Higher-order modified Starobinsky inflation

Abstract

An extension of the Starobinsky model is proposed. Besides the usual Starobinsky Lagrangian, a term proportional to the derivative of the scalar curvature, ${\nabla }_{\mu }R{\nabla }^{\mu }R$, is considered. The analyzis is done in the Einstein frame with the introduction of a scalar field and a vector field. We show that inflation is attainable in our model, allowing for a graceful exit. We also build the cosmological perturbations and obtain the leading-order curvature power spectrum, scalar and tensor tilts and tensor-to-scalar ratio. The tensor and curvature power spectrums are compared to the most recent observations from BICEP2/Keck collaboration. We verify that the scalar-to-tensor rate $r$ can be expected to be up to three times the values predicted by Starobinsky model.

32 pages, 10 figures, minor changes, new references added

References in corpus (21)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Effective Field Theory for Inflation
• BICEP2 / Keck Array x: Constraints on Primordial Gravitational Waves using Planck, WMAP, and New BICEP2/Keck Observations through the 2015 Season
• On Inflation with Non-minimal Coupling
• Cosmological inflation in $F(R,\mathcal{G})$ gravity
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Multiple field inflation
• Counting ghosts in the "ghost-free" non-local gravity
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• $R^2$ inflation to probe non-perturbative quantum gravity
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• Inflation in an effective gravitational model & asymptotic safety
• Irreducible forms for the metric variations of the action terms of sixth-order gravity and approximated stress-energy tensor
• Inflation with a Weyl term, or ghosts at work
• On higher derivative corrections to the $R+R^2$ inflationary model
• Super-Planckian excursions of the inflaton and quantum corrections
• Cosmology with a light ghost
• Gravitational Waves and Perspectives for Quantum Gravity
• String-Inspired Infinite-Derivative Theories of Gravity: A Brief Overview
• Mutated hybrid inflation in $f(R,\square R)$-gravity
• A Revision to the Issue of Frames by Non-minimal Large Field Inflation

Cited by in corpus (16)

• Slow-roll inflation in f(R,T) gravity and a modified Starobinsky-like inflationary model
• On the superstring-inspired quantum correction to the Starobinsky model of inflation
• Higher-order extension of Starobinsky inflation: initial conditions, slow-roll regime, and reheating phase
• $f\left(R,{\nabla }_{{\mu }_1}R,\dots ,{\nabla }_{{\mu }_1}\dots {\nabla }_{{\mu }_n}R\right)$ theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach
• Neutron Stars in Modified Teleparallel Gravity
• Observational constraints on varying fundamental constants in a minimal CPC model
• Gravitational waves in higher-order $R^2$ gravity
• Gravitational waves from inspiraling black holes in quadratic gravity
• Spherically Symmetric Solutions in Higher-Derivative Theories of Gravity
• Modified Starobinsky inflation by the $R\ln \left(\square \right)R$ term
• Second-order corrections to Starobinsky inflation
• Removal of instabilities of the higher derivative theories in the light of antilinearity
• Gravitational Waves Emission in Quadratic Gravity: longitudinal modes, angular momentum emission, and positivity of the radiated power
• Classical and quantum cosmology of $K$-essentially modified $R^2$ and pure $R^p$ gravity
• A connection between Gravitational Scalar-Tensor theories and Generalized Hybrid theories
• Higher-order gravity models: corrections up to cubic curvature invariants and inflation