VCDM and Cuscuton

Abstract

We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theories. We confirm that all acceptable Cuscuton solutions are always solutions for VCDM theory. However, the inverse does not hold. We find that VCDM allows for the existence of exact General Relativity (GR) solutions with or without the presence of matter fields and a cosmological constant. We determine the conditions of existence for such GR-VCDM solutions in terms of the trace of the extrinsic curvature and on the fields which define the VCDM theory. On the other hand, for the Cuscuton theory, we find that the same set of exact GR solutions (such as Schwarzschild and Kerr spacetimes) is not compatible with timelike configurations of the Cuscuton field and therefore cannot be considered as acceptable solutions. Nonetheless, in Cuscuton theory, there could exist solutions which are not the same but close enough to GR solutions. We also show the conditions to determine intrinsic-VCDM solutions, i.e. solutions which differ from GR and do not belong to the Cuscuton model. We finally show that in cosmology a mapping between VCDM and the Cuscuton is possible, for a generic form of the VCDM potential. In particular, we find that for a quadratic potential in VCDM theory, this mapping is well defined giving an effective redefinition of the Planck mass for the cosmological background solutions of both theories.

19 pages+appendices, 1 figure, match with published version

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• Bouncing Cosmology in VCDM
• A General Model for Dark Energy Crossing the Phantom Divide
• Dynamical Dark Energy in Minimally Modified Gravity
• ${\Lambda }_{\mathrm{s}}$CDM cosmology from a type-II minimally modified gravity
• Multi-field Cuscuton Cosmology
• Gravitational collapse and formation of a black hole in a type II minimally modified gravity theory
• Cuscuton Bounce Beyond the Linear Regime: Bispectrum and Strong Coupling Constraints
• Joint Constraints on Neutrinos and Dynamical Dark Energy in Minimally Modified Gravity
• Minimally modified gravity with auxiliary constraints formalism
• How Much NEC Breaking Can the Universe Endure?
• Self-tuning of the cosmological constant in brane-worlds with $P(X,\varphi )$
• Gravitational collapse and odd-parity black hole perturbations in Minimal Theory of Bigravity
• Spatially covariant gravity with two degrees of freedom in the presence of an auxiliary scalar field: Hamiltonian analysis
• Kinematic Probes of Type-II MMG: Padé Cosmographic Analysis of VCDM