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Register a new userLarge tensor spectrum of BICEP2 in the natural SUSY hybrid model
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The large tensor spectrum recently observed by the BICEP2 Collaboration requires a super-Planckian field variation of the inflaton in the single-field inflationary scenario. The required slow-roll parameter epsilon approx 0.01 would restrict the e-folding number to around 7 in (sub-)Planckian inflationary models. To overcome such problems, we consider a two-field scenario based on the natural assisted supersymmetric (SUSY) hybrid model (natural SUSY hybrid inflation [1]), which combines the SUSY hybrid and the natural inflation models. The axionic inflaton field from the natural inflation sector can admit the right values for the tensor spectrum as well as a spectral index of 0.96 with a decay constant smaller than the Planck scale, f lesssim M_P. On the other hand, the vacuum energy of 2 x 10^{16} GeV with 50 e-folds is provided by the inflaton coming from the SUSY hybrid sector, avoiding the eta problem. These are achieved by introducing both the U(1)_R and a shift symmetry, and employing the minimal Kahler potential.
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We revisit the recently proposed multi-natural inflation and its realization in supergravity in light of the BICEP2 results. Multi-natural inflation is a single-field inflation model where the inflaton potential consists of multiple sinusoidal functions, and it is known that a sizable running spectral index can be generated, which relaxes the tension between the BICEP2 and the Planck results. In this paper we show that multi-natural inflation can accommodate a wide range of values of $(n_s, r)$, including the spectral index close to or even above unity. This will be be favored if the tension is resolved by other sources such as dark radiation, hot dark matter, or non-zero neutrino mass. We also discuss the implications for the implementation in string theory.
Supersymmetric (SUSY) models and dynamical breaking of symmetries have been used to explain hierarchies of mass scales. We find that a chiral representation, $overline{bf 10}, oplus, overline{bf 5}, oplus, 2cdot{bf 5}$ in SUSY SU(5) in the hidden sector, breaks global SUSY dynamically, by producing a composite field $phi$ below the SU(5) confinement scale. This dynamincal SUSY breaking can have two important applications, one in particle physics and the other in cosmology. Gavitational effects transmit this dynamical breaking to the standard model(SM) superpartners and the quintessential vacuum energy. The SM superpartners feel the effects just by the magnitude of the gravitino mass while the smallness of the quintessential vacuum energy is due to the composite nature of a singlet field $phi$. The composite $phi$ carries a global charge which is hardly broken in SUSY and hence its phase can be used toward a quintessential axion for dark energy of the Universe.
The QCD axion solving the strong CP problem may originate from antisymmetric tensor gauge fields in compactified string theory, with a decay constant around the GUT scale. Such possibility appears to be ruled out now by the detection of tensor modes by BICEP2 and the PLANCK constraints on isocurvature density perturbations. A more interesting and still viable possibility is that the string theoretic QCD axion is charged under an anomalous U(1)_A gauge symmetry. In such case, the axion decay constant can be much lower than the GUT scale if moduli are stabilized near the point of vanishing Fayet-Illiopoulos term, and U(1)_A-charged matter fields get a vacuum value far below the GUT scale due to a tachyonic SUSY breaking scalar mass. We examine the symmetry breaking pattern of such models during the inflationary epoch with the Hubble expansion rate 10^{14} GeV, and identify the range of the QCD axion decay constant, as well as the corresponding relic axion abundance, consistent with known cosmological constraints. In addition to the case that the PQ symmetry is restored during inflation, there are other viable scenarios, including that the PQ symmetry is broken during inflation at high scales around 10^{16}-10^{17} GeV due to a large Hubble-induced tachyonic scalar mass from the U(1)_A D-term, while the present axion scale is in the range 10^{9}-5times 10^{13} GeV, where the present value larger than 10^{12} GeV requires a fine-tuning of the axion misalignment angle. We also discuss the implications of our results for the size of SUSY breaking soft masses.
Generically, the gravitational-wave or tensor-mode contribution to the primordial curvature spectrum of inflation is tiny if the field-range of the inflaton is much smaller than the Planck scale. We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models. More specifically, we consider models where an axion-like shift symmetry keeps the inflaton potential flat (up to non-perturbative cosine-shaped modulations), but inflation nevertheless ends in a waterfall-regime, as is typical for hybrid inflation. In such hybrid natural inflation scenarios (examples are provided by Wilson line inflation and fluxbrane inflation), the slow-roll parameter $epsilon$ can be sizable during an early period (relevant for the CMB spectrum). Subsequently, $epsilon$ quickly becomes very small before the tachyonic instability eventually terminates the slow roll regime. In this scenario, one naturally generates a considerable tensor-mode contribution in the curvature spectrum, collecting nevertheless the required amount of e-foldings during the final period of inflation. While non-observation of tensors by Planck is certainly not a problem, a discovery in the medium to long term future is realistic.
We propose a landscape of many axions, where the axion potential receives various contributions from shift symmetry breaking effects. We show that the existence of the axion with a super-Planckian decay constant is very common in the axion landscape for a wide range of numbers of axions and shift symmetry breaking terms, because of the accidental alignment of axions. The effective inflation model is either natural or multi-natural inflation in the axion landscape, depending on the number of axions and the shift symmetry breaking terms. The tension between BICEP2 and Planck could be due to small modulations to the inflaton potential or steepening of the potential along the heavy axions after the tunneling. The total duration of the slow-roll inflation our universe experienced is not significantly larger than $60$ if the typical height of the axion potentials is of order $(10^{16-17}{rm ,GeV})^4$.
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