Inflationary model in minimally modified gravity theories

Abstract

We have investigated inflationary model constructed from minimally modified gravity (MMG) theories. The MMG theory in the form of $f(\mathbf{H})\propto {\mathbf{H}}^{1+p}$ gravity where, $\mathbf{H}$ is the Hamiltonian constraint in the Einstein gravity and $p$ is constant, has been studied. An inflation is difficult to be achieved in this theory of gravity unless an additional scalar field playing a role of inflaton is introduced in the model. We have found that the inflaton with exponential potential can drive inflation with graceful exist different from the case of Einstein gravity. The slow-roll parameter for both the exponential and the power-law potentials is inversely proportional to number of e-folding similar to the case of the Einstein gravity. We also have found for the scalar perturbation that the curvature perturbation in the comoving gauge on super Hubble radius scales grows rapidly during inflation unless $p=0$. For the tensor modes, the amplitude of the perturbations is constant on large scales, and sound speed of the perturbations can diviate from unity and can vary with time depending on the form of $f(\mathbf{H})$.

arXiv comment19 pages, 7 figures, references added, accepted for publication in Physical Review D, clarifications of the definition for the curvature perturbation, corrected typos

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• Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling
• Testing gravity with the cosmic microwave background: constraints on modified gravity with two tensorial degrees of freedom
• Inflation with antisymmetric tensor field: new candidates
• Observational Constraints and Preheating in Cuscuton Inflation
• Inflation using a triplet of Antisymmetric tensor fields
• Scalar and vector modes in inflation with antisymmetric tensor field
• Inflation in a scalar-vector gravity theory
• Spatially covariant gravity with two degrees of freedom in the presence of an auxiliary scalar field: Hamiltonian analysis