Parity-violating extensions of standard electromagnetism produce cosmic birefringence, the in vacuo rotation of the linear polarisation direction of a photon during propagation. We employ {it Planck} 2018 CMB polarised data to constrain anisotropic b
irefringence, modeled by its angular power spectrum $C_{ell}^{alpha alpha}$, and the cross-correlation with CMB temperature maps, $C_{ell}^{alpha T}$, at scales larger than $sim$15 degrees. We present joint limits on the scale invariant quantity, $A^{alpha alpha} equiv ell (ell +1) , C_{ell}^{alpha alpha} / 2 pi$, and on the analogous amplitude for the cross-correlation, $A^{alpha T} equiv ell (ell +1) , C_{ell}^{alpha T} / 2 pi$. We find no evidence of birefringence within the error budget and obtain $A^{alpha alpha} < 0.104 , mbox{[deg$^2$]}$ and $A^{alpha T}=1.50^{+2.41}_{-4.10} , mbox{[$mu$K$cdot$deg] both at } 95 % mbox{ C.L.}$. The latter bound appears competitive in constraining a few early dark energy models recently proposed to alleviate the $H_{0}$ tension. Slicing the joint likelihood at $A^{alpha T}=0$, the bound on $A^{alpha alpha}$ becomes tighter at $A^{alpha alpha} < 0.085 , mbox{[deg$^2$]}$ at 95$% mbox{ C.L.}$. In addition we recast the constraints on $A^{alpha alpha}$ as a bound on the amplitude of primordial magnetic fields responsible for Faraday rotation, finding $B_{1 {tiny mbox{Mpc}}} < 26.9$ nG and $B_{1 {tiny mbox{Mpc}}} < 24.3$ nG at 95$%$ C.L. for the marginalised and sliced case respectively.
We use the 2015 Planck likelihood in combination with the Bicep2/Keck likelihood (BKP and BK14) to constrain the chirality, $chi$, of primordial gravitational waves in a scale-invariant scenario. In this framework, the parameter $chi$ enters theory a
lways coupled to the tensor-to-scalar ratio, $r$, e.g. in combination of the form $chi cdot r$. Thus, the capability to detect $chi$ critically depends on the value of $r$. We find that with present data set $chi$ is textit{de facto}unconstrained. We also provide forecasts for $chi$ from future CMB experiments, including COrE+, exploring several fiducial values of $r$. We find that the current limit on $r$ is tight enough to disfavor a neat detection of $chi$. For example, in the unlikely case in which $rsim0.1(0.05)$, the maximal chirality case, i.e. $chi = pm1$, could be detected with a significance of $sim2.5(1.5)sigma$ at best. We conclude that the two-point statistics at the basis of CMB likelihood functions is currently unable to constrain chirality and may only provide weak limits on $chi$ in the most optimistic scenarios. Hence, it is crucial to investigate the use of other observables, e.g. provided by higher order statistics, to constrain these kind of parity violating theories with the CMB.
We perform a wavelet analysis of the temperature and polarization maps of the Cosmic Microwave Background (CMB) delivered by the WMAP experiment in search for a parity violating signal. Such a signal could be seeded by new physics beyond the standard
model, for which the Lorentz and CPT symmetries may not hold. Under these circumstances, the linear polarization direction of a CMB photon may get rotated during its cosmological journey, a phenomenon also called cosmological birefringence. Recently, Feng et al. have analyzed a subset the WMAP and BOOMERanG 2003 angular power spectra of the CMB, deriving a constraint that mildly favors a non zero rotation. By using wavelet transforms we set a tighter limit on the CMB photon rotation angle Deltaalpha= -2.5 pm 3.0 (Deltaalpha= -2.5 pm 6.0) at the one (two) sigma level, consistent with a null detection.
We present a fast algorithm for generating full sky, high resolution ($sim 5$) simulations of the CMB anisotropy pattern. We also discuss the inverse problem, that of evaluating from such a map the full set of $a_{ell m}$s and the spectral coefficien
ts $C_ell$. We show that using an Equidistant Cylindrical Projection of the sky substantially speeds up the calculations. Thus, generating and/or inverting a full sky, high resolution map can be easily achieved with present day computer technology.
