The Reconstruction of $f(\varphi )R$ and Mimetic Gravity from Viable Slow-roll Inflation

Abstract

In this work, we extend the bottom-up reconstruction framework of $F(R)$ gravity to other modified gravities, and in particular for $f(\varphi )R$ and mimetic $F(R)$ gravities. We investigate which are the important conditions in order for the method to work, and we study several viable cosmological evolutions, focusing on the inflationary era. Particularly, for the $f(\varphi )R$ theory case, we specify the functional form of the Hubble rate and of the scalar-to-tensor ratio as a function of the $e$-foldings number and accordingly, the rest of the physical quantities and also the slow-roll and the corresponding observational indices can be calculated. The same method is applied in the mimetic $F(R)$ gravity case, and in both cases we thoroughly analyze the resulting free parameter space, in order to show that the viability of the models presented is guaranteed and secondly that there is a wide range of values of the free parameters for which the viability of the models occurs. In addition, the reconstruction method is also studied in the context of mimetic $F(R)=R$ gravity. As we demonstrate, the resulting theory is viable, and also in this case, only the scalar-to-tensor ratio needs to be specified, since the rest follow from this condition. Finally, we discuss in brief how the reconstruction method could function for other modified gravities.

28 pages, NPB Accepted

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• Inflation in mimetic $f(R,T)$ gravity
• Dynamical system approach of non-minimal coupling in AdS/CFT cosmology
• Reconstructing G-inflation: From the attractors $n_S(N)$ and $r(N)$
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• Consistency between black hole and mimetic gravity -- Case of $(2+1)$-dimensional gravity
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• Testing scale-invariant inflation against cosmological data
• New anisotropic star solutions in mimetic gravity
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• Linearized modified gravity theories and gravitational waves physics in the GBD theory
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• WIMPs in Dilatonic Einstein Gauss-Bonnet Cosmology
• Hamiltonian analysis of Mimetic gravity with higher derivatives
• Viable Inflationary Evolution from Loop Quantum Cosmology Scalar-Tensor Theory
• Black holes with Lagrange multiplier and potential in mimetic-like gravitational theory: multi-horizon black holes
• Multi-field Mimetic Gravity
• Cosmological Dark sector from a Mimetic-Metric-Torsion perspective
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• More accurate slow-roll approximations for inflation in scalar-tensor theories
• Isotropic stellar model in mimetic theory
• Higher dimensional charged static and rotating solutions in mimetic gravity
• Gauss-Bonnet Cosmology: large-temperature behaviour and bounds from Gravitational Waves
• New inflationary exact solution from Lie symmetries
• Dual models for p-form mimetic gravity and their connection to perfect fluids consisting of (p+1)-branes
• Loop-corrected scalar potentials and late-time acceleration in f(R) gravity