A class of minimally modified gravity theories

Lin, C.; Mukohyama, Shinji

doi:10.1088/1475-7516/2017/10/033

Cited by 90 publications

(157 citation statements)

References 57 publications

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“…Note our analysis also implies that the second TTDoF condition (87) is also needed in general. Another class of Lorentz breaking gravity theories with two tensorial DoFs dubbed as the "minimally modified gravity" was proposed in [32], in which the Lagrangian is linear in the lapse function. It is also interesting that the condition derived in [32] is a special case of the second TTDoF condition (74) in our work, while the first TTDoF condition is automatically satisfied.…”

Section: Discussionmentioning

confidence: 99%

“…In this section, we consider some special cases, and compare our results with the previous works on Lorentz breaking scalartensor theories with two DoFs. These include the "cuscuton theory" [13] and its extensions [16] as well as the "minimally modified gravity" proposed in [32].…”

Section: Applicationsmentioning

confidence: 99%

“…Thus one needs to impose further constraints on the form of the theory in order to reduce the number of DoFs, i.e., to eliminate the scalar type DoF. A class of "minimally modified gravity" was proposed in [32,33] (see also [34]), which studied the Lagrangian that is linear in the lapse function and derived the conditions for having two tensorial DoFs at the level of Lagrangian. The conditions were also studied directly at the level of the Hamiltonian [35].…”

Section: Introductionmentioning

confidence: 99%

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Spatially covariant gravity theories with two tensorial degrees of freedom: The formalism

Gao

Yao

2020

Phys. Rev. D

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Within the general framework of spatially covariant theories of gravity, we study the conditions for having only the two tensorial degrees of freedom. Generally, there are three degrees of freedom propagating in the theory, of which two are tensorial and one is of the scalar type. Through a detailed Hamiltonian analysis, we find two necessary and sufficient conditions to evade the scalar type degree of freedom. The first condition implies that the lapse-extrinsic curvature sector must be degenerate. The second condition ensures that the dimension of the phase space at each spacetime point is even, so that the scalar type degree of freedom is eliminated completely. We also compare our results with the previous studies, and apply our formalism to a simple example, in which the Lagrangian is quadratic in the extrinsic curvature. *

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Section: Discussionmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spatially covariant gravity theories with two tensorial degrees of freedom: The formalism

Gao

Yao

2020

Phys. Rev. D

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“…6 There could be a first class constraint in Φ I ≈ 0, Ψ i ≈ 0 or a tertiary constraint from d dt Ψ ≈ 0 depending on the Lagrangian which give further reductions of the number of degrees of freedom. The resultant theory would be a class of the minimally modified gravity theories [49,75] or the cuscuton theories [76][77][78]. However, we do not discuss whether such additional reductions exist and only focus on the fact the the Lagrangian is free from the Ostrogradsky ghost.…”

Section: Counting the Number Of Degrees Of Freedommentioning

confidence: 99%

Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?

Aoki

Shimada

2019

Phys. Rev. D

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We reveal the existence of a certain hidden symmetry in general ghost-free scalar-tensor theories which can only be seen when generalizing the geometry of the spacetime from Riemannian. For this purpose, we study scalar-tensor theories in the metric-affine (Palatini) formalism of gravity, which we call scalar-metric-affine theories for short, where the metric and the connection are independent. We show that the projective symmetry, a local symmetry under a shift of the connection, can provide a ghost-free structure of scalar-metric-affine theories. The ghostly sector of the secondorder derivative of the scalar is absorbed into the projective gauge mode when the unitary gauge can be imposed. Incidentally, the connection does not have the kinetic term in these theories and then it is just an auxiliary field. We can thus (at least in principle) integrate the connection out and obtain a form of scalar-tensor theories in the Riemannian geometry. The projective symmetry then hides in the ghost-free scalar-tensor theories. As an explicit example, we show the relationship between the quadratic order scalar-metric-affine theory and the quadratic U-degenerate theory. The explicit correspondence between the metric-affine (Palatini) formalism and the metric one could be also useful for analyzing phenomenology such as inflation.1 In the paper [16], U-degenerate theories and DHOST theories are classified: U-degenerate theories are not degenerate in an arbitrary gauge but degenerate in the unitary gauge while DHOST theories are degenerate under any gauge. However, in the present paper, we will just call theories "U-degenerate theories" if the Lagrangian is degenerate at least in the unitary gauge for simplicity.

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“…This issue is entangled with the nature of the identically conserved pieces that can be added to the stress-energy tensor. Disregarding higher-derivative interactions becomes more questionable due to the existence of higher-derivative theories with just two degrees of freedom that reduce to gravitons at the linear level [31,32] (see also [33,34]).…”

Section: General Relativity As a Constructible Theorymentioning

confidence: 99%

Taming higher-derivative interactions and bootstrapping gravity with soft theorems

Carballo-Rubio

Filippo

Moynihan

2019

J. Cosmol. Astropart. Phys.

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On-shell constructibility is redefining our understanding of perturbative quantum field theory.The tree-level S-matrix of constructible theories is completely determined by a set of recurrence relations and a reduced number of scattering amplitudes. In this paper, we revisit the on-shell constructibility of gravitational theories making use of new results on soft theorems and recurrence relations. We show that using a double complex shift and an all-line soft deformation allows us to relax the technical conditions for constructibility, in order to include more general propagators and higher-derivative interactions that prevent using conventional Britto-Cachazo-Feng-Witten (BCFW) shifts. From this result we extract a set of criteria that guarantee that a given gravitational action has the same tree-level S-matrix in Minkowski spacetime as general relativity, which implies the equivalence at all orders in perturbation theory between these classical field theories on asymptotically flat spacetimes. As a corollary we deduce that the scattering amplitudes of general relativity and unimodular gravity are the same for an arbitrary number of external particles (as long as the S-matrix of the latter is unitary), thus extending previous works that were able to deal only with n = 4 and n = 5 amplitudes.

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A class of minimally modified gravity theories

Cited by 90 publications

References 57 publications

Spatially covariant gravity theories with two tensorial degrees of freedom: The formalism

Spatially covariant gravity theories with two tensorial degrees of freedom: The formalism

Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?

Taming higher-derivative interactions and bootstrapping gravity with soft theorems

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