Microwave Background Anisotropies Research Articles

Inevitable imprints of patchy reionization on the cosmic microwave background anisotropy

ABSTRACT Reionization of the cosmic neutral hydrogen by the first stars in the Universe is an inhomogeneous process, which produces spatial fluctuations in free electron density. These fluctuations lead to observable signatures in cosmological probes like the cosmic microwave background (CMB). We explore the effect of the electron density fluctuations on CMB using photon-conserving seminumerical simulations of reionization named SCRIPT. We show that the amplitude of the kinematic Sunyaev–Zeldovich (kSZ) and the B-mode polarization signal depends on the patchiness in the spatial distribution of electrons along with the dependence on mid-point and extent of the reionization history. Motivated by this finding, we provide new scaling relations for the amplitude of kSZ and the B-mode polarization signal which can capture the effects arising from the mean optical depth, width of reionization, and spatial fluctuations in the electron density arising from patchy reionization. We show that the amplitude of the kSZ and the B-mode polarization signal exhibits different dependency on the width of reionization and the patchiness of reionization, and hence a joint study of these CMB probes will be able to break the degeneracy. By combining external data sets from 21-cm measurements, the degeneracy can be further lifted by directly exploring the sizes of the ionized regions.

Hyrec-2: A highly accurate sub-millisecond recombination code

We present the new recombination code hyrec-2, which achieves the same accuracy as the state-of-the-art codes hyrec and cosmorec and, at the same time, surpasses the computational speed of the code recfast commonly used for cosmic microwave background (CMB) anisotropy data analyses. hyrec-2 is based on an effective four-level atom model, accounting exactly for the nonequilibrium of highly excited states of hydrogen, and very accurately for radiative transfer effects with a correction to the Lyman-$\ensuremath{\alpha}$ escape rate. The latter is computed with the original hyrec and tabulated as a function of temperature, along with its derivatives with respect to the relevant cosmological parameters. This enables the code to keep the same accuracy as the original hyrec over the full 99.7% confidence region of cosmological parameters currently allowed by Planck, while running in under one millisecond on a standard laptop. Our code leads to no noticeable bias in any cosmological parameters even in the case of an ideal cosmic-variance-limited experiment up to $\ensuremath{\ell}=5000$. Beyond CMB anisotropy calculations, hyrec-2 will be a useful tool to compute various observables that depend on the recombination and thermal history, such as the recombination spectrum or the 21-cm signal.

Cornering (quasi) degenerate neutrinos with cosmology

In light of the improved sensitivities of cosmological observations, we examine the status of quasi-degenerate neutrino mass scenarios. Within the simplest extension of the standard cosmological model with massive neutrinos, we find that quasi-degenerate neutrinos are severely constrained by present cosmological data and neutrino oscillation experiments. We find that Planck 2018 observations of cosmic microwave background (CMB) anisotropies disfavour quasi-degenerate neutrino masses at 2.4 Gaussian σ’s, while adding baryon acoustic oscillations (BAO) data brings the rejection to 5.9σ’s. The highest statistical significance with which one would be able to rule out quasi-degeneracy would arise if the sum of neutrino masses is ∑mv = 60 meV (the minimum allowed by neutrino oscillation experiments); indeed a sensitivity of 15 meV, as expected from a combination of future cosmological probes, would further improve the rejection level up to 17σ. We discuss the robustness of these projections with respect to assumptions on the underlying cosmological model, and also compare them with bounds from β decay endpoint and neutrinoless double beta decay studies.

Baryogenesis in cosmological models with symmetric and asymmetric quantum bounces

The baryon-antibaryon asymmetry (excess of matter over antimatter in our Universe), indicated by observational data from the Cosmic Microwave Background anisotropies, predictions of primordial Nucleosynthesis, and the absence of intense radiation from matter-antimatter annihilation, constitutes an unsolved puzzle in cosmology. Two mechanisms for baryon asymmetry have been proposed as extensions of the Standard Model of Particle Physics at high energies. They rely on new couplings involving the baryon number current, one with a scalar field, called Spontaneous Baryogenesis, and the other with space-time curvature, named Gravitational Baryogenesis. These two mechanisms are investigated in the context of many bouncing scenarios, either symmetric or asymmetric around the bounce. It is shown that the constraints on the free parameters of these scenarios, imposed to yield the observed baryon-to-entropy ratio, are mild, already containing the values compatible with other observational constraints coming from the features of the power spectra of cosmological perturbations. Hence, realistic bouncing models can yield the observed baryon-antibaryon asymmetry if one of the two mechanisms proposed takes place in nature.

Seeding Primordial Black Holes in Multifield Inflation.

The inflationary origin of primordial black holes (PBHs) relies on a large enhancement of the power spectrum Δ_{ζ} of the curvature fluctuation ζ at wavelengths much shorter than those of the cosmic microwave background anisotropies. This is typically achieved in models where ζ evolves without interacting significantly with additional (isocurvature) scalar degrees of freedom. However, quantum gravity inspired models are characterized by moduli spaces with highly curved geometries and a large number of scalar fields that could vigorously interact with ζ (as in the cosmological collider picture). Here we show that isocurvature fluctuations can mix with ζ inducing large enhancements of its amplitude. This occurs whenever the inflationary trajectory experiences rapid turns in the field space of the model leading to amplifications that are exponentially sensitive to the total angle swept by the turn, which induce characteristic observable signatures on Δ_{ζ}. We derive accurate analytical predictions and show that the large enhancements required for PBHs demand noncanonical kinetic terms in the action of the multifield system.

Planck2018 results

We report on the implications for cosmic inflation of the 2018 release of thePlanckcosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from the two previousPlanckcosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles.Plancktemperature, polarization, and lensing data determine the spectral index of scalar perturbations to bens = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence ofns, either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combiningPlanckwith a compilation of baryon acoustic oscillation data. ThePlanck95% CL upper limit on the tensor-to-scalar ratio,r0.002 < 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtainr0.002 < 0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential,V″(ϕ) < 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005 Mpc−1 ≲ k ≲ 0.2 Mpc−1. A complementary analysis also finds no evidence for theoretically motivated parameterized features in thePlanckpower spectra. For the case of oscillatory features that are logarithmic or linear ink, this result is further strengthened by a new combined analysis including thePlanckbispectrum data. The newPlanckpolarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively.Planckpower spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.

Planck2018 results

We present cosmological parameter results from the final full-missionPlanckmeasurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5σlevel. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ωch2 = 0.120 ± 0.001, baryon density Ωbh2 = 0.0224 ± 0.0001, scalar spectral indexns = 0.965 ± 0.004, and optical depthτ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ* = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constantH0 = (67.4 ± 0.5) km s−1 Mpc−1; matter density parameter Ωm = 0.315 ± 0.007; and matter fluctuation amplitudeσ8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to beNeff = 2.99 ± 0.17, in agreement with the Standard Model predictionNeff = 3.046, and find that the neutrino mass is tightly constrained to ∑mν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ΩK = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to bew0 = −1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratior0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. ThePlanckbase-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6σ, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by thePlanckdata.

Extended reionization in models beyond ΛCDM with Planck 2018 data

We provide an update on the constraints on extended reionization histories with the Planck 2018 cosmic microwave background anisotropy data. The Planck 2018 data on large angular scales improve the measurement of the E-mode polarization reionization bump at low multipoles providing the possibility to improve our previous results [1]. Using a minor modification to the original Poly-reion model [2] for the reionization history, we find that the Planck 2018 data significantly improve all our previous results: we find as optical depth of τ=0.0572−0.0075+0.0064 at 68% CL, that early onsets of reionization are strongly disfavoured, i.e. redshift when the reionization begins, zxe=0=18.18−10.89 +1.61 at 68% CL, and that reionization duration (defined between 10% and 99% reionization) is significantly reduced, i.e. ΔzReion=4.59−2.45+1.67 at 68% CL . We explore possible correlations between reionization histories and cosmological parameters, including important extensions beyond ΛCDM . We find that the degeneracy between reionization and scalar spectral index, neutrino mass sum, spatial curvature, dark matter annihilation and other non-standard models are significantly reduced.The reduction of the error bars and the degeneracies, together with the shift towards lower values of the optical depth that we observe in the Poly-reion model are mainly driven by the new low-ℓ polarization likelihood of Planck 2018 baseline based on the HFI data. This is confirmed also by the results derived without this likelihood and the ones with different alternatives to the baseline that are presented for a subset of models.

A new pressure-parametric cosmological model

We put forward a pressure-parametric model to study the tiny deviation from cosmological constant(CC) behavior of the dark sector accelerating the expansion of the Universe. Data from cosmic microwave background (CMB) anisotropies, baryonic acoustic oscillations (BAO), Type Ia supernovae (SN Ia) observation are applied to constrict the model parameters. The constraint results show that such model suffers with [Formula: see text] tension as well. To realize this model more physically, we reconstruct it with the quintessence and phantom scalar fields, and find out that although the model predicts a quintessence-induced acceleration of the Universe at past and present, at some moment of the future, dark energy’s density have a disposition to increase.

Optimal Boltzmann hierarchies with nonvanishing spatial curvature

Within cosmological perturbation theory, the cosmic microwave background anisotropies are usually computed from a Boltzmann hierarchy coupled to the perturbed Einstein equations. In this setup, one set of multipoles describes the temperature anisotropies, while two other sets, of electric and magnetic types, describe the polarization anisotropies. In order to reduce the number of multipoles types needed for polarization, and thus to speed up the numerical resolution, an optimal hierarchy has been proposed in the literature for Einstein-Boltzmann codes. However, it has been recently shown that the separability between directional and orbital eigenfunctions employed in the optimal hierarchy is not correct in the presence of spatial curvature. We investigate how the assumption of separability affects the optimal hierarchy, and show that it introduces relative errors of order $\Omega_K$ with respect to the full hierarchy. Despite of that, we show that the optimal hierarchy still gives extremely good results for temperature and polarization angular spectra, with relative errors that are much smaller than cosmic variance even for curvatures as large as $|\Omega_K|=0.1$. Still, we find that the polarization angular spectra from tensor perturbations are significantly altered when using the optimal hierarchy, leading to errors that are typically of order $50 |\Omega_K| \%$ on that component.

Using quasar X-ray and UV flux measurements to constrain cosmological model parameters

ABSTRACT Risaliti and Lusso have compiled X-ray and UV flux measurements of 1598 quasars (QSOs) in the redshift range 0.036 ≤ z ≤ 5.1003, part of which, z ∼ 2.4 − 5.1, is largely cosmologically unprobed. In this paper we use these QSO measurements, alone and in conjunction with baryon acoustic oscillation (BAO) and Hubble parameter [H(z)] measurements, to constrain cosmological parameters in six different cosmological models, each with two different Hubble constant priors. In most of these models, given the larger uncertainties, the QSO cosmological parameter constraints are mostly consistent with those from the BAO + H(z) data. A somewhat significant exception is the non-relativistic matter density parameter Ωm0 where QSO data favour Ωm0 ∼ 0.5 − 0.6 in most models. As a result, in joint analyses of QSO data with H(z) + BAO data the 1D Ωm0 distributions shift slightly towards larger values. A joint analysis of the QSO + BAO + H(z) data is consistent with the current standard model, spatially-flat ΛCDM, but mildly favours closed spatial hypersurfaces and dynamical dark energy. Since the higher Ωm0 values favoured by QSO data appear to be associated with the z ∼ 2 − 5 part of these data, and conflict somewhat with strong indications for Ωm0 ∼ 0.3 from most z < 2.5 data as well as from the cosmic microwave background anisotropy data at z ∼ 1100, in most models, the larger QSO data Ωm0 is possibly more indicative of an issue with the z ∼ 2 − 5 QSO data than of an inadequacy of the standard flat ΛCDM model.

Implications for cosmology from ground-based Cosmic Microwave Background observations

Cosmic Microwave Background (CMB) anisotropy encodes a lot of information about our Universe. In this paper we take the ground-based CMB observations (GCMB), including the South Pole Telescope (SPT), SPTpol and the Atacama Cosmology Telescope Polarimeter (ACTPol), as a new probe to the CMB anisotropy independent of two satellite observations, i.e. Wilkinson Microwave Anisotropy Probe (WMAP) and Planck. The combination of current GCMB data is consistent with WMAP and Planck. In the spatially flat ΛCDM model, the Hubble constant is H0=69.72± 1.63 km/s/Mpc at 68% confidence level (CL). Combining with baryon acoustic oscillation (BAO) and the Pantheon sample of Type Ia supernovae (SN), we find that H0=68.40± 0.58 km/s/Mpc (68% CL) in the spatially flat ΛCDM cosmology which has a tension with local measurement given by Riess et al. in 2019 at 3.7σ level, and Ωk=−0.0013± 0.0039 and Neff=2.90± 0.41 (68% CL) in the extended cosmological models.

Quantifying the impacts of future gravitational-wave data on constraining interacting dark energy

In this work, we investigate the impacts of the future gravitational-wave (GW) standard siren observation by the Einstein Telescope (ET) on constraining the interacting dark energy (IDE) models. We simulate 1000 GW events in the redshift range of 0≲ z ≲ 50 based on the 10-year observation of the ET . We combine the simulated GW data with the current mainstream cosmological electromagnetic observations including the cosmic microwave background anisotropies, the baryon acoustic oscillations, and the type Ia supernovae to constrain the IDE models. We consider typical IDE models in the context of a perturbed universe. To avoid the large-scale instability problem for IDE models, we apply the extended parameterized post-Friedmann approach to calculate the cosmological perturbations. We find that the addition of the GW standard siren data could significantly improve the constraint accuracies for most of the cosmological parameters (e.g., H0, w, and Ωm). For the coupling parameter β, the constraint errors could also be slightly improved when adding the GW data in the cosmological fit.

Constraints on active and sterile neutrinos in an interacting dark energy cosmology

We investigate the impacts of dark energy on constraining massive (active/sterile) neutrinos in interacting dark energy (IDE) models by using the current observations. We employ two typical IDE models, the interacting $w$ cold dark matter (I$w$CDM) model and the interacting holographic dark energy (IHDE) model, to make an analysis. To avoid large-scale instability, we use the parameterized post-Friedmann approach to calculate the cosmological perturbations in the IDE models. The cosmological observational data used in this work include the Planck cosmic microwave background (CMB) anisotropies data, the baryon acoustic oscillation data, the type Ia supernovae data, the direct measurement of the Hubble constant, the weak lensing data, the redshift-space distortion data, and the CMB lensing data. We find that the dark energy properties could influence the constraint limits of active neutrino mass and sterile neutrino parameters in the IDE models. We also find that the dark energy properties could influence the constraints on the coupling strength parameter $\beta$, and a positive coupling constant, $\beta>0$, can be detected at the $2.5\sigma$ statistical significance for the IHDE+$\nu_s$ model by using the all-data combination. In addition, we also discuss the "Hubble tension" issue in these scenarios. We find that the $H_0$ tension can be effectively relieved by considering massive sterile neutrinos, and in particular in the IHDE+$\nu_s$ model the $H_0$ tension can be reduced to be at the $1.28\sigma$ level.

Prospects for improving cosmological parameter estimation with gravitational-wave standard sirens from Taiji

Taiji, a space-based gravitational-wave observatory, consists of three satellites forming an equilateral triangle with arm length of 3×106 km, orbiting around the Sun. Taiji is able to observe the gravitational-wave standard siren events of massive black hole binary (MBHB) merger, which is helpful in probing the expansion of the universe. In this paper, we preliminarily forecast the capability of Taiji for improving cosmological parameter estimation with the gravitational-wave standard siren data. We simulate five-year standard siren data based on three fiducial cosmological models and three models of MBHB's formation and growth. It is found that the standard siren data from Taiji can effectively break the cosmological parameter degeneracies generated by the cosmic microwave background (CMB) anisotropies data, especially for dynamical dark energy models. The constraints on cosmological parameters are significantly improved by the data combination CMB + Taiji, compared to the CMB data alone. Compared to the current optical cosmological observations, Taiji can still provide help in improving the cosmological parameter estimation to some extent. In addition, we consider an ideal scenario to investigate the potential of Taiji on constraining cosmological parameters. We conclude that the standard sirens of MBHB from Taiji will become a powerful cosmological probe in the future.

Forecast for weighing neutrinos in cosmology with SKA

We investigate what role the SKA neutral hydrogen (HI) intensity mapping (IM) and galaxy sky surveys will play in weighing neutrinos in cosmology. We use the simulated data of the baryon acoustic oscillation (BAO) measurements from the HI surveys based on SKA1 (IM) and SKA2 (galaxy) to do the analysis. For the current observations, we use the Planck 2015 cosmic microwave background (CMB) anisotropies observation, the optical BAO measurements, the type Ia supernovae (SN) observation (Pantheon compilation), and the latest H0 measurement. We consider three mass ordering cases for massive neutrinos, i.e., the normal hierarchy (NH), inverted hierarchy (IH), and degenerate hierarchy (DH) cases. It is found that the SKA observation can significantly improve the constraints on Ωm and H0. Compared to the current observation, the SKA1 data can improve the constraints on Ωm by about 33%, and on H0 by about 36%; the SKA2 data can improve the constraints on Ωm by about 58%, and on H0 by about 66%. It is also found that the SKA observation can only slightly improve the constraints on ∑mv. Compared to the current observation, the SKA1 data can improve the constraints on ∑mv by about 4%, 3%, and 10%, for the NH, IH, and DH cases, respectively; the SKA2 data can improve the constraints on ∑mv by about 7%, 7%, and 16%, for the NH, IH, and DH cases, respectively.

The exponential tail of inflationary fluctuations: consequences for primordial black holes

The curvature perturbations produced during an early era of inflation are known to have quasi-Gaussian distribution functions close to their maximum, where they are well constrained by measurements of the cosmic microwave background anisotropies and of the large-scale structures. In contrast, the tails of these distributions are poorly known, although this part is the relevant one for rare, extreme objects such as primordial black holes. We show that these tails are highly non-Gaussian, and cannot be described with standard non-Gaussian expansions, that are designed to approximate the distributions close to their maximum only. Using the stochastic-δ N formalism, we develop a generic framework to compute the tails, which are found to have an exponential, rather than Gaussian, decay. These exponential tails are inevitable, and do not require any non-minimal feature as they simply result from the quantum diffusion of the inflaton field along its potential. We apply our formalism to a few relevant single-field, slow-roll inflationary potentials, where our analytical treatment is confirmed by comparison with numerical results. We discuss the implications for the expected abundance of primordial black holes in these models, and highlight that it can differ from standard results by several orders of magnitude. In particular, we find that potentials with an inflection point overproduce primordial black holes, unless slow roll is violated.

Prospect for constraining holographic dark energy with gravitational wave standard sirens from the Einstein Telescope

We study the holographic dark energy (HDE) model by using the future gravitational wave (GW) standard siren data observed from the Einstein Telescope (ET) in this work. We simulate 1000 GW standard siren data based on a 10-year observation of the ET to make this analysis. We find that all the cosmological parameters in the HDE model can be tremendously improved by including the GW standard siren data in the cosmological fit. The GW data combined with the current cosmic microwave background anisotropies, baryon acoustic oscillations, and type Ia supernovae data will measure the cosmological parameters Omega _{mathrm{m}}, H_0, and c in the HDE model to be at the accuracies of 1.28%, 0.59%, and 3.69%, respectively. A comparison with the cosmological constant model and the constant-w dark energy model shows that, compared to the standard model, the parameter degeneracies will be broken more thoroughly in a dynamical dark energy model. We find that the GW data alone can provide a fairly good measurement for H_0, but for other cosmological parameters the GW data alone can only provide rather weak measurements. However, due to the fact that the parameter degeneracies can be broken by the GW data, the standard sirens can play an essential role in improving the parameter estimation.

Generalized Brans-Dicke theories in light of evolving dark energy

The expansion history of the Universe reconstructed from a combination of recent data indicates a preference for a changing Dark Energy (DE) density. Moreover, the DE density appears to be increasing with cosmic time, with its equation of state being below -1 on average, and possibly crossing the so-called phantom divide. Scalar-tensor theories, in which the scalar field mediates a force between matter particles, offer a natural framework in which the effective DE equation of state can be less than -1 and cross the phantom barrier. We consider the generalized Brans-Dicke (GBD) class of scalar-tensor theories and reconstruct their Lagrangian given the effective DE density extracted from recent data. Then, given the reconstructed Lagrangian, we solve for the linear perturbations and investigate the characteristic signatures of these reconstructed GBD in the cosmological observables, such as the cosmic microwave background (CMB) anisotropy, the galaxy number counts, and their cross-correlations. In particular, we demonstrate that the Integrated Sachs-Wolfe (ISW) effect probed by the cross-correlation of CMB with the matter distribution can rule out scalar-tensor theories as the explanation of the observed DE dynamics independently from the laboratory and solar system fifth force constraints.

Beyond Optical Depth: Future Determination of Ionization History from the Cosmic Microwave Background.

We explore the fundamental limits to which reionization histories can be constrained using only large-scale cosmic microwave background (CMB) anisotropy measurements. The redshift distribution of the fractional ionization x e (z) affects the angular distribution of CMB polarization. We project constraints on the reionization history of the universe using low-noise full-sky temperature and E-mode measurements of the CMB. We show that the measured TE power spectrum, , has roughly one quarter of the constraining power of on the reionization optical depth τ, and its addition improves the precision on τ by 20% over using only. We also use a two-step reionization model with an additional high-redshift step, parameterized by an early ionization fraction , and a late reionization step at z re. We find that future high signal-to-noise measurements of the multipoles 10 ⩽ ℓ < 20 are especially important for breaking the degeneracy between and z re. In addition, we show that the uncertainties on these parameters determined from a map with sensitivity 10 μK arcmin are less than 5% larger than the uncertainties in the noiseless case, making this noise level a natural target for future large sky area E-mode measurements.