Physics Letters B 802 (2020) 135240
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Joint constraint on primordial gravitational waves and polarization
rotation angle with current CMB polarization data
Hua Zhai
a,b,∗
, Si-Yu Li
c
, Mingzhe Li
d
, Xinmin Zhang
a,b
a
Theoretical Physics Division, Institute of High Energy Physics (IHEP), Chinese Academy of Sciences, 19B Yuquan Road, Shijingshan District, Beijing 100049, China
b
University of Chinese Academy of Sciences, Beijing, China
c
Key Laboratory of Particle Astrophysics, Institute of High Energy Physics (IHEP), Chinese Academy of Sciences, 19B Yuquan Road, Shijingshan District, Beijing
100049, China
d
Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui 230026, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
21 October 2019
Received
in revised form 23 December 2019
Accepted
16 January 2020
Available
online 21 January 2020
Editor:
H. Peiris
Keywords:
Primordial
gravitational waves
CPT
symmetry violation
Polarization
rotation angle
Global
fitting
High
CMB power spectra
Cosmological CPT violation will rotate the polarized direction of CMB photons, convert partial CMB E
mode into B mode and vice versa. It will generate non-zero EB, TB spectra and change the EE, BB, TE
spectra. This phenomenon gives us a way to detect the CPT-violation signature from CMB observations,
and also provides a new mechanism to produce B mode polarization. In this paper, we perform a global
analysis on tensor-to-scalar ratio r and polarization rotation angles based on current CMB datasets with
both low (Planck, BICEP2/Keck Array) and high (POLARBEAR, SPTpol, ACTPol). Benefited from the high
precision of CMB data, we obtain the isotropic rotation angle
¯
α = 0.0
◦
± 0.37
◦
at 68% CL, the variance
of the anisotropic rotation angles C
α
(0) < 0.0032 rad
2
, the scale invariant power spectrum D
αα
∈[2,350]
<
4.65 × 10
−5
rad
2
and r < 0.059 at 95% CL. Our result shows that with the polarization rotation effect, the
95% upper limit on r gets tightened by 14%.
© 2020 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
In the standard model of particle physics, the Charge-Parity-
Time
Reversal (CPT) symmetry is an exact symmetry and occupies
a fundamental status. So probing CPT violation is an important way
to test the standard model, and a very useful approach to search-
ing
for the new physics. Up to now, CPT symmetry has passed a
number of high-precision experimental tests and no definite sig-
nal
of its violation has been observed in the laboratory. So, the
CPT violation, if exist, should be very small to be amenable to the
laboratory experimental limits.
However,
the CPT symmetry could be dynamically broken in the
expanding universe. For instances, in Refs. [1–5], the cosmological
CPT violation has been considered to generate the baryon number
asymmetry in the early universe. A notable property of this kind
of baryogenesis models is that the CPT violation at present time is
too small to be detected by the laboratory experiments, but large
enough in the early universe to account for the observed baryon
number asymmetry. As shown in Refs. [6–8], such type of CPT vi-
*
Corresponding author.
E-mail
address: zhaihua@ihep.ac.cn (H. Zhai).
olations might be observed by the cosmological probes. With the
accumulation of high-quality observational data, especially those
from the cosmic microwave background (CMB) experiments, cos-
mological
observation becomes a powerful way to test CPT sym-
metry.
Generally
the cosmological CPT violation in the photon sector
can be modeled by the coupling between photons and an external
field θ(x) through the Chern-Simons Lagrangian,
L
cs
= θ(x)F
μν
F
μν
, (1)
where F
μν
= ∂
μ
A
ν
− ∂
ν
A
μ
is the electromagnetic tensor and
F
μν
= (1/2)
μνρσ
F
ρσ
is its dual. If θ is a constant, the Chern-
Simons
term will have no effect on the dynamics of photons
because the Pontryagin density F
μν
F
μν
is a total derivative and
the vacuum here is topological trivial. There are at least two ap-
proaches
to get θ(x) as a variable. With the first approach, θ(x) =
p
μ
x
μ
is constructed by a non-dynamical vector p
μ
. However when
considering the couplings to gravity, this case is not compatible
with general relativity and its covariant extensions [9]. In the sec-
ond
approach, θ(x) = f (φ(x)), where f (φ (x)) is a general function
of a dynamical scalar field φ(x). Such a scalar field may be the dy-
https://doi.org/10.1016/j.physletb.2020.135240
0370-2693/
© 2020 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
.