Physics Letters B 781 (2018) 639–644
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Scalar field dark matter with spontaneous symmetry breaking and the
3.5 keV line
Catarina Cosme
a,∗
, João G. Rosa
b
, O. Bertolami
a
a
Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto and Centro de Física do Porto, Rua do Campo Alegre 687, 4169-007 Porto,
Portugal
b
Departamento de Física da Universidade de Aveiro and Center for Research and Development in Mathematics and Applications (CIDMA), Campus de Santiago,
3810-183 Aveiro, Portugal
a r t i c l e i n f o a b s t r a c t
Article history:
Received
13 March 2018
Received
in revised form 27 April 2018
Accepted
27 April 2018
Available
online 1 May 2018
Editor: M.
Trodden
Keywords:
Dark
matter
Scalar
field
Higgs
boson
We show that the present dark matter abundance can be accounted for by an oscillating scalar field
that acquires both mass and a non-zero expectation value from interactions with the Higgs field. The
dark matter scalar field can be sufficiently heavy during inflation, due to a non-minimal coupling to
gravity, so as to avoid the generation of large isocurvature modes in the CMB anisotropies spectrum. The
field begins oscillating after reheating, behaving as radiation until the electroweak phase transition and
afterwards as non-relativistic matter. The scalar field becomes unstable, although sufficiently long-lived
to account for dark matter, due to mass mixing with the Higgs boson, decaying mainly into photon pairs
for masses below the MeV scale. In particular, for a mass of ∼ 7keV, which is effectively the only free
parameter, the model predicts a dark matter lifetime compatible with the recent galactic and extragalactic
observations of a 3.5 keV X-ray line.
© 2018 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
.
One of the most important open problems in modern cos-
mology
is the nature of dark matter (DM), an invisible form of
matter that can explain the observed structure of the Universe
on large scales, the galaxy rotation curves and the anisotropies
in the Cosmic Microwave Background (CMB). However, despite the
large number of candidates, there are still no definite answers con-
cerning
its origin [1]. An interesting possibility is an interaction
between DM and the Higgs field, widely known as “Higgs-portal
DM”. This has been extensively studied in the literature, namely in
the context of thermal production [2–14]. However, the lack of ev-
idence
for WIMP-like particles in the various ongoing experiments
[15]suggests looking for alternative candidates, such as oscillating
scalar fields, as considered e.g. in Refs. [16–18].
In
this Letter, we show for the first time that a scalar field dark
matter coupled to the Higgs field can naturally explain the 3.5 keV
X-ray line detected by the XMM-Newton observatory. Our model
considers a complex scalar field, , interacting with the Higgs
doublet, H, only through scale-invariant interactions given by the
Lagrangian density:
*
Corresponding author.
E-mail
addresses: catarinacosme @fc .up .pt (C. Cosme), joao .rosa @ua .pt (J.G. Rosa),
orfeu .bertolami @fc .up .pt (O. Bertolami).
L
int
=±g
2
|
|
2
|
H
|
2
+λ
φ
|
|
4
+ V
(
H
)
+ξ
R
|
|
2
, (1)
where the Higgs potential V (H) has the standard “mexican hat“
shape. We assume that the scale invariance of the interactions
is a consequence of an underlying scale invariance of the full the-
ory,
that is spontaneously broken in the Higgs and gravitational
sectors by some mechanism that has no influence on the effective
dynamics of the dark matter scalar field (see also Ref. [19]). This
allows for the Higgs-dark scalar interaction with coupling, g, the
dark scalar field quartic self-interactions with coupling, λ
φ
, and for
a non-minimal coupling, ξ , of the DM to the Ricci scalar, R.
The
interaction Lagrangian (1)also exhibits a U(1) symmetry
and we may consider two cases. When the Higgs-dark scalar in-
teraction
has a positive sign, the U(1) symmetry remains unbroken
and the DM field is stable. For a negative coupling, the U(1) sym-
metry
can be spontaneously broken in the vacuum and the DM
field may decay, allowing for astrophysical signatures, as we will
see below. In this Letter, we focus on the latter case, leaving the
discussion of the former to a longer companion paper.
The
background dynamics of the homogeneous dark scalar field
mode is determined by the equation of motion:
¨
φ +
3H
˙
φ +
V
(
φ
)
+
2ξ Rφ = 0 , (2)
where = φ/
√
2since the complex phase has a trivial dynam-
ics.
From the associated energy-momentum tensor, we obtain the
https://doi.org/10.1016/j.physletb.2018.04.062
0370-2693/
© 2018 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
.