doi:10.1103/physrevd.102.063506

Cited by 5 publications

(1 citation statement)

References 88 publications

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“…*2 Also, the quadratic/cubic DHOST class itself is closed under the disformal transformation [10]. Applications of the disformal transformation have been extensively explored in various contexts; inflation [32][33][34][35][36], cosmic microwave background [37][38][39], dark matter and dark energy [40][41][42][43][44][45][46], cosmological perturbations [47][48][49][50][51][52][53][54], solar system tests and screening mechanisms [41,[55][56][57][58][59], relativistic stars [60][61][62][63], and black holes [64][65][66][67][68][69][70][71][72][73][74][75][76][77].…”

Section: Introductionmentioning

confidence: 99%

Invertible disformal transformations with higher derivatives

Takahashi,

Motohashi,

Minamitsuji

2021

Preprint

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We consider a higher-derivative generalization of disformal transformations and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These conditions allow us to systematically construct the inverse transformation in a fully covariant manner. Applying the invertible generalized disformal transformation to known ghost-free scalar-tensor theories, we obtain a novel class of ghost-free scalar-tensor theories, whose action contains the third-or higher-order derivatives of the scalar field as well as nontrivial higherorder derivative couplings to the curvature tensor.*1 Relaxing the degeneracy conditions so that the higher-derivative terms are degenerate only in the unitary gauge, we obtain a broader class of scalar-tensor theories [13][14][15][16][17]. In that case, there is an apparent extra DOF in a generic gauge, but it satisfies an elliptic differential equation and hence is an instantaneous (or "shadowy") mode [14,17]. *2 However, in two spacetime dimensions, the Horndeski class is closed under the disformal transformation of the form (1) [31].

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Section: Introductionmentioning

confidence: 99%

Invertible disformal transformations with higher derivatives

Takahashi,

Motohashi,

Minamitsuji

2021

Preprint

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Palatini-Higgs inflation with nonminimal derivative coupling

et al. 2020

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Invertible disformal transformations with higher derivatives

2022

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Invertible disformal transformations serve as a useful tool to explore ghost-free scalar-tensor theories. In this paper, we construct a generalization of invertible disformal transformations that involves arbitrary higher-order covariant derivatives of the scalar field. As a result, we obtain a more general class of ghost-free scalar-tensor theories than ever. Notably, our generalization is such that matter fields can be consistently coupled to these theories without introducing an unwanted extra degree of freedom in the unitary gauge. I. INTRODUCTIONGeneral relativity (GR) has passed various gravitational experiments as well as cosmological observations and is now commonly accepted as the standard model of gravitation and cosmology. Nevertheless, there are several motivations to study modifications/extensions of GR. For instance, GR is expected to be a low-energy effective theory and should be modified at high energies. Also, extended gravitational theories serve as good candidates that can be tested against GR [1][2][3]. In general, modified gravity models involve additional degrees of freedom (DOFs) on top of the metric, of which scalar-tensor theories (i.e., those involving a single scalar field besides the metric) have been studied extensively. The most general class of scalar-tensor theories with second-order Euler-Lagrange equations is now known as the Horndeski class [4][5][6]. Note that the second-order nature of the Euler-Lagrange equations guarantees the absence of Ostrogradsky ghosts, i.e., unstable extra DOFs associated with higher-order equations of motion [7].A more general class of ghost-free scalar-tensor theories was constructed in Refs. [8][9][10] by imposing the degeneracy condition [8,[11][12][13][14][15] on the higher-derivative terms, and this class is called the degenerate higher-order scalar-tensor (DHOST) class. (See Refs. [16,17] for reviews.) The DHOST class consists of many subclasses, and one of them can be obtained by the (conformal or) disformal transformation [18][19][20] of the Horndeski class, which we call the disformal Horndeski (DH) class. Note in passing that a ghost-free theory is mapped to another ghost-free theory by the disformal transformation since it is invertible in general [21,22]. Interestingly, DHOST theories that lie outside the DH class are known to exhibit ghost/gradient instabilities (or otherwise the metric becomes nondynamical) on a cosmological background [23][24][25]. Therefore, when one applies the DHOST theories to phenomenology, one usually focuses on the DH class. It was then realized that the framework of ghost-free scalar-tensor theories can be further extended by requiring the degeneracy only in the unitary gauge where the time coordinate is chosen so that the scalar field is spatially uniform. Such an extension was dubbed the U-DHOST class [26], which is equivalent to spatially covariant gravity [27][28][29][30] in the unitary gauge. Note that the scalar field profile has to be timelike in order to be consistent with the unitary gauge. Away from th...

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Potential-driven inflation with disformal coupling to gravity

Cited by 5 publications

References 88 publications

Invertible disformal transformations with higher derivatives

Invertible disformal transformations with higher derivatives

Palatini-Higgs inflation with nonminimal derivative coupling

Invertible disformal transformations with higher derivatives

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