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de Rham, C., & Motohashi, H. (2017). Caustics for spherical waves. Phys. Rev. D, 95(6), 064008–13pp.
Abstract: We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an SO(p)-symmetry in an arbitrary number of space dimensions. We show that the pure Galileon, the DBI-Galileon, and the extreme-relativistic Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple SO(p)-waves and the existence of either a global Galilean symmetry or a global (extreme-) relativistic Galilean symmetry.
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Motohashi, H., & Hu, W. (2017). Generalized slow roll in the unified effective field theory of inflation. Phys. Rev. D, 96(2), 023502–17pp.
Abstract: We provide a compact and unified treatment of power spectrum observables for the effective field theory (EFT) of inflation with the complete set of operators that lead to second-order equations of motion in metric perturbations in both space and time derivatives, including Horndeski and Gleyzes-Langlois-Piazza-Vernizzi theories. We relate the EFT operators in ADM form to the four additional free functions of time in the scalar and tensor equations. Using the generalized slow-roll formalism, we show that each power spectrum can be described by an integral over a single source that is a function of its respective sound horizon. With this correspondence, existing model independent constraints on the source function can be simply reinterpreted in the more general inflationary context. By expanding these sources around an optimized freeze-out epoch, we also provide characterizations of these spectra in terms of five slow-roll hierarchies whose leading-order forms are compact and accurate as long as EFT coefficients vary only on time scales greater than an e-fold. We also clarify the relationship between the unitary gauge observables employed in the EFT and the comoving gauge observables of the postinflationary universe.
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Motohashi, H., & Hu, W. (2017). Primordial black holes and slow-roll violation. Phys. Rev. D, 96(6), 063503–9pp.
Abstract: For primordial black holes (PBH) to be the dark matter in single-field inflation, the slow-roll approximation must be violated by at least O(1) in order to enhance the curvature power spectrum within the required number of e-folds between cosmic microwave background scales and PBH mass scales. Power spectrum predictions which rely on the inflaton remaining on the slow-roll attractor can fail dramatically leading to qualitatively incorrect conclusions in models like an inflection potential and misestimate the mass scale in a running mass model. We show that an optimized temporal evaluation of the Hubble slow-roll parameters to second order remains a good description for a wide range of PBH formation models where up to a 10(7) amplification of power occurs in 10 e-folds or more.
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Motohashi, H., & Starobinsky, A. A. (2017). f (R) constant-roll inflation. Eur. Phys. J. C, 77(8), 538–8pp.
Abstract: The previously introduced class of two-parametric phenomenological inflationary models in general relativity in which the slow-roll assumption is replaced by the more general, constant-roll condition is generalized to the case of f (R) gravity. A simple constant-roll condition is defined in the original Jordan frame, and exact expressions for a scalaron potential in the Einstein frame, for a function f (R) (in the parametric form) and for inflationary dynamics are obtained. The region of the model parameters permitted by the latest observational constraints on the scalar spectral index and the tensor-to-scalar ratio of primordial metric perturbations generated during inflation is determined.
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Motohashi, H., & Starobinsky, A. A. (2017). Constant-roll inflation: Confrontation with recent observational data. EPL, 117(3), 39001–3pp.
Abstract: The previously proposed class of phenomenological inflationary models in which the assumption of inflaton slow-roll is replaced by the more general, constant-roll condition is compared with the most recent cosmological observational data, mainly the Planck ones. Models in this two-parametric class which remain viable appear to be close to the slow-roll ones, and their inflaton potentials are close to (but still different from) that of the natural inflation model. The permitted regions for the two model parameters are presented.
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Ramirez, H., Passaglia, S., Motohashi, H., Hu, W., & Mena, O. (2018). Reconciling tensor and scalar observables in G-inflation. J. Cosmol. Astropart. Phys., 04(4), 039–20pp.
Abstract: The simple m(2)phi(2) potential as an inflationary model is coming under increasing tension with limits on the tensor-to-scalar ratio r and measurements of the scalar spectral index n(s). Cubic Galileon interactions in the context of the Horndeski action can potentially reconcile the observables. However, we show that this cannot be achieved with only a constant Galileon mass scale because the interactions turn off too slowly, leading also to gradient instabilities after inflation ends. Allowing for a more rapid transition can reconcile the observables but moderately breaks the slow-roll approximation leading to a relatively large and negative running of the tilt alpha(s) that can be of order n(s) – 1. We show that the observables on CMB and large scale structure scales can be predicted accurately using the optimized slow-roll approach instead of the traditional slow-roll expansion. Upper limits on vertical bar alpha(s)vertical bar place a lower bound of r greater than or similar to 0.005 and, conversely, a given r places a lower bound on vertical bar alpha(s)vertical bar, both of which are potentially observable with next generation CMB and large scale structure surveys.
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Takahashi, K., Motohashi, H., Suyama, T., & Kobayashi, T. (2017). General invertible transformation and physical degrees of freedom. Phys. Rev. D, 95(8), 084053–12pp.
Abstract: An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.
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