Density perturbations in $f(R,\varphi )$-gravity with an application to the (varying power)-law model

Abstract

Density perturbations in the cosmic microwave background within general $f(R,\varphi )$ models of gravity are investigated. The general dynamical equations for the tensor and scalar modes in any $f(R,\varphi )$ gravity model are derived. An application of the equations to the (varying power)-law modified gravity toy-model is then made. Formulas and numerical values for the tensor-to-scalar ratio, the scalar tilt and the tensor tilt are all obtained within this specific model. While the model cannot provide a theoretical reason for the value of the energy scale at which inflation should occur, it is found, based on the latest observations of the density perturbations in the sky, that the model requires inflation to occur at an energy scale less than the GUT-scale; namely, $\sim 10^{14}\mathrm{GeV}$. The different energy intervals examined here show that the density perturbations recently obtained from observations are recovered naturally, with very high precision, and without fine tuning the model's parameters.

arXiv comment12 pp. Matches the published version

References in corpus (49)

• Planck 2015 results. XIII. Cosmological parameters
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• f(R) theories
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
• Conditions for the cosmological viability of f(R) dark energy models
• The Large Scale Structure of f(R) Gravity
• Scalar-tensor gravity in an accelerating universe
• Where new gravitational physics comes from: M-theory?
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Inflationary cosmology in modified gravity theories
• The pattern of growth in viable f(R) cosmologies
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• Dynamics of Linear Perturbations in f(R) Gravity
• The Best Inflationary Models After Planck
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Stability of Cosmological Solution in f(R) Models of Gravity
• Cosmological observations in scalar-tensor quintessence
• Cluster Constraints on f(R) Gravity
• Testing Gravity Against Early Time Integrated Sachs-Wolfe Effect
• Cosmological Constraints on f(R) Acceleration Models
• Modified-Source Gravity and Cosmological Structure Formation
• Constraints on f(R) gravity from probing the large-scale structure
• On the evolution of density perturbations in f(R) theories of gravity
• Non-linear Evolution of Matter Power Spectrum in Modified Theory of Gravity
• Inflation and the Theory of Cosmological Perturbations
• Density perturbations in general modified gravitational theories
• The dispersion of growth of matter perturbations in f(R) gravity
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• The growth of matter perturbations in f(R) models
• Observational signatures of Jordan-Brans-Dicke theories of gravity
• The growth of matter perturbations in some scalar-tensor DE models
• Theoretical Priors On Modified Growth Parametrisations
• The effect of modified gravity on weak lensing
• Analytic solution for matter density perturbations in a class of viable cosmological f(R) models
• Observational Constraints on Exponential Gravity
• Gravitational Waves in Viable f(R) Models
• Characterizing the linear growth rate of cosmological density perturbations in an f(R) model
• Solar system tests of f(R) gravity
• The imprint of $f(R)$ gravity on weak gravitational lensing I: Connection between observables and large scale structure
• Cosmological perturbations in $F(R)$ gravity
• $f(R)$-Modified Gravity, Wald Entropy, and the Generalized Uncertainty Principle
• Higher Order Curvature Theories of Gravity Matched with Observations: a Bridge Between Dark Energy and Dark Matter Problems
• A (varying power)-law modified gravity
• Radiative Corrections in the (Varying Power)-Law Modified Gravity

Cited by in corpus (4)

• Noether charge and black hole entropy in teleparallel gravity
• Revisiting the dynamics of interacting vector-like dark energy
• Testing scale-invariant inflation against cosmological data
• On the initial conditions of scalar and tensor fluctuations in $f(R,\varphi )$ gravity