Towards a viable effective field theory of mimetic gravity

Ganz, Alexander; Bartolo, N.; Matarrese, S.

doi:10.1088/1475-7516/2019/12/037

Cited by 17 publications

(11 citation statements)

References 39 publications

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“…Note added: after the submission of this paper to arXiv, we note that a new paper [68] appeared. The authors in [68] discussed mimetic gravity theories with direct couplings between the curvature and higher derivatives of the scalar field only up to the quintic order. They first acquired effective field theories with three DOFs, and found that there are in general four or more DOFs for a generic scalar field.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Hamiltonian analysis of Mimetic gravity with higher derivatives

Zheng

2021

J. High Energ. Phys.

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Two types of mimetic gravity models with higher derivatives of the mimetic field are analyzed in the Hamiltonian formalism. For the first type of mimetic gravity, the Ricci scalar only couples to the mimetic field and we demonstrate the number of degrees of freedom (DOFs) is three. Then in both Einstein frame and Jordan frame, we perform the Hamiltonian analysis for the extended mimetic gravity with higher derivatives directly coupled to the Ricci scalar. We show that different from previous studies working at the cosmological perturbation level, where only three propagating DOFs show up, this generalized mimetic model, in general, has four DOFs. To understand this discrepancy, we consider the unitary gauge and find out that the number of DOFs reduces to three. We conclude that the reason why this system looks peculiar is that the Dirac matrix of all secondary constraints becomes singular in the unitary gauge, resulting in extra secondary constraints and thus reducing the number of DOFs. Furthermore, we give a simple example of a dynamic system to illustrate how gauge choice can affect the number of secondary constraints as well as the DOFs when the rank of the Dirac matrix is gauge dependent.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Hamiltonian analysis of Mimetic gravity with higher derivatives

Zheng

2021

J. High Energ. Phys.

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“…However, in general its modified Einstein equation contains higher mixed derivatives of the metric in the synchronous frame t = φ. While it was found in [17] that these mixed derivatives can change the sign of the gradient term of scalar metric perturbations and help to prevent a gradient instability, it was later realized in [18], [19] that this comes at the price of introducing an additional hidden degree of freedom. Even tough this second scalar degree of freedom does not show up when perturbing around a homogeneous background in unitary gauge, it was found in [19] that already for perturbations around Minkowski spacetime with non-homogeneous mimetic field profile it can lead to instabilities.…”

Section: The Theorymentioning

confidence: 99%

“…While it was found in [17] that these mixed derivatives can change the sign of the gradient term of scalar metric perturbations and help to prevent a gradient instability, it was later realized in [18], [19] that this comes at the price of introducing an additional hidden degree of freedom. Even tough this second scalar degree of freedom does not show up when perturbing around a homogeneous background in unitary gauge, it was found in [19] that already for perturbations around Minkowski spacetime with non-homogeneous mimetic field profile it can lead to instabilities. Since this type of higher mixed derivatives is not present in L nhd , one could hope that no such additional degree of freedom will appear in this theory.…”

Section: The Theorymentioning

confidence: 99%

“…Since this type of higher mixed derivatives is not present in L nhd , one could hope that no such additional degree of freedom will appear in this theory. A full Hamiltonian analysis similar to [18], [19], [20], [21] would of course be a more involved task beyond the scope of this paper.…”

Section: The Theorymentioning

confidence: 99%

“…Metric perturbations in different versions of mimetic gravity and also in different gauges have been analysed already a number of times, e.g. in [17], [19], [20], [23], [24], [25]. See appendix A for the calculation of second order actions around a non-flat Friedmann background in a more general theory.…”

Section: Metric Perturbations In Comoving Gaugementioning

confidence: 99%

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On Stability of Asymptotically Free Mimetic Hořava Gravity

Russ

2021

Preprint

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Asymptotically free mimetic gravity has been introduced as a proposal for a classical limiting curvature theory with the purpose of singularity resolution. It was found that in a spatially flat universe an initial stage of exponential expansion with graceful exit is a generic consequence, regardless of the matter content. In this work I will analyze stability of cosmological perturbations in such a model, considering only the degrees of freedom of pure mimetic gravity. I show that the addition of Hořava-gravity-like higher order spatial curvature terms can lift the gradient instability of scalar perturbations, even when their squared speed of sound is negative throughout. Calculating the primordial spectra of tensor and scalar perturbations in the simplest single component model, I find that the initially scale invariant spectra turn out to be destroyed later by the rapidly varying speed of sound at horizon exit.

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Mimetic inflation

Mansoori

Talebian

Firouzjahi

2021

J. High Energ. Phys.

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We study inflationary solution in an extension of mimetic gravity with the higher derivative interactions coupled to gravity. Because of the higher derivative interactions the setup is free from the ghost and gradient instabilities while it hosts a number of novel properties. The dispersion relation of scalar perturbations develop quartic momentum correction similar to the setup of ghost inflation. Furthermore, the tilt of tensor perturbations can take either signs with a modified consistency relation between the tilt and the amplitude of tensor perturbations. Despite the presence of higher derivative interactions coupled to gravity the tensor perturbations propagate with the speed equal to the speed of light as required by the LIGO observations. Furthermore, the higher derivative interactions induce non-trivial interactions in cubic Hamiltonian, generating non-Gaussianities in various shapes such as the equilateral, orthogonal and squeezed configurations with observable amplitudes.

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Towards a viable effective field theory of mimetic gravity

Cited by 17 publications

References 39 publications

Hamiltonian analysis of Mimetic gravity with higher derivatives

Hamiltonian analysis of Mimetic gravity with higher derivatives

On Stability of Asymptotically Free Mimetic Hořava Gravity

Mimetic inflation

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