Evidence from the BICEP2 experiment for a significant gravitational-wave background has focussed attention on inflaton potentials V (φ) ∝ φ α with α = 2 ("chaotic" or "m 2 φ 2 " inflation) or with smaller values of α, as may arise in axion-monodromy models. Here we show that reheating considerations may provide additional constraints to these models. The reheating phase preceding the radiation era is modeled by an effective equation-of-state parameter wre. The canonical reheating scenario is then described by wre = 0. The simplest α = 2 models are consistent with wre = 0 for values of ns well within the current 1σ range. Models with α = 1 or α = 2/3 require a more exotic reheating phase, with −1/3 < wre < 0, unless ns falls above the current 1σ range. Likewise, models with α = 4 require a physically implausible wre > 1/3, unless ns is close to the lower limit of the 2σ range. For m 2 φ 2 inflation and canonical reheating as a benchmark, we derive a relation log 10 Tre/10 6 GeV ≃ 2000 (ns − 0.96) between the reheat temperature Tre and the scalar spectral index ns. Thus, if ns is close to its central value, then Tre 10 6 GeV, just above the electroweak scale. If the reheat temperature is higher, as many theorists may prefer, then the scalar spectral index should be closer to ns ≃ 0.965 (at the pivot scale k = 0.05 Mpc −1 ), near the upper limit of the 1σ error range. Improved precision in the measurement of ns should allow m 2 φ 2 , axion-monodromy, and φ 4 models to be distinguished, even without precise measurement of r, and to test the m 2 φ 2 expectation of ns ≃ 0.965. PACS numbers:Introduction. The imprint of inflationary gravitational waves in the cosmic microwave background polarization [1] reported by the BICEP2 collaboration [2] implies, if confirmed, that the inflaton field φ traversed a distance large compared with the Planck mass during inflation [3,4]. One particularly simple and elegant model for large-field inflation is "m 2 φ 2 " inflation [5, 6] (derived originally as a simple example of chaotic inflation [7]), in which the inflaton potential is simply a quadratic function of φ. Ref. [8] recently argued that this is perhaps the simplest and most elegant model. They then derived a consistency relation between the scalar spectral index (now constrained to be n s − 1 = −0.0397 ± 0.0073 [9]) and tensor-to-scalar ratio (roughly r ∼ 0.2 according to Ref. [2]) that can be tested with higher-precision measurements of n s and in particular of r. Another promising candidate large-field model, axion monodromy which suggests a potential V ∝ φ [10] or V ∝ φ 2/3 [11], has also been receiving considerable attention. We parametrize all these models by a power-law potential V ∝ φ α .

We report the detection of new binary black hole merger events in the publicly available data from the second observing run of advanced LIGO and advanced Virgo (O2). The mergers were discovered using the new search pipeline described in Venumadhav et al.[1], and are above the detection thresholds as defined in Abbott et al. [2]. Three of the mergers (GW170121, GW170304, GW170727) have inferred probabilities of being of astrophysical origin pastro > 0.98. The remaining three (GW170425, GW170202, GW170403) are less certain, with pastro ranging from 0.5 to 0.8. The newly found mergers largely share the statistical properties of previously reported events, with the exception of GW170403, the least secure event, which has a highly negative effective spin parameter χ eff . The most secure new event, GW170121 (pastro > 0.99), is also notable due to its inferred negative value of χ eff , which is inconsistent with being positive at the ≈ 95.8% confidence level. The new mergers nearly double the sample of gravitational wave events reported from O2, and present a substantial opportunity to explore the statistics of the binary black hole population in the Universe. The number of detected events is not surprising since we estimate that the detection volume of our pipeline is nearly twice that of other pipelines. The increase in volume is larger when the constituent detectors of the network have very different sensitivities, as is likely to be the case in current and future runs.

We report a new binary black hole merger in the publicly available LIGO First Observing Run (O1) data release. The event has a false alarm rate of one per six years in the detector-frame chirp-mass range M det ∈ [20, 40]M in a new independent analysis pipeline that we developed. Our best estimate of the probability that the event is of astrophysical origin is Pastro ∼ 0.71 . The estimated physical parameters of the event indicate that it is the merger of two massive black holes, M det = 31 +2 −3 M with an effective spin parameter, χ eff = 0.81 +0.15 −0.21 , making this the most highly spinning merger reported to date. It is also among the two highest redshift mergers observed so far. The high aligned spin of the merger supports the hypothesis that merging binary black holes can be created by binary stellar evolution.