Hayato Motohashi

Ultra Slow-Roll Inflation and the non-Gaussianity Consistency Relation

Ultra slow-roll inflation has recently been used to challenge the non-Gaussianity consistency relation. We show that this inflationary scenario belongs to a one parameter class of models and we study its properties and observational predictions. We demonstrate that the power spectrum remains scale-invariant and that the bi-spectrum is of the local type with fnl=5(3-ns)/4 which, indeed, represents a modification of the consistency relation. However, we also show that the system is unstable and suffers from many physical problems among which is the difficulty to correctly WMAP normalize the model. We conclude that ultra slow-roll inflation remains a very peculiar case, the physical relevance of which is probably not sufficient to call into question the validity of the consistency relation.

Phantom Boundary Crossing and Anomalous Growth Index of Fluctuations in Viable f(R) Models of Cosmic Acceleration

The evolution of a background space-time metric and subhorizon matter density perturbations in the Universe is numerically analyzed in viable f (R) models of present dark energy and cosmic acceleration. It is found that viable models generically exhibit recent crossing of the phantom boundary wDE = �1. Furthermore, it is shown that, as a consequence of the anomalous growth of density perturbations during the end of the matter-dominated stage, their growth index evolves nonmonotonically with time and may even become negative temporarily. Subject Index: 451, 453, 460

Healthy degenerate theories with higher derivatives

In the context of classical mechanics, we study the conditions under which higher-order derivative theories can evade the so-called Ostrogradsky instability. More precisely, we consider general Lagrangians with second order time derivatives, of the form

Black hole perturbation in the most general scalar-tensor theory with second-order field equations. II. The even-parity sector

L(\ddot\phi^a,\dot\phi^a,\phi^a;\dot q^i,q^i)

Analytic solution for matter density perturbations in a class of viable cosmological f(R) models

with

Third order equations of motion and the Ostrogradsky instability

a = 1,\cdots, n

Primordial Black Holes and Slow-Roll Violation

and

Matter Power Spectrum in f(R) Gravity with Massive Neutrinos

i = 1,\cdots, m

Constant-roll inflation: Confrontation with recent observational data

. For

f ( R ) constant-roll inflation

n=1