Theories with limited extrinsic curvature and a nonsingular anisotropic universe

Abstract

We propose a class of theories that can limit scalars constructed from the extrinsic curvature. Applied to cosmology, this framework allows us to control not only the Hubble parameter but also anisotropies without the problem of Ostrogradsky ghost, which is in sharp contrast to the case of limiting spacetime curvature scalars. Our theory can be viewed as a generalization of mimetic and cuscuton theories (thus clarifying their relation), which are known to possess a structure that limits only the Hubble parameter on homogeneous and isotropic backgrounds. As an application of our framework, we construct a model where both anisotropies and the Hubble parameter are kept finite at any stage in the evolution of the universe in the diagonal Bianchi type I setup. The universe starts from a constant-anisotropy phase and recovers Einstein gravity at low energies. We also show that the cosmological solution is stable against a wide class of perturbation wavenumbers, though instabilities may remain for arbitrary initial conditions.

19 pages, 2 figures; v2: matches published version

References in corpus (26)

• Inflationary Universe with Anisotropic Hair
• Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Cosmology with Mimetic Matter
• The Nature of Primordial Fluctuations from Anisotropic Inflation
• Unifying framework for scalar-tensor theories of gravity
• Scalar-Scalar, Scalar-Tensor, and Tensor-Tensor Correlators from Anisotropic Inflation
• Predictions from an anisotropic inflationary era
• Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB
• Cuscuton Cosmology: Dark Energy meets Modified Gravity
• Cuscuton and low energy limit of Horava-Lifshitz gravity
• Hamiltonian analysis of spatially covariant gravity
• Extended mimetic gravity: Hamiltonian analysis and gradient instabilities
• Mimetic dark matter, ghost instability and a mimetic tensor-vector-scalar gravity
• A Class of Minimally Modified Gravity Theories
• Fundamental theorem on gauge fixing at the action level
• Inevitable ghost and the degrees of freedom in f(R,G) gravity
• A Safe Beginning for the Universe?
• Cuscuton gravity as a classically stable limiting curvature theory
• Spatially covariant gravity: Perturbative analysis and field transformations
• Higher derivative scalar-tensor theory and spatially covariant gravity: the correspondence
• A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
• Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity
• Einstein-Aether Theory
• Mimetic gravity: mimicking the dynamics of the primeval universe in the context of loop quantum cosmology
• Dark Energy, Black Hole Entropy, and the First Precision Measurement in Quantum Gravity