RIKEN Accel. Prog. Rep. 47 (2014)

HIGHLIGHTS OF THE YEAR

Primordial spectra from sudden turning trajectory†
T. Noumi∗1 and M. Yamaguchi∗2Inﬂation is strongly supported by recent observations of cosmic microwave background (CMB)
anisotropies.1,2) In particular, single ﬁeld slow-roll
inﬂation predicts almost adiabatic, Gaussian, andscale invariant primordial curvature perturbations,and these predictions well ﬁt the observational results.
On the other hand, high energy theories such as supergravity and superstring theory generically predict
additional scalar ﬁelds other than inﬂaton. To reconcile such a generic prediction of theories with recent
observations, it may be suggested that only one lightﬁeld plays a role of inﬂaton while the others are heavy.
In fact, eﬀects of such heavy ﬁelds are generically suppressed by their mass and the inﬂationary dynamics
can be well approximated by single ﬁeld inﬂation.
While such a scenario can explain the current observational results well, it would be quite interesting if
we could detect some deviation from single ﬁeld slowroll inﬂation in the current and future observational
experiments: such a deviation would be useful as aprobe of high energy physics. In this report, we would
like to investigate a possibility that heavy ﬁelds can affect inﬂationary dynamics and imprint some featureson primordial spectra.
One typical situation heavy ﬁelds matter is the casewhen heavy ﬁelds are excited by the sudden turn of thepotential and oscillates with high frequency.3–7) In general, oscillations of heavy ﬁelds generate the following
two signiﬁcant eﬀects: the modiﬁcation of the Hubble
parameter and the conversion eﬀect, that is, the mixing between adiabatic and isocurvature (heavy ﬁeld)
modes. We investigate these eﬀects in detail and evaluate the power spectra and bispectra of the primordial curvature perturbations in two-ﬁeld inﬂationarymodels with the canonical kinetic terms and a sudden
turning potential.
Suppose that the background trajectory is ﬁrst along
the bottom of the potential (the slow-roll direction).
The trajectory starts oscillating at the turning point
and such a heavy ﬁeld oscillation induces a deviationfrom single ﬁeld slow-roll inﬂation. The primordialpower spectrum of scalar curvature perturbations canthen be calculated as2]
[HsrPζ (k) =1 + CHubble (k) + Cconv (k) , (1)22
8π Msr ϵsr

m = 20Hsr

C
α2kk∗
Fig. 1. Deviation in the primordial power spectrum. Theorange/red/blue are −CHubble , Cconv , and C = CHubble +Cconv , respectively. Free parameters of our model are
the heavy field mass m, the turning angular α, and theturning scale k∗ . Here we used m = 20sr and assumed
that α is small enough, say α ∼ O(0.1).

The deviation CHubble is from the Hubble deformationeﬀect and Cconv is from the conversion eﬀect. As depicted in Fig. 1, the parametric resonance ampliﬁcation occurs from both of the two eﬀects and the peakat the turning scale arises from the conversion eﬀect.
It is, however, explicitly shown that resonance eﬀects
from the two eﬀects accidentally cancel each other out
for the case with the canonical kinetic terms. As a consequence, the peak at the turning scale becomes clear
and this feature characterizes this class of models withheavy ﬁeld oscillations.
We also evaluated primordial bispectra, whose main
source comes again from the Hubble deformation eﬀect
and the conversion interaction. We ﬁnd resonance andpeak features in the bispectra as in the case of power
spectra. Although the size of bispectra is not necessarily large, our results may be useful for probing theseeﬀects observationally.
In this work, we discussed two-ﬁeld models with asudden turning potential as a phenomenological toy
model, and clariﬁed features of heavy ﬁeld oscillations.
It would be interesting to investigate more realistic
models with heavy ﬁeld oscillations e.g. based on
string theory. It must be important to discuss theirdetectability in the current and future observations.
Referenceswhere the ﬁrst term represents the almost scaleinvariant power spectrum in single ﬁeld slow-roll inﬂation. The last two terms are the scale-dependent
deviation originated from the heavy ﬁeld oscillations.
†∗1∗2

Condensed from the article in JCAP 1312 (2013) 038
RIKEN Nishina Center
Department of Physics, Tokyo Institute of Technology- xxvii -1) G. Hinshaw et al.: arXiv:1212.5226.
2) P. A. R. Ade et al.: arXiv:1303.5082.
3) X. Chen: JCAP 1201, 038 (2012).
4) G. Shiu and J. Xu: Phys. Rev. D 84, 103509 (2011).
5) S. Cespedes, V. Atal and G. A. Palma: JCAP 1205,008 (2012).
6) A. Achucarro, J. -O. Gong, S. Hardeman, G. A. Palmaand S. P. Patil: JHEP 1205, 066 (2012).
7) X. Gao, D. Langlois and S. Mizuno: JCAP 1210, 40(2012).