Cosmic Microwave Background Quadrupole Research Articles

Novel cosmological tests from combining galaxy lensing and the polarized Sunyaev-Zel’dovich effect

The polarized Sunyaev-Zel'dovich (pSZ) effect is sourced by the Thomson scattering of CMB photons from distant free electrons and yields a novel view of the CMB quadrupole throughout the observable Universe. Galaxy shear measures the shape distortions of galaxies, probing both their local environment and the intervening matter distribution. Both observables give interesting constraints on the cosmological model; here we ask: what can be learnt from their combination? The pSZ-shear cross-spectrum measures the shear-galaxy-polarization bispectrum and contains contributions from (1) the Sachs-Wolfe (SW) effect, (2) the integrated Sachs-Wolfe (ISW) effect, and (3) inflationary gravitational waves. Since the modes contributing to the pSZ signal are not restricted to the Earth's past lightcone, the low-redshift cross-spectra could provide a novel constraint on dark energy via the ISW effect, whilst the SW signal couples scalar modes at very different times but at similar positions; this provides a unique probe of the Universe's homogeneous time evolution. We give expressions for all major contributions to the shear, galaxy, and pSZ auto- and cross-spectra, and evaluate their detectability via Fisher forecasts. Despite significant theoretical utility, the cross-spectra will be challenging to detect: combining CMB-S4 with Rubin yields a $1.6\sigma$ detection of the ISW contribution, which increases to $5.2\sigma$ for a futuristic experiment involving CMB-HD and a higher galaxy sample density. For parity-even (parity-odd) tensors, we predict a $1\sigma$ limit of $\sigma(r) = 0.9$ ($0.2$) for CMB-S4 and Rubin, or $0.3$ ($0.06$) for the more futuristic setup. Whilst this is significantly better than the constraints from galaxy shear alone (and less sensitive to systematics), it is unlikely to be competitive, but may serve as a useful cross-check.

Measuring the cosmological density field twice: A novel test of dark energy using the CMB quadrupole

The scattering of cosmic microwave background (CMB) radiation in galaxy clusters induces polarization signals according to the quadrupole anisotropy in the photon distribution at the cluster location. This `remote quadrupole' derived from the measurements of the induced polarization provides an opportunity for reconstructing primordial fluctuations on large scales. We discuss that comparing the local CMB quadrupoles predicted by these reconstructed primordial fluctuations and the direct measurements done by CMB satellites may enable us to test the dark energy beyond cosmic variance limits.

Easing cosmic tensions with an open and hotter universe

Despite the great observational success of the standard cosmological model some discrepancies in the inferred parameter constraints have manifested among a number of cosmological data sets. These include a tension between the expansion rate of our Cosmos as inferred from the cosmic microwave background (CMB) and as found from local measurements, the preference for an enhanced amplitude of CMB lensing, a somewhat low quadrupole moment of the CMB fluctuations as well as a preference for a lower amplitude of matter fluctuations in large-scale structure surveys than inferred from the CMB. We analyse these observational tensions under the addition of spatial curvature and a free CMB background temperature that may deviate from its locally measured value. With inclusion of these parameters, we observe a trend in the parameter constraints from CMB and baryon acoustic oscillation data towards an open and hotter universe with larger current expansion rate, standard CMB lensing amplitudes, lower amplitude of matter fluctuations, and marginally lower CMB quadrupole moment, consistently reducing the individual tensions among the cosmological data sets. Combining this data with local distance measurements, we find a preference for an open and hotter universe beyond the 99.7% confidence level. Finally, we briefly discuss a local void as a possible source for a deviation of the locally measured CMB temperature from its background value and as mimic of negative spatial curvature for CMB photons. This interpretation implies a $\sim$20% underdensity in our local neighbourhood of $\sim$10-100 Mpc in diameter, which is well within cosmic variance.

Screening anisotropy via energy-momentum squared gravity: ΛCDM model with hidden anisotropy

We construct a generalization of the standard $\Lambda$CDM model, wherein we simultaneously replace the spatially flat Robertson-Walker metric with its simplest anisotropic generalization (LRS Bianchi I metric), and couple the cold dark matter to the gravity in accordance with the energy-momentum squared gravity (EMSG) of the form $f(T_{\mu\nu}T^{\mu\nu})\propto T_{\mu\nu}T^{\mu\nu}$. These two modifications -- namely, two new stiff fluid-like terms of different nature -- can mutually cancel out, i.e., the shear scalar can be screened completely, and reproduce mathematically exactly the same Friedmann equation of the standard $\Lambda$CDM model. This evades the BBN limits on the anisotropy, and thereby provides an opportunity to manipulate the cosmic microwave background quadrupole temperature fluctuation at the desired amount. We further discuss the consequences of the model on the very early times and far future of the Universe. This study presents also an example of that the EMSG of the form $f(T_{\mu\nu}T^{\mu\nu})\propto T_{\mu\nu}T^{\mu\nu}$, as well as similar type other constructions, is not necessarily relevant only to very early Universe but may even be considered in the context of a major problem of the current cosmology related to the present-day Universe, the so-called $H_0$ problem.

Probing phenomenological emergent dark energy model in a Bianchi type-I spacetime with the recent observational data

In this work, we investigate the recently introduced phenomenological emergent dark energy (PEDE) model and the anisotropic extension of PEDE ( A PEDE) via Bianchi type-I spacetime metric with the latest observational data involving both low and high redshift datasets as, Hubble, Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO) and Pantheon. We perform Bayesian inference analysis to carry out a detailed comparison of these models with the standard Λ CDM and anisotropic Λ CDM ( A Λ CDM) models. The 68% confidence limit (CL) constraints on Hubble constant with joint data combination for both PEDE and A PEDE models yield H 0 = 70 . 8 ± 0 . 5 km s − 1 Mpc − 1 , consistent with the local value H 0 = 69 . 8 ± 0 . 8 km s − 1 Mpc − 1 based on a calibration of the Tip of the Red Giant Branch applied to supernovae Type Ia. In addition, this value provides ∼ 2 . 1 σ tension in comparison with the local measurement value 74 . 03 ± 1 . 42 km s − 1 Mpc − 1 from Hubble Space Telescope observations of Cepheids in the Large Magellanic Cloud. The phantom like behaviour of dark energy in PEDE and A PEDE models lead to an early redshift transition in comparison with Λ CDM and A Λ CDM models. Further, we observe that the upper bound on the expansion anisotropy parameter Ω σ 0 for A PEDE at 95% CL is approximately of the order 1 0 − 18 with all data combinations, unable to make any relevant change in the CMB quadrupole problem. Moreover, we find that the expansion anisotropy for A PEDE ( A Λ CDM) model does not alter the conclusions for PEDE ( Λ CDM) model. The statistical results for both PEDE and A PEDE models in comparison with the base Λ CDM show a good fit with the data combination of Hubble+CMB, while the addition of BAO or Pantheon with other data combinations lead to a very strong evidence against the PEDE models.

Towards testing CMB anomalies using the kinetic and polarized Sunyaev-Zel’dovich effects

Measurements of the Cosmic Microwave Background (CMB) temperature anisotropies on large angular scales have uncovered a number of anomalous features of marginal statistical significance, such as a hemispherical power asymmetry, lack of power on large angular scales, and features in the power spectrum. Because the primary CMB temperature has been measured at the cosmic variance limit, determining if these anomalies are hints of new physics as opposed to foregrounds, systematics, or simply statistical flukes, requires new observables. In this paper, we highlight the potential contribution that future measurements of the kinetic Sunyaev-Zel'dovich effect (kSZ) and the polarized Sunyaev Zel'dovich effect (pSZ) could make in determining the physical nature of several CMB anomalies. The kSZ and pSZ effects, temperature and polarization anisotropies induced by scattering from free electrons in the reionized Universe, are the dominant blackbody contribution to the CMB on small angular scales. Using the technique of SZ tomography, measurements of kSZ and pSZ effects can be combined with galaxy surveys to reconstruct the remote CMB dipole and quadrupole fields, providing a 3-dimensional probe of large scale modes inside our Hubble volume. Building on previous work, we forecast the additional constraining power that these observables might offer for a representative set of anomaly models. We find that the remote CMB dipole and quadrupole contain a similar amount of information on anomaly models as the primary CMB polarization. The information from CMB temperature, polarization, and the remote dipole and quadrupole fields is complementary, and the full set of observables can improve constraints on anomaly models by a factor of $\sim 2-4$ using next-generation CMB experiments and galaxy surveys. This could be sufficient to definitively establish the physical origin of several CMB anomalies.

Primordial gravitational wave phenomenology with polarized Sunyaev Zel’dovich tomography

The detection and characterization of primordial gravitational waves through their impact on the polarization anisotropies of the cosmic microwave background (CMB) is a primary science goal of current and future observations of the CMB. An ancillary dataset that will become accessible with the great leaps in sensitivity of CMB experiments is the polarized Sunyaev Zel'dovich (pSZ) effect, small-scale CMB polarization anisotropies induced by scattering from free electrons in the post-reionization Universe. The cross correlation of the pSZ effect with galaxy surveys, a technique known as pSZ tomography, can be used to reconstruct the remote quadrupole field: the CMB quadrupole observed from different locations in the Universe. Primordial gravitational waves leave a distinct imprint on the remote quadrupole field, making pSZ tomography a potential new method to characterize their properties. Building on previous work, we explore the utility of the full set of correlations between the primary CMB and the reconstructed remote quadrupole field to both provide exclusion limits on the amplitude of primordial gravitational waves, as well as to provide constraints on several phenomenological models of the tensor sector: axion gauge field inflation, general models with chiral tensors, and models with modified late-time decay of tensors. We find that relatively futuristic experimental requirements are necessary to provide competitive exclusion limits compared with the primary CMB. However, pSZ tomography can be a powerful probe of the late-time evolution of tensors and, through cross-correlations with the primary CMB, can provide mild improvements on parameter constraints in various models with chiral primordial gravitational waves.

Forecasted constraints on modified gravity from Sunyaev-Zel’dovich tomography

Observational cosmology has become an important laboratory for testing General Relativity, with searches for modified gravity forming a significant portion of the science case for existing and future surveys. In this paper, we illustrate how future measurements of the Cosmic Microwave Background (CMB) temperature and polarization anisotropies can be combined with large galaxy surveys to improve constraints on modified gravity using the technique of Sunyaev Zel'dovich (SZ) tomography. SZ tomography uses the correlations between the kinetic/polarized SZ contributions to the small-angular scale CMB and the distribution of structure measured in a galaxy redshift survey to reconstruct the remote dipole and quadrupole fields, e.g. the CMB dipole and quadrupole observed throughout the Universe. We compute the effect of a class of modifications of gravity on the remote dipole and quadrupole fields, illustrating that these observables combine a number of the desirable features of existing probes. We then perform a fisher forecast of constraints on a two-parameter class of modifications of gravity for next-generation CMB experiments and galaxy surveys. By incorporating information from the reconstructed remote dipole and quadrupole fields, we find that it is possible to improve the constraints on this model by a factor of $\sim 2$ beyond what is possible with a galaxy survey alone. We conclude that SZ tomography is a promising method for testing gravity with future cosmological datasets.

Constraints on a Bianchi type I spacetime extension of the standard ΛCDM model

We consider the simplest anisotropic generalization, as a correction, to the standard $\Lambda$CDM model, by replacing the spatially flat Robertson-Walker metric by the Bianchi type-I metric, which brings in a new term $\Omega_{\sigma 0}a^{-6}$ (mimicking the stiff fluid) in the average expansion rate $H(a)$ of the Universe. From Hubble and Pantheon data, relevant to the late Universe ($z\lesssim 2.4$), we obtain the constraint $\Omega_{\sigma0}\lesssim10^{-3}$, in line with the model-independent constraints. When the baryonic acoustic oscillations and cosmic microwave background (CMB) data are included, the constraint improves by 12 orders of magnitude, i.e., $\Omega_{\sigma0}\lesssim10^{-15}$. We find that this constraint could alter neither the matter-radiation equality redshift nor the peak of the matter perturbations. Demanding that the expansion anisotropy has no significant effect on the standard big bang nucleosynthesis (BBN), we find the constraint $\Omega_{\sigma0}\lesssim10^{-23}$. We show explicitly that the constraint from BBN renders the expansion anisotropy irrelevant to make a significant change in the CMB quadrupole temperature, whereas the constraint from the cosmological data in our model provides the temperature change up to $\sim11\, \rm mK$, though it is much beyond the CMB quadrupole temperature.

Anisotropic thermal Sunyaev-Zel’dovich effect and the possibility of an independent measurement of the CMB dipole, quadrupole, and octupole

We consider the effect of the cosmic microwave background (CMB) frequency spectral distortions arising due to the Compton scattering of the anisotropic radiation on Sunyaev-Zel'dovich (SZ) clusters. We derive the correction to the thermal SZ effect due to the presence of multipoles with $\ell=1,2,3$ in the anisotropy of the CMB radiation. We show that this effect gives us an opportunity for an independent evaluation of the CMB dipole, quadrupole and octupole angular anisotropy in our location using distorted signal from the nearby galaxy clusters and to distinguish between the Sachs-Wolfe (SW) and the Integrated Sachs-Wolfe (ISW) effects by combining such signals from distant and nearby clusters. The future space mission 'Millimetron' will have unprecedented sensitivity, which will make it possible to observe the spectral distortion we are considering.

Reconstruction of the remote dipole and quadrupole fields from the kinetic Sunyaev Zel’dovich and polarized Sunyaev Zel’dovich effects

The kinetic Sunyaev Zel'dovich (kSZ) and polarized Sunyaev Zel'dovich (pSZ) effects are temperature and polarization anisotropies induced by the scattering of CMB photons from structure in the post-reionization Universe. In the case of the kSZ effect, small angular scale anisotropies in the optical depth are modulated by the cosmic microwave background (CMB) dipole field, i.e. the CMB dipole observed at each spacetime point, which is sourced by the primordial dipole and especially the local peculiar velocity. In the case of the pSZ effect, similar small-scale anisotropies are modulated by the CMB quadrupole field, which receives contributions from both scalar and tensor modes. Statistical anisotropies in the cross correlations of CMB temperature and polarization with tracers of the inhomogeneous distribution of electrons provide a means of isolating and reconstructing the dipole and quadrupole fields. In this paper, we present a set of unbiased minimum variance quadratic estimators for the reconstruction of the dipole and quadrupole fields, and forecast the ability of future CMB experiments and large scale structure surveys to perform this reconstruction. Consistent with previous work, we find that a high fidelity reconstruction of the dipole and quadrupole fields over a variety of scales is indeed possible, and demonstrate the sensitivity of the pSZ effect to primordial tensor modes. Using a principle component analysis, we estimate how many independent modes could be accessed in such a reconstruction. We also comment on a few first applications of a detection of the dipole and quadrupole fields, including a reconstruction of the primordial contribution to our locally observed CMB dipole, a test of statistical homogeneity on large scales from the first modes of the quadrupole field, and a reconstruction technique for the primordial potential on the largest scales.

Detecting primordial gravitational waves with circular polarization of the redshifted 21 cm line. I. Formalism

We propose a new method to measure the tensor-to-scalar ratio $r$ using the circular polarization of the 21 cm radiation from the pre-reionization epoch. Our method relies on the splitting of the $F=1$ hyperfine level of neutral hydrogen due to the quadrupole moment of the cosmic microwave background (CMB). We show that unlike the Zeeman effect, where ${M}_{F}=\ifmmode\pm\else\textpm\fi{}1$ have opposite energy shifts, the CMB quadrupole shifts ${M}_{F}=\ifmmode\pm\else\textpm\fi{}1$ together relative to ${M}_{F}=0$. This splitting leads to a small circular polarization of the emitted 21 cm radiation. In this paper (Paper I in a series on this effect), we present calculations on the microphysics behind this effect, accounting for all processes that affect the hyperfine transition. We conclude with an analytic formula for the circular polarization from the Dark Ages as a function of pre-reionization parameters and the value of the remote quadrupole of the CMB. We also calculate the splitting of the $F=1$ hyperfine level due to other anisotropic radiation sources and show that they are not dominant. In a companion paper (Paper II) we make forecasts for measuring the tensor-to-scalar ratio $r$ using future radio arrays.

Beyond the Boost: Measuring the Intrinsic Dipole of the Cosmic Microwave Background Using the Spectral Distortions of the Monopole and Quadrupole.

We present a general framework for the accurate spectral modeling of the low multipoles of the cosmic microwave background (CMB) as observed in a boosted frame. In particular, we demonstrate how spectral measurements of the low multipoles can be used to separate the motion-induced dipole of the CMB from a possible intrinsic dipole component. In a moving frame, the leakage of an intrinsic dipole moment into the CMB monopole and quadrupole induces spectral distortions with distinct frequency functions that, respectively, peak at 337 and 276GHz. The leakage into the quadrupole moment also induces a geometrical distortion to the spatial morphology of this mode. The combination of these effects can be used to lift the degeneracy between the motion-induced dipole and any intrinsic dipole that the CMB might possess. Assuming the current peculiar velocity measurements, the leakage of an intrinsic dipole with an amplitude of ΔT=30 μK into the monopole and quadrupole moments will be detectable by a PIXIE-like experiment at ∼40 nK (2.5σ) and ∼130 nK (11σ) level at their respective peak frequencies.

Constraining cosmological ultralarge scale structure using numerical relativity

Cosmic inflation, a period of accelerated expansion in the early universe, can give rise to large amplitude ultra-large scale inhomogeneities on distance scales comparable to or larger than the observable universe. The cosmic microwave background (CMB) anisotropy on the largest angular scales is sensitive to such inhomogeneities and can be used to constrain the presence of ultra-large scale structure (ULSS). We numerically evolve nonlinear inhomogeneities present at the beginning of inflation in full General Relativity to assess the CMB quadrupole constraint on the amplitude of the initial fluctuations and the size of the observable universe relative to a length scale characterizing the ULSS. To obtain a statistically significant number of simulations, we adopt a toy model in which inhomogeneities are injected along a preferred direction. We compute the likelihood function for the CMB quadrupole including both ULSS and the standard quantum fluctuations produced during inflation. We compute the posterior given the observed CMB quadrupole, finding that when including gravitational nonlinearities, ULSS curvature perturbations of order unity are allowed by the data, even on length scales not too much larger than the size of the observable universe. Our results illustrate the utility and importance of numerical relativity for constraining early universe cosmology.

The Weird Side of the Universe: Preferred Axis

In both WMAP and Planck observations on the temperature anisotropy of cosmic microwave background (CMB) radiation a number of large-scale anomalies were discovered in the past years, including the CMB parity asymmetry in the low multipoles. By defining a directional statistics, we find that the CMB parity asymmetry is directional dependent, and the preferred axis is stable, which means that it is independent of the chosen CMB map, the definition of the statistic, or the CMB masks. Meanwhile, we find that this preferred axis strongly aligns with those of the CMB quadrupole, octopole, as well as those of other large-scale observations. In addition, all of them aligns with the CMB kinematic dipole, which hints to the non-cosmological origin of these directional anomalies in cosmological observations.

Simulating the universe(s) III: observables for the full bubble collision spacetime

This is the third paper in a series establishing a quantitative relation between inflationary scalar field potential landscapes and the relic perturbations left by the collision between bubbles produced during eternal inflation. We introduce a new method for computing cosmological observables from numerical relativity simulations of bubble collisions in one space and one time dimension. This method tiles comoving hypersurfaces with locally-perturbed Friedmann-Robertson-Walker coordinate patches. The method extends previous work, which was limited to the spacetime region just inside the future light cone of the collision, and allows us to explore the full bubble-collision spacetime. We validate our new methods against previous work, and present a full set of predictions for the comoving curvature perturbation and local negative spatial curvature produced by identical and non-identical bubble collisions, in single scalar field models of eternal inflation. In both collision types, there is a non-zero contribution to the spatial curvature and cosmic microwave background quadrupole. Some collisions between non-identical bubbles excite wall modes, giving extra structure to the predicted temperature anisotropies. We comment on the implications of our results for future observational searches. For non-identical bubble collisions, we also find that the surfaces of constant field can readjust in the presence of a collision to produce spatially infinite sections that become nearly homogeneous deep into the region affected by the collision. Contrary to previous assumptions, this is true even in the bubble into which the domain wall is accelerating.

Preferred axis of CMB parity asymmetry in the masked maps

Both WMAP and Planck data show a significant odd-multipole preference in the large scales of the cosmic microwave background (CMB) temperature anisotropies. If this pattern originates from cosmological effects, then it can be considered a crucial clue for a violation in the cosmological principle. By defining various direction dependent statistics in the full-sky Planck 2015 maps (see, for instance, Naselsky et al. (2012); W. Zhao (2014)), we found that the CMB parity asymmetry has a preferred direction, which is independent of the choices of the statistics. In particular, this preferred axis is strongly aligned with those in the CMB quadrupole and octopole, as well as that in the CMB kinematic dipole, which hints to their non-cosmological origin. In realistic observations, the foreground residuals are inevitable, and should be properly masked out in order to avoid possible misinterpretation of the results. In this paper, we extend our previous analyses to the masked Planck 2015 data. By defining a similar direction dependent statistic in the masked map, we find a preferred direction of the CMB parity asymmetry, in which the axis also coincides with that found in the full-sky analysis. Therefore, our conclusions on the CMB parity violation and its directional properties are confirmed.

Directional dependence of CMB parity asymmetry

Parity violation in the cosmic microwave background (CMB) radiation has been confirmed by recent Planck observation. In this paper, we extend our previous work [P. Naselsky et al., Astrophys. J. 749, 31 (2012)] on the directional properties of CMB parity asymmetry by considering the Planck data of the CMB temperature anisotropy. We define six kinds of the directional statistics and find that they all indicate the odd-parity preference of CMB data. In addition, we find the preferred axes of all these statistics strongly correlate with the preferred axes of the CMB kinematic dipole, quadrupole, and octopole. The alignment between them is confirmed at more than $3\ensuremath{\sigma}$ confidence level, which implies that the CMB parity asymmetry, and the anomalies of the CMB quadrupole and octopole, may have the common physical, contaminated, or systematic origin. In addition, they all should be connected with the possible contamination of the residual dipole component.

Missing completely of the CMB quadrupole in WMAP data

In cosmic microwave background (CMB) experiments, foreground-cleaned temperature maps are still contaminated by the residual dipole due to uncertainties of the Doppler dipole direction and microwave radiometer sidelobe. To obtain reliable CMB maps, such contamination has to be carefully removed from...

COSMIC MICROWAVE BACKGROUND INDUCED POLARIZATION FROM SINGLE SCATTERING BY CLUSTERS OF GALAXIES AND FILAMENTS

We present light-cone-integrated simulations of the cosmic microwave background (CMB) polarization signal induced by a single scattering in the direction of clusters of galaxies and filaments. We characterize the statistical properties of the induced polarization signals from the presence of the CMB quadrupole component (pqiCMB) and as the result of the transverse motion of ionized gas clouds with respect to the CMB rest frame (p?2 t SZ). From adiabatic N-body/hydrodynamic simulations, we generated 28 random sky patches integrated along the light cone, each with about 0.86?deg2 and angular resolution of 6''. Our simulation method involves a box-stacking scheme that allows to reconstruct the CMB quadrupole component and the gas physical properties along the line of sight. We find that the linear polarization degree in the logarithmic scale of both effects follows approximately a Gaussian distribution and the mean total signal is about 10?8 and 10?10 for the pqiCMB and p?2 t SZ effects, respectively. The polarization angle is consistent with a flat distribution in both cases. From the mean distributions of the polarization degree with redshift, the highest peak is found at z 1 for the induced CMB quadrupole and at z 0.5 for the kinematic component. Our results suggest that most of the contribution for the total polarization signal arises from z 4 for the pqiCMB and z 3 for p?2 t SZ. The spectral dependency of both integrated signals is strong, increasing with the frequency, especially in the case of the p?2 t SZ signal, which increases by a factor of 100 from 30?GHz to 675?GHz. The maxima values found at the highest frequency are about 3 ?K and 13 ?K for the pqiCMB and p?2 t SZ, respectively. The angular power spectra of these effects peak at large multipoles ? > 104, being of the order of 10?5 ?K2 for pqiCMB polarization and 10?7 ?K2 for the p?2 t SZ effect. Therefore, these effects will not be a relevant source of contamination for measurements of the primary polarization modes, and at larger multipoles of roughly ? > 40, 000, pqiCMB may be the dominant component over the primary and lensing signals.