Abstract
We put forward novel extensions of Starobinsky inflation, involving a class of 'geometric' higher-curvature corrections that yield second-order Friedmann-Lema\^itre equations and second-order-in-time linearized equations around cosmological backgrounds. We determine the range of models within this class that admit an extended phase of slow roll inflation as an attractor. By embedding these theories in anti-de Sitter space, we derive holographic 'unitarity' bounds on the two dominant higher-order curvature corrections. Finally we compute the leading corrections to the spectral properties of scalar and tensor primordial perturbations, including the modified consistency relation $r=-8n_{T}$. Remarkably, the range of models singled out by holography nearly coincides with the current observational bounds on the scalar spectral tilt. Our results indicate that future observations have the potential to discriminate between different higher-curvature corrections considered here.
Highlights
Starobinsky realised long ago that the trace anomaly of a large number of light matter fields can support a de Sitter phase in the early universe [1,2]
It has long been known that other higher derivative terms featuring in the trace anomaly as well as the nonlocal effects it gives rise to, affect the details of the pattern of primordial perturbations. Since this class of models is most naturally viewed in the context of an effective field theory (EFT) expansion around general relativity (GR), there is no justification to exclude on ad hoc grounds yet further higher derivative contributions to the action
At higher orders in the derivative expansion many more terms can be added to the action, but for simplicity, we focus on the geometric terms we have described in the previous subsection
Summary
Starobinsky realised long ago that the trace anomaly of a large number of light matter fields can support a de Sitter phase in the early universe [1,2]. It has long been known that other higher derivative terms featuring in the trace anomaly as well as the nonlocal effects it gives rise to, affect the details of the pattern of primordial perturbations (see, e.g., [1,2,5]) Since this class of models is most naturally viewed in the context of an effective field theory (EFT) expansion around general relativity (GR), there is no justification to exclude on ad hoc grounds yet further higher derivative contributions to the action. These considerations are no longer of merely theoretical interest since the generation of CMB experiments has the potential to unlock this region of parameter space, opening up the bright prospect to observationally differentiate between variations of trace anomaly inflation. We compute in particular the changes to the tensor to scalar ratio r, the scalar tilt ns and the consistency relation r 1⁄4 −8nT and quantify the promising prospects to observationally discriminate between these variations of R2 inflation
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