Reconstructing the local potential of inflation with BICEP2 data

Abstract

We locally reconstruct the inflationary potential by using the current constraints on r and ns from BICEP2 data. Assuming small and negligible αs, the inflationary potential is approximately linear in ∆φ ∼ M pl range but becomes non-linear in ∆φ ∼ 10M pl range. However if we vary the value of αs within the range given by constraints from Planck measurement, the local reconstruction is only valid in the range of ∆φ ∼ 0.4M pl , which challenges the inflationary background from the point of view of effective field theory. We show that, within the range of ∆φ ∼ 0.4M pl , the inflation potential can be precisely reconstructed. With the current reconstruction, we show that V (φ) ∼ φ 2 and φ 3 are consistent, while φ model is ruled out by 95% confidence level of the reconstructed range of potential. This sets up a strong limit of large-field inflation models.

Global dynamics and inflationary center manifold and slow-roll approximants

“…It should, however, be pointed out that discussions about the recent results of BICEP2 [1] (see e.g. [2,3] as examples of recent reactions to BICEP2) also motivate taking a renewed look at the classic problem of a minimally coupled scalar field with a quadratic potential.…”

The reconstruction of inflationary potentials

“…In addition to the parametrization of ǫ, the reconstruction of the inflaton potential from the parametrization of ns with ns − 1 = −α/N , and from the assumption between the amplitude of the power spectrum − ln ∆ 2 R and ns − 1 were also considered (Chiba 2015;Creminelli et al 2015;Gobbetti et al 2015). On the other hand, the reconstruction of the inflaton potential from the power spectra by the method of functional reconstruction were usually applied (Hodges & Blumenthal 1990;Copeland et al 1993;Liddle & Turner 1994;Lidsey et al 1997;Peiris & Easther 2006;Norena et al 2012;Choudhury & Mazumdar 2014a;Ma & Wang 2014;Myrzakulov et al 2015;Choudhury 2016).…”

Reconstruction of α -attractor supergravity models of inflation

“…These definitions provide a modelindependent constraint on the shape of the inflaton potential, as they are directly connected with the first and second order derivatives of the potential. This formalism has been used for example by [53], for comparing theory with observations. Even if further approaches for the reconstruction problem have been discussed in the literature (refs in Sec.…”

“…Among the different algorithms proposed in the literature [52][53][54][55][56][57][58][59][60][61][62][63], we will focus on the simple approach based on constraining the local shape of the potential during the pure accelerated phase. This is done by implementing a Taylor expansion around the vacuum expectation value of the inflaton field at horizon crossing, φ * , and by connecting the coefficients of the expansion to the observables n s and r (details in [52,53]). In its simplicity, this procedure provides a model independent estimation of the inflationary potential around φ * .…”