Natural inflation: consistency with cosmic microwave background observations of Planck and BICEP2

Abstract

Natural inflation is a good fit to all cosmic microwave background (CMB) data and may be the correct description of an early inflationary expansion of the Universe. The large angular scale CMB polarization experiment BICEP2 has announced a major discovery, which can be explained as the gravitational wave signature of inflation, at a level that matches predictions by natural inflation models. The natural inflation (NI) potential is theoretically exceptionally well motivated in that it is naturally flat due to shift symmetries, and in the simplest version takes the formA tensor-to-scalar ratio r > 0.1 as seen by BICEP2 requires the height of any inflationary potential to be comparable to the scale of grand unification and the width to be comparable to the Planck scale. The Cosine Natural Inflation model agrees with all cosmic microwave background measurements as long as f > ∼ m Pl (where m Pl = 1.22 × 10 19 GeV) and Λ ∼ mGUT ∼ 10 16 GeV. This paper also discusses other variants of the natural inflation paradigm: we show that axion monodromy with potential V ∝ φ 2/3 is inconsistent with the BICEP2 limits at the 95% confidence level, and low-scale inflation is strongly ruled out. Linear potentials V ∝ φ are inconsistent with the BICEP2 limit at the 95% confidence level, but are marginally consistent with a joint Planck/BICEP2 limit at 95%. We discuss the pseudo-Nambu Goldstone model proposed by Kinney and Mahanthappa as a concrete realization of low-scale inflation. While the low-scale limit of the model is inconsistent with the data, the large-field limit of the model is marginally consistent with BICEP2. All of the models considered predict negligible running of the scalar spectral index, and would be ruled out by a detection of running.

Hybrid Natural Inflation

“…Among the many models proposed to implement the inflationary paradigm [1][2][3][4][5][6], Natural Inflation (NI) [7][8][9][10] is particularly appealing because its origins lie in well motivated physics. In this scheme the inflaton potential has the form V I (φ) = ∆ 4 1 + cos φ f , (1.1) where the inflaton, φ, is a pseudo-Goldstone boson associated with a spontaneously broken global symmetry and is thus protected from large radiative corrections to its mass.…”

Monodromy inflation in SUSY QCD

“…The value of r cited by BICEP2 after subtracting estimated foreground dust contributions is r = 0.16. A joint likelihood fit between Planck and BICEP2 suggests r ≈ 0.15 ± .05 [15]. 8 Note that Wnp ∼ Λ …”

“…We review them here in brief. For a precise study and detailed review of natural inflation in light of BICEP2, see [15], in particular figures 1 and 5 (note that for comparison, the reduced Planck mass used in this work must be converted to the Planck mass used in [15]). The slow-roll parameters take the NI form,…”

“…Discussed principally in string theory [8,9], the basic idea is to consider axions with subplanckian decay constants, f a < M pl , and dynamics that permit angular excursions much larger than 2π. 1 Following the BICEP2 announcement, there have been a number of studies updating and extending earlier work on natural inflation [15] and monodromy inflation [16][17][18][19][20][21].…”

Phase locked inflation. Effectively trans-Planckian natural inflation

“…The shape of the inflaton potential is well controlled by small explicit breaking of the spontaneously broken symmetry. After the announcement of a large tensor fraction in the CMB, r = O(0.1), by the BICEP2 collaboration [9], natural inflation has received renewed attention since it shows a perfect fit with the BICEP2 result [10].…”