$R^2\log R$ quantum corrections and the inflationary observables

Abstract

We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is $f(R)=R+\alpha R^2+\beta R^2\ln R$. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index $n_s$ and the tensor to scalar ratio yield $10^{-4}\lesssim r\lesssim 0.03$ and $0.94\lesssim n_s\lesssim 0.99$. i.e. $r$ is an order of magnitude bigger or smaller than the original Starobinsky model which predicted $r\sim 10^{-3}$. Further enhancement of $r$ gives a scale invariant $n_s\sim 1$ or higher. Other inflationary observables are $d{n}_s/d\ln k\gtrsim -5.2\times 10^{-4},\mu \lesssim 2.1\times 10^{-8},y\lesssim 2.6\times 10^{-9}$. Despite the enhancement in $r$, if the recent BICEP2 measurement stands, this model is disfavoured.

arXiv commentLaTeX, 9+1 pages, 5 figures

References in corpus (11)

• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• Planck 2013 results. XXII. Constraints on inflation
• The Primordial Inflation Explorer (PIXIE): A Nulling Polarimeter for Cosmic Microwave Background Observations
• Inflationary spacetimes are not past-complete
• Probing the inflaton: Small-scale power spectrum constraints from measurements of the CMB energy spectrum
• Improved constraints on the primordial power spectrum at small scales from ultracompact minihalos
• Planck Data Reconsidered
• A new probe of the small-scale primordial power spectrum: astrometric microlensing by ultracompact minihalos
• Cosmic Microwave Background Observables of Small Field Models of Inflation
• One-loop Modified Gravity in de Sitter Universe, Quantum Corrected Inflation, and its Confrontation with the Planck Result
• Constraining the primordial power spectrum from SNIa lensing dispersion

Cited by in corpus (23)

• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• Consistency relation for $R^p$ inflation
• Inflation in scale-invariant theories of gravity
• A simple $F(\mathcal{R},\varphi )$ deformation of Starobinsky inflationary model
• Inflation in an effective gravitational model & asymptotic safety
• Reinterpretation of the Starobinsky model
• Disentangling the $f(R)$ - Duality
• f(R) and Brans-Dicke Theories and the Swampland
• A viable logarithmic f(R) model for inflation
• The f(R) Gravity Function of the Linde Quintessence
• Dynamically Generated Inflation from Non-Riemannian Volume Forms
• Saddle point inflation from higher order corrections to Higgs/Starobinsky inflation
• Gravitational waves in Modified Gauss-Bonnet Gravity
• Exploring the inflation of $F(R)$ gravity
• Is asymptotically safe inflation eternal?
• Multi-phase induced inflation in theories with non-minimal coupling to gravity
• Saddle point inflation from $f(R)$ theory
• Darkflation -- one scalar to rule them all?
• Electroweak Vacuum Stability and the Higgs Field Relaxation via Gravitational Effects
• Gravity Rainbow Effects on Higher Curvature Modification of R2 inflation
• Modified Starobinsky Inflation
• Linear signal recovery from $b$-bit-quantized linear measurements: precise analysis of the trade-off between bit depth and number of measurements
• Back-reaction in massless de Sitter QFTs: holography, gravitational DBI action and f(R) gravity