Axion cold dark matter: status after Planck and BICEP2
Eleonora Di Valentino,1 Elena Giusarma,1 Massimiliano Lattanzi,2
Alessandro Melchiorri,1 and Olga Mena3
1Physics Department and INFN, Universita di Roma La Sapienza,
Ple Aldo Moro 2, 00185, Rome, Italy2Dipartimento di Fisica e
Science della Terra, Universita di Ferrara and INFN,
sezione di Ferrara, Polo Scientifico e Tecnologico - Edficio C
Via Saragat, 1, I-44122 Ferrara Italy3IFIC, Universidad de
Valencia-CSIC, 46071, Valencia, Spain
We investigate the axion dark matter scenario (ADM), in which
axions account for all of the darkmatter in the Universe, in light
of the most recent cosmological data. In particular, we use
thePlanck temperature data, complemented by WMAP E-polarization
measurements, as well as therecent BICEP2 observations of B-modes.
Baryon Acoustic Oscillation data, including those fromthe Baryon
Oscillation Spectroscopic Survey, are also considered in the
numerical analyses.
We find that, in the minimal ADM scenario, the full dataset
implies that the axion mass ma =82.2 1.1eV (corresponding to the
Peccei-Quinn symmetry being broken at a scale fa = (7.540.10) 1010
GeV), or ma = 76.6 2.6eV (fa = (8.08 0.27) 1010 GeV) when we allow
for a non-standard effective number of relativistic species Neff .
We also find a 2 preference for Neff > 3.046.The limit on the
sum of neutrino masses is
m < 0.25 eV at 95% CL for Neff = 3.046, or
m < 0.47 eV when Neff is a free parameter.Considering
extended scenarios where either the dark energy equation-of-state
parameter w, the
tensor spectral index nt or the running of the scalar index
dns/d ln k are allowed to vary does notchange significantly the
axion mass-energy density constraints. However, in the case of the
fulldataset exploited here, there is a preference for a non-zero
tensor index or scalar running, driven bythe different tensor
amplitudes implied by the Planck and BICEP2 observations.
Dark matter axions with mass in the 70 80eV range can, in
principle, be detected by lookingfor axion-to-photon conversion
occurring inside a tunable microwave cavity permeated by a
high-intensity magnetic field, and operating at a frequency ' 20
GHz. This is out of the reach ofcurrent experiments like ADMX
(limited to a maximum frequency of a few GHzs), but is, on theother
hand, within the reach of the upcoming ADMX-HF experiment, that
will explore the 4 40GHz frequency range and then being sensitive
to axions masses up to 150eV.
PACS numbers: 98.80.-k 95.85.Sz, 98.70.Vc, 98.80.Cq
I. INTRODUCTION
In the past few years, a great deal of observationalevidence has
accumulated in support of the CDM cos-mological model, that is to
date regarded as the stan-dard model of cosmology. One of the great
puzzles re-lated to the CDM model, however, is the nature of
thedark matter (DM) component that, according to the re-cent Planck
observations [13], makes up roughly 27%of the total matter-energy
content of the Universe. Awell-motivated DM candidate is the axion,
that was firstproposed by Peccei and Quinn [4] to explain the
strongCP problem, i.e., the absence of CP violation in
stronginteractions.
Here we consider the hypothesis that the axion ac-counts for all
the DM present in the Universe. We putthis axion dark matter (ADM)
scenario under scrutinyusing the most recent cosmological data, in
particularthe observations of cosmic microwave background
(CMB)temperature [13] and polarization anisotropies (includ-ing the
recent BICEP2 detection of B-mode polarization[5, 6]) and of Baryon
Acoustic Oscillations (BAO) [711].The ADM model has also been
revisited by other au-thors [12, 13] in light of BICEP2 data, and
our analysesin the minimal CDM scenario agree with these previ-ous
works. However, in order to assess the robustness ofthe
cosmological constraints presented in the literature,
as well as the tension between BICEP2 and Planck mea-surements
of the tensor-to scalar ratio, here we also con-sider extensions of
the simplest ADM model. The effectsof additional relativistic
degrees of freedom, of neutrinomasses, of a dark energy
equation-of-state parameter andof a free-tensor spectral index are
carefully explored.
The paper is structured as follows. Section II intro-duces
axions in cosmology and derives the excluded sce-narios after
BICEP2 data. Section III describes the anal-ysis method and the
data used to analyse the ADM mod-els that survive after applying
BICEP2 bounds on grav-itational waves and Planck isocurvature
constraints. InSec. IV we present our main results and we draw
ourconclusions in Sec. V.
II. AXION COSMOLOGY
In order to solve the strong CP problem dynamically,Peccei and
Quinn postulated the existence of a new globalU(1) (quasi-)
symmetry, often denoted U(1)PQ, that isspontaneously broken at the
Peccei-Quinn (PQ) scale fa.The spontaneous breaking of the PQ
symmetry gener-ates a pseudo Nambu-Goldstone boson, the axion,
whichcan be copiously produced in the universes early stages,both
via thermal and non-thermal processes. Thermalaxions with sub-eV
masses contribute to the hot dark
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matter component of the universe, as neutrinos, and
thecosmological limits on their properties have been
recentlyupdated and presented in Refs. [14, 15].
Here we focus on axion-like particles produced non-thermally, as
they were postulated as natural candidatesfor the cold dark matter
component [1620]. The historyof axions start at the PQ scale fa.
For temperaturesbetween this scale and the QCD phase transition
QCD,the axion is, for practical purposes, a massless particle.When
the universes temperature approaches QCD, theaxion acquires a mass
via instanton effects. The effectivepotential V for the axion field
a(x) is generated throughnon-pertubative QCD effects [21] and,
setting the coloranomaly N = 1, it may be written as
V (a) = f2am2a(T )
[1 cos
(a
fa
)], (1)
where the axion mass is a function of temperature. In-troducing
the misalignment angle a/fa, the fieldevolves according to the
Klein-Gordon equation on a flatFriedmann-Robertson-Walker
background:
+ 3H +m2a(T ) = 0 , (2)
where the axion temperature-dependent mass is [21]
ma(T ) =
{Cma(T = 0)(QCD/T )
4 T & QCD
ma(T = 0) T . QCD(3)
where C ' 0.018 is a model dependent factor, seeRefs [21, 22],
QCD ' 200 MeV and the zero-temperaturemass ma(T = 0) is related to
the PQ scale:
ma ' 6.2eV(
fa1012 GeV
)1. (4)
The axion is effectively massless at T QCD, as it canbe seen
from Eq. (3).
The PQ symmetry breaking can occur before or afterinflation. If
there was an inflationary period in the uni-verse after or during
the PQ phase transition, there will
exist, together with the standard adiabatic
perturbationsgenerated by the inflaton field, axion isocurvature
pertur-bations, associated to quantum fluctuations in the
axionfield. In this scenario, i.e. when the condition
fa >
(HI2
), (5)
is satisfied, the initial misalignment angle i should
beidentical in the whole observable universe, with a vari-ance
given by
2 =(HI
2fa
)2, (6)
and corresponding to quantum fluctuations in the mass-less axion
field
2a =(HI2
)2, (7)
where HI is the value of the Hubble parameter duringinflation.
These quantum fluctuations generate an axionisocurvature power
spectrum
a(k) = k3|2a|/22 =
H2I2
2i f2a . (8)
The Planck data, combined with the 9-year polarizationdata from
WMAP [23] constrain the primordial isocur-vature fraction (defined
as the ratio of the isocurvatureperturbation spectrum to the sum of
the adiabatic andisocurvature spectra) to be [24]
iso < 0.039 , (9)
at 95% CL and at a scale k = 0.05 Mpc1. This limitcan be used to
exclude regions in the parameter space ofthe PQ scale and the scale
of inflation HI , since they arerelated via
HI = 0.96 107 GeV(iso0.04
)1/2(a
0.120
)1/2(fa
1011 GeV
)0.408, (10)
where a is the axion mass-energy density. In this sce-nario, in
which the PQ symmetry is not restored afterinflation, and therefore
the condition fa >
(HI2
)holds,
and assuming that the dark matter is made of axions pro-duced by
the misalignment mechanism [39], Planck datahas set a 95% CL upper
bound on the energy scale of
inflation [24]
HI 0.87 107 GeV(
fa1011 GeV
)0.408. (11)
Very recently the BICEP2 collaboration has reported6 evidence
for the detection of primordial gravitationalwaves, with a tensor
to scalar ratio r = 0.2+0.070.05, pointing
