Physics Letters B 752 (2016) 169–174
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Physics Letters B
www.elsevier.com/locate/physletb
Primordial monopoles, proton decay, gravity waves and GUT inflation
Vedat Nefer ¸Seno
˘
guz
a,∗
, Qaisar Shafi
b
a
Department of Physics, Mimar Sinan Fine Arts University, 34380 ¸Si ¸sli,
˙
Istanbul,
Turkey
b
Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
23 October 2015
Accepted
13 November 2015
Available
online 18 November 2015
Editor: M.
Cveti
ˇ
c
We consider non-supersymmetric GUT inflation models in which intermediate mass monopoles may
survive inflation because of the restricted number of e-foldings experienced by the accompanying
symmetry breaking. Thus, an observable flux of primordial magnetic monopoles, comparable to or a
few orders below the Parker limit may be present in the galaxy. The mass scale associated with
the intermediate symmetry breaking is 10
13
GeV for an observable flux level, with the corresponding
monopoles an order of magnitude or so heavier. Examples based on SO(10) and E
6
yield such
intermediate mass monopoles carrying respectively two and three units of Dirac magnetic charge. For
GUT inflation driven by a gauge singlet scalar field with a Coleman–Weinberg or Higgs potential,
compatibility with the Planck measurement of the scalar spectral index yields a Hubble constant (during
horizon exit of cosmological scales) H ∼ 7–9 ×10
13
GeV, with the tensor to scalar ratio r predicted to be
0.02. Proton lifetime estimates for decays mediated by the superheavy gauge bosons are also provided.
© 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
The observed quantization of electric charge is elegantly ex-
plained
by invoking the presence of magnetic monopoles, as
shown by Dirac more than eighty years ago [1]. Contemporary
unified theories with electric charge quantization based on groups
such as SU(4) × SU(2)
L
× SU(2)
R
[2], SU(5) [3], SO(10) or E
6
, pre-
dict
the existence of topologically stable magnetic monopoles [4],
and one expects that these monopoles are produced in the early
universe.
Despite
the presence of fractionally charged quarks, the light-
est
SU(5) monopole carries a single unit of Dirac magnetic charge.
This comes about because the unbroken gauge symmetry SU(3)
c
×
U (1)
em
share a Z
3
symmetry [5]. The SU(5) monopole ends up
carrying some color magnetic flux that is screened due to color
confinement. The SU(5) monopoles are superheavy with a mass
about an order of magnitude larger than M
GUT
∼ 2 ×10
16
GeV.
In
non-supersymmetric GUTs such as SO(10) broken to the
Standard Model (SM) via G
422
= SU(4)
c
× SU(2)
L
× SU(2)
R
, there
appears a new scenario for monopole charges and masses. The
SO(10) breaking to G
422
yields, just as in SU(5), a superheavy
*
Corresponding author.
E-mail
address: nefer.senoguz@msgsu.edu.tr (V.N. ¸Seno
˘
guz).
monopole with a single unit of Dirac magnetic charge [6]. The
subsequent breaking of G
422
at some intermediate mass scale M
I
yields monopoles that carry two units of Dirac charge and mass
that can be a few orders of magnitude smaller than the mass of
the SU(5) monopole [6].
It
was argued a long time ago by Lazarides and Shafi [7] that
within the framework of GUT inflation driven by a gauge singlet
scalar inflaton field [8], these somewhat lighter monopoles may
not be entirely inflated away.
1
The superheavy monopoles pro-
duced
during the first stage of symmetry breaking experience at
least the 50–60 e-foldings of observable inflation. The somewhat
lighter monopoles, produced during the intermediate symmetry
breaking with mass determined by M
I
and comparable to the
Hubble constant H during inflation, may undergo a significantly
reduced number of e-foldings. Therefore, there arises the excit-
ing
possibility that these monopoles, lighter than M
GUT
, may be
present in our galaxy at an observable number density, compara-
ble
to or a few orders of magnitude below the Parker bound [10].
In
recent years the WMAP [11] and Planck [12,13] satellite ex-
periments
have provided a fairly accurate determination of the
scalar spectral index n
s
and an upper bound for the tensor to scalar
ratio r 0.1. In the framework of GUT inflation driven by a gauge
1
For an earlier discussion of this with cosmic strings, see Ref. [9].
http://dx.doi.org/10.1016/j.physletb.2015.11.037
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
.