We study the properties of gravitational wave (GW) signals produced by first-order phase transitions during the inflation era. We show that the power spectrum of a GW oscillates with its wave number. This signal can be observed directly by future terrestrial and spatial GW detectors and through the B-mode spectrum in the CMB. This oscillatory feature of the GW is generic for any approximately instantaneous sources occurring during inflation and is distinct from the GW from phase transitions after inflation. The details of the GW spectrum contain information about the scale of the phase transition and the later evolution of the universe.

We study implications of perturbative unitarity for quasi-single field inflation with the inflaton and one massive scalar. Analyzing high energy scattering, we show that non-Gaussianities with vertical bar f(NL)vertical bar greater than or similar to 1 cannot be realized without turning on interactions which violate unitarity at a high energy scale. Then, we provide a relation between f(NL) and the scale of new physics that is required for UV completion. In particular we find that for the Hubble scale H greater than or similar to 6 x 10(9) GeV, Planck suppressed operators can easily generate too large non-Gaussanities and so it is hard to realize successful quasi-single field inflation without introducing a mechanism to suppress quantum gravity corrections. Also we generalize the analysis to the regime where the isocurvature mode is heavy and the inflationary dynamics is captured by the inflaton effective theory. Requiring perturbative unitarity of the two-scalar UV models with the inflaton and one heavy scalar, we clarify the parameter space of the P(X, phi) model which is UV completable by a single heavy scalar.

We study semiclassical spiky strings in de Sitter space and the corresponding Regge trajectories, generalizing the analysis in anti-de Sitter space. In particular we demonstrate that each Regge trajectory has a maximum spin due to de Sitter acceleration, similarly to the folded string studied earlier. While this property is useful for the spectrum to satisfy the Higuchi bound, it makes a nontrivial question how to maintain mildness of high-energy string scattering which we are familiar with in flat space and anti-de Sitter space. Our analysis implies that in order to have infinitely many higher spin states, one needs to consider infinitely many Regge trajectories with an increasing folding number.

We discuss two possible scenarios, namely the curvaton mechanism and the dark matter density modulation, where non-Gaussianity signals of superheavy dark matter produced by gravity can be enhanced and observed. In both scenarios, superheavy dark matter couples to an additional light field as a mediator. In the case of derivative coupling, the resulting non-Gaussianities induced by the light field can be large, which can provide inflationary evidences for these superheavy dark matter scenarios.

We study the spectrum of semiclassical rotating strings in de Sitter space and its consistency. Even though a naive extrapolation of the linear Regge trajectory on flat space implies a violation of the Higuchi bound (a unitarity bound on the mass of higher-spin particles in de Sitter space), the curved space effects turn out to modify the trajectory to respect the bound. Interestingly, as a consequence of accelerated expansion, there exists a maximum spin for each Regge trajectory, which is helpful to make the spectrum consistent with the Higuchi bound, but at the same time, it could be an obstruction to stringy UV completion based on an infinite higher-spin tower. By pushing further this observation, we demonstrate that the vacuum energy V inflating the Universe has to be bounded by the string scale M-s as V less than or similar to M-s(4), if UV completion is achieved with the leading Regge trajectory of higher spin states up to the 4D Planck scale. Its application to inflation in the early Universe implies an upper bound on the tensor-to-scalar ratio, r less than or similar to 0.01 x (M-s/10(16) GeV)(4), which is within the scope of the near future CMB experiments. We also discuss another possibility that UV completion is achieved by multiple Regge trajectories.