Abstract
If we posit the validity of the consistency relations, the tensor spectral index and the relative amplitude of the scalar and tensor power spectra are both fixed by a single slow roll parameter. The physics of the protoinflationary transition can break explicitly the consistency relations causing a reduction of the inflationary curvature scale in comparison with the conventional lore. After a critical scrutiny, we argue that the inflationary curvature scale, the total number of inflationary efolds and, ultimately, the excursion of the inflaton across its Planckian boundary are all characterized by a computable theoretical error. While these considerations ease some of the tensions between the Bicep2 data and the other satellite observations, they also demand an improved understanding of the protoinflationary transition whose physical features may be assessed, in the future, through a complete analysis of the spectral properties of the B mode autocorrelations.
Highlights
Inflation must have a limited duration since it cannot extend indefinitely in the past
The lack of past geodesic completeness of a quasi–de Sitter stage of expansion suggests that the initial phase of inflation can be plausibly divided into a preinflationary phase where the background geometry decelerates1 (i.e., a_ > 0 but ä < 0) followed by the protoinflationary epoch of expansion when ä changes its sign
The consistency relations are essential for the determination of the inflationary curvature scale as well as for the typical value of the inflationary potential [3] at the horizon crossing
Summary
Inflation must have a limited duration since it cannot extend indefinitely in the past. The lack of past geodesic completeness of a quasi–de Sitter stage of expansion suggests that the initial phase of inflation can be plausibly divided into a preinflationary phase where the background geometry decelerates (i.e., a_ > 0 but ä < 0) followed by the protoinflationary epoch of expansion when ä changes its sign. These periods of evolution are likely to be driven by an irrotational fluid. It has been recently argued that the consistency relations can be violated by the protoinflationary physics [4]: a protoinflationary phase containing gravitons and fluid phonons can impact differently on the tensor to scalar ratio. V we collect the concluding remarks and draw some general lessons
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