Details
| Original language | English |
|---|---|
| Article number | 046 |
| Number of pages | 26 |
| Journal | Journal of Cosmology and Astroparticle Physics |
| Volume | 2023 |
| Issue number | 8 |
| Publication status | Published - 18 Aug 2023 |
Abstract
Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of the metric can be considered a subclass of a more general type of transformation, so-called disformal transformation. Here, we investigate the implications of pure disformal symmetry in the Universe. We derive the form of general disformal invariant tensors from which we build the most general disformal invariant action. We argue that, in cosmology, disformal symmetry amounts to require that the lapse function is fully replaced by a (time-like) scalar field at the level of the action. We then show that disformal symmetry is in general an exactly equivalent formulation of general mimetic gravity. Lastly, we go beyond mimetic gravity and find that a particular class of invariance leads to seemingly Ostrogradski-like (with higher derivatives) Lagrangians, which are nevertheless absent of Ostrogradski ghosts in a cosmological background, despite having an additional degree of freedom. We also propose an application of our formalism to find new invertible disformal transformations, where the coefficient involves higher derivatives and curvature, further expanding the theory space of scalar-tensor theories.
Keywords
- Cosmological perturbation theory in GR and beyond, gravity, modified gravity
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Astronomy and Astrophysics
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In: Journal of Cosmology and Astroparticle Physics, Vol. 2023, No. 8, 046, 18.08.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Disformal symmetry in the Universe
T2 - mimetic gravity and beyond
AU - Domènech, Guillem
AU - Ganz, Alexander
N1 - Funding Information: G.D. is supported by the DFG under the Emmy-Noether program grant no. DO 2574/1-1, project number 496592360. A.G. receives support by the grant No. UMO-2021/40/C/ST9/00015 from the National Science Centre, Poland. Calculations of the disformal invariant tensors were cross-checked with the Mathematica package xAct
PY - 2023/8/18
Y1 - 2023/8/18
N2 - Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of the metric can be considered a subclass of a more general type of transformation, so-called disformal transformation. Here, we investigate the implications of pure disformal symmetry in the Universe. We derive the form of general disformal invariant tensors from which we build the most general disformal invariant action. We argue that, in cosmology, disformal symmetry amounts to require that the lapse function is fully replaced by a (time-like) scalar field at the level of the action. We then show that disformal symmetry is in general an exactly equivalent formulation of general mimetic gravity. Lastly, we go beyond mimetic gravity and find that a particular class of invariance leads to seemingly Ostrogradski-like (with higher derivatives) Lagrangians, which are nevertheless absent of Ostrogradski ghosts in a cosmological background, despite having an additional degree of freedom. We also propose an application of our formalism to find new invertible disformal transformations, where the coefficient involves higher derivatives and curvature, further expanding the theory space of scalar-tensor theories.
AB - Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of the metric can be considered a subclass of a more general type of transformation, so-called disformal transformation. Here, we investigate the implications of pure disformal symmetry in the Universe. We derive the form of general disformal invariant tensors from which we build the most general disformal invariant action. We argue that, in cosmology, disformal symmetry amounts to require that the lapse function is fully replaced by a (time-like) scalar field at the level of the action. We then show that disformal symmetry is in general an exactly equivalent formulation of general mimetic gravity. Lastly, we go beyond mimetic gravity and find that a particular class of invariance leads to seemingly Ostrogradski-like (with higher derivatives) Lagrangians, which are nevertheless absent of Ostrogradski ghosts in a cosmological background, despite having an additional degree of freedom. We also propose an application of our formalism to find new invertible disformal transformations, where the coefficient involves higher derivatives and curvature, further expanding the theory space of scalar-tensor theories.
KW - Cosmological perturbation theory in GR and beyond
KW - gravity
KW - modified gravity
UR - http://www.scopus.com/inward/record.url?scp=85169314397&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2304.11035
DO - 10.48550/arXiv.2304.11035
M3 - Article
AN - SCOPUS:85169314397
VL - 2023
JO - Journal of Cosmology and Astroparticle Physics
JF - Journal of Cosmology and Astroparticle Physics
SN - 1475-7516
IS - 8
M1 - 046
ER -