Inflationary behavior of $R^2$ gravity in a conformal framework

Abstract

Models of inflation are tightly constrained by the PLANCK satellite data. Among them, Starobinsky's model with an exponential type potential seems to be challenged by the recent BICEP2 results. The model is based on the existence of $R^2$ terms in the Einstein-Hilbert action, which have their origin in the conformal-anomaly. Conformal (or Weyl) gravitational theories are relevant when matter fields become effectively massless; i.e. their masses are negligible in comparison with the spacetime curvature. These theories may include other, additional scalar fields. We show that their presence under general conditions does not destabilize the inflationary behaviour encountered in the Starobinsky model, although the issue of the exact quantitative agreement with existing data, like the tensor to scalar ratio, rests on the choice of parameters.

arXiv comment17 pages, 8 figures, revised version, references and text added, typos corrected

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• Restricted Weyl invariance in four-dimensional curved spacetime
• Higher-Derivative $f(R,\square R,T)$ Theories of Gravity
• Reconciling Induced-Gravity Inflation in Supergravity With The Planck 2013 & BICEP2 Results
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