On the dipole straylight contamination in spinning space missions dedicated to CMB anisotropy

We present an analysis of the dipole straylight contamination (DSC) for spinning space-missions designed to measure CMB anisotropies. Although this work is mainly devoted to the {\sc Planck} project, it is relatively general and allows to focus on the most relevant DSC implications. We first study a simple analytical model for the DSC in which the pointing direction of the main spillover can be assumed parallel or not to the spacecraft spin axis direction and compute the time ordered data and map. The map is then analysed paying particular attention to the DSC of the low multipole coefficients of the map. Through dedicated numerical simulations we verify the analytical results and extend the analysis to higher multipoles and to more complex (and realistic) cases by relaxing some of the simple assumptions adopted in the analytical approach. We find that the systematic effect averages out in an even number of surveys, except for a contamination of the dipole itself that survives when spin axis and spillover directions are not parallel and for a contamination of the other multipoles in the case of complex scanning strategies. In particular, the observed quadrupole can be affected by the DSC in an odd number of surveys or in the presence of survey uncompleteness or over-completeness. Various aspects relevant in CMB space projects (such as implications for calibration, impact on polarization measurements, accuracy requirement in the far beam knowledge for data analysis applications, scanning strategy dependence) are discussed.Comment: 21 pages, 13 Figures, 1 Table. To appear in MNRAS. Accepted 2006 July 13. Received 2006 July 13; in original form 2006 June 7. This work has been done in the framework of the Planck LFI activitie

Testing chirality of primordial gravitational waves with Planck and future CMB data: no hope from angular power spectra

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 always 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 $r\sim0.1(0.05)$, 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.Comment: 15 pages, 3 figures. Updated to match published versio

A note on the birefringence angle estimation in CMB data analysis

Parity violating physics beyond the standard model of particle physics induces a rotation of the linear polarization of photons. This effect, also known as cosmological birefringence (CB), can be tested with the observations of the cosmic microwave background (CMB) anisotropies which are linearly polarized at the level of $5-10\%$. In particular CB produces non-null CMB cross correlations between temperature and B mode-polarization, and between E- and B-mode polarization. Here we study the properties of the so called D-estimators, often used to constrain such an effect. After deriving the framework of both frequentist and Bayesian analysis, we discuss the interplay between birefringence and weak-lensing, which, albeit parity conserving, modifies pre-existing TB and EB cross correlation.Comment: 12 pages. Accepted for publication in JCA

Boundaries and the Casimir effect in non-commutative space-time

We calculate modifications to the scalar Casimir force between two parallel plates due to space-time non-commutativity. We devise a heuristic approach to overcome the difficulties of describing boundaries in non-commutative theories and predict that boundary corrections are of the same order as non-commutative volume corrections. Further, both corrections have the form of more conventional finite surface effects.Comment: 9 pages, 2 figure

Cosmic Birefringence: Cross-Spectra and Cross-Bispectra with CMB Anisotropies

Parity-violating extensions of Maxwell electromagnetism induce a rotation of the linear polarization plane of photons during propagation. This effect, known as cosmic birefringence, impacts on the Cosmic Microwave Background (CMB) observations producing a mixing of $E$ and $B$ polarization modes which is otherwise null in the standard scenario. Such an effect is naturally parametrized by a rotation angle which can be written as the sum of an isotropic component $\alpha_0$ and an anisotropic one $\delta\alpha(\hat{\mathbf{n}})$. In this paper we compute angular power spectra and bispectra involving $\delta\alpha$ and the CMB temperature and polarization maps. In particular, contrarily to what happens for the cross-spectra, we show that even in absence of primordial cross-correlations between the anisotropic birefringence angle and the CMB maps, there exist non-vanishing three-point correlation functions carrying signatures of parity-breaking physics. Furthermore, we find that such angular bispectra still survive in a regime of purely anisotropic cosmic birefringence, which corresponds to the conservative case of having $\alpha_0=0$. These bispectra represent an additional observable aimed at studying cosmic birefringence and its parity-violating nature beyond power spectrum analyses. They provide also a way to perform consistency checks for specific models of cosmic birefringence. Moreover, we estimate that among all the possible birefringent bispectra, $\langle\delta\alpha\, TB\rangle$ and $\langle\delta\alpha\,EB\rangle$ are the ones which contain the largest signal-to-noise ratio. Once the cosmic birefringence signal is taken to be at the level of current constraints, we show that these bispectra are within reach of future CMB experiments, as LiteBIRD.Comment: 22 pages, 5 figures; added references; typos corrected; matches published versio

Probing Axions through Tomography of Anisotropic Cosmic Birefringence

Cosmic birefringence is the in-vacuo rotation of the linear polarization plane experienced by photons of the Cosmic Microwave Background (CMB) radiation when theoretically well-motivated parity-violating extensions of Maxwell electromagnetism are considered. If the angle, parametrizing such a rotation is dependent on the photon's direction, then this phenomenon is called Anisotropic Cosmic Birefringence (ACB). In this paper, we perform for the first time a tomographic treatment of the ACB, by considering photons emitted both at the recombination and reionization epoch. This allows one to extract additional and complementary information about the physical source of cosmic birefringence with respect to the isotropic case. We focus here on the case of an axion-like field $\chi$, whose coupling with the electromagnetic sector induces such a phenomenon, by using an analytical and numerical approach (which involves a modification of the CLASS code). We find that the anisotropic component of cosmic birefringence exhibits a peculiar behavior: an increase of the axion mass implies an enhancement of the anisotropic amplitude, allowing to probe a wider range of masses with respect to the purely isotropic case. Moreover, we show that at large angular scales, the interplay between the reionization and recombination contributions to ACB is sensitive to the axion mass, so that at sufficiently low multipoles, for sufficiently light masses, the reionization contribution overtakes the recombination one, making the tomographic approach to cosmic birefringence a promising tool for investigating the properties of this axion-like field.Comment: 24 pages, 5 figures. Added brief information about the algorithms used for reionization and recombination in Fig