Physics Letters B 752 (2016) 108–112
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Single-superfield helical-phase inflation
Sergei V. Ketov
a,b,c
, Takahiro Terada
d,e,∗
a
Department of Physics, Tokyo Metropolitan University, Minami-ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan
b
Kavli Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo, Chiba 277-8568, Japan
c
Institute of Physics and Technology, Tomsk Polytechnic University, 30 Lenin Ave., Tomsk 634050, Russian Federation
d
Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
e
Deutsches Elektronen-Synchrotron (DESY), 22607 Hamburg, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received
16 September 2015
Received
in revised form 19 October 2015
Accepted
13 November 2015
Available
online 17 November 2015
Editor:
J. Hisano
Large-field inflation in supergravity requires the approximate global symmetry needed to protect flatness
of the scalar potential. In helical-phase inflation, the U(1) symmetry of the Kähler potential is assumed,
the phase part of the complex scalar of a chiral superfield plays the role of inflaton, and the radial part is
strongly stabilized. The original model of helical phase inflation, proposed by Li, Li and Nanopoulos (LLN),
employs an extra (stabilizer) superfield. We propose a more economical new class of the helical phase
inflationary models without a stabilizer superfield. As the specific examples, the quadratic, the natural,
and the Starobinsky-type inflationary models are studied in our approach.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Inflation well explains the origin of primordial density fluctu-
ations,
as well as flatness and homogeneity of our Universe. The
general idea is so far quite successful, and inflationary models are
confronted with precise observational data [1,2]. Since inflation is
a high-energy phenomenon, it is important to study it in a more
fundamental framework such as supergravity [3] which is well mo-
tivated
by particle physics and string theory. In particular, should
tensor perturbations be detected in a near future, it would im-
ply
large (trans-Planckian) excursions of the inflaton field [4]. Then
the Planck-suppressed corrections cannot be neglected. Even if su-
persymmetry
is broken at a higher scale than that of inflation,
supergravity corrections have substantial impact on the scalar po-
tential.
As
is well known, a generic scalar potential in supergravity
tends to be very steep in the large-field region, because of the ex-
ponential
factor of the Kähler potential. Accordingly, it is hard to
achieve flatness of the scalar potential along the whole inflation-
ary
trajectory in the case of large-field models. Therefore, some
symmetries are usually imposed in the inflationary model building
in supergravity. A good example is the axion-like shift symmetry
in the non-SUSY model [5] and in the supergravity-based models
[6,7].
*
Corresponding author.
E-mail
addresses: ketov@tmu.ac.jp (S.V. Ketov),
takahiro@hep-th.phys.s.u-tokyo.ac.jp (T. Terada).
The similar approach, assuming the global U(1) symmetry and
the related monodromy structure of the superpotential, is known
as the helical-phase inflation, because its inflaton is identified
with the phase component of a complex scalar field rolling down
a helicoid potential [8–11]. Like in the more conventional shift-
symmetric
approach, a stabilizer superfield is used in all the
known helical-phase inflationary models. Actually, the inflation-
ary
models with the non-compact U(1) and those based on the
shift symmetry (with or without a stabilizer superfield) are equiv-
alent,
being related by the inflaton superfield redefinition
U(1)
=
exp(
shift
). Still, it makes sense to study them separately because
adding a simple symmetry-breaking or stabilizing term in one
approach often leads to a complicated structure in the other ap-
proach.
In
the shift-symmetric approach, a stabilizer superfield is
needed to ensure positivity of the potential. In our previous work
[12,13] (see also Ref. [14]), we proposed the alternative framework
to achieve the same goal by stabilizing the scalar superpartner of
the inflaton. In our approach, a number of the physical degrees of
freedom was reduced, while a quartic shift-symmetric term was
added to the Kähler potential.
In this letter, we study the helical-phase inflation without a
stabilizer superfield. In Sec. 2 the radial part is stabilized by em-
ploying
a higher-order (polynomial) term in the Kähler poten-
tial,
similarly to Refs. [12,13]. The inflaton is identified with the
Pseudo-Nambu–Goldstone boson of the approximate U(1) symme-
try
of the Kähler potential. A few particular models are studied in
Sec. 3. We conclude in Sec. 4. Throughout the paper, we use the
natural (reduced) Planck units, c =
¯
h = M
P
/
√
8π = 1.
http://dx.doi.org/10.1016/j.physletb.2015.11.039
0370-2693/
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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