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We discuss the future detectability of gravitational-wave induced lensing from high-sensitivity cosmic microwave background (CMB) experiments. Gravitational waves can induce a rotational component of the weak-lensing deflection angle, usually referred to as the curl mode, which would be imprinted on the CMB maps. Using the technique of reconstructing lensing signals involved in CMB maps, this curl mode can be measured in an unbiased manner, offering an independent confirmation of the gravitational waves complementary to B-mode polarization experiments. Based on the Fisher matrix analysis, we first show that with the noise levels necessary to confirm the consistency relation for the primordial gravitational waves, the future CMB experiments will be able to detect the gravitational-wave induced lensing signals. For a tensorto-scalar ratio of r ≲ 0.1, even if the consistency relation is difficult to confirm with a high significance, the gravitational-wave induced lensing will be detected at more than 3σ significance level. Further, we point out that high-sensitivity experiments will be also powerful to constrain the gravitational waves generated after the recombination epoch. Compared to the B-mode polarization, the curl mode is particularly sensitive to gravitational waves generated at low redshifts (z ≲ 10) with a low frequency (k ≲ 10-3 Mpc-1), and it could give a much tighter constraint on their energy density ΩGW by more than 3 orders of magnitude. [ABSTRACT FROM AUTHOR]

We present constraints on a cosmic string network with a measurement of weak gravitational lensing from CMB temperature map. The cosmic string network between the observer and last scattering surface of CMB photons generates vector and/or tensor metric perturbations, and the deflection of CMB photons by these gravitational fields has a curl mode which is not produced by the scalar metric perturbations. In this paper, we use the power spectrum of curl mode obtained from Planck to constrain the string tension, Gμ, and the reconnection probability, P. In demonstrating the parameter constraints with Planck curl mode, we also measure the lensing power spectrum from the Atacama Cosmology Telescope (ACT) 2008 season data, which have better angular resolution with lower instrumental noise on a much smaller chunk of the sky. Assuming P=1, the upper bound on tension is Gμ=6.6×10-2 with 2σ (95% C.L.), using curl mode from Planck, which is weaker than that from the small-scale temperature power spectrum. For small values of P, however, the constraint from curl mode becomes tighter compared to that from the temperature power spectrum. For P≤ 10-2, we obtain the constraint on the combination of the string parameters as GμP-1 ≤3.4×10-5 at more than 2σ (95% C.L.). [ABSTRACT FROM AUTHOR]

We introduce and validate a delensing framework for the Simons Observatory (SO), which will be used to improve constraints on inflationary gravitational waves by reducing the lensing noise in measurements of the B modes in CMB polarization. SO will initially observe CMB by using three small aperture telescopes and one large-aperture telescope. While polarization maps from small-aperture telescopes will be used to constrain inflationary gravitational waves, the internal CMB lensing maps used to delens will be reconstructed from data from the large-aperture telescope. Since lensing maps obtained from the SO data will be noise dominated on subdegree scales, the SO lensing framework constructs a template for lensing-induced B modes by combining internal CMB lensing maps with maps of the cosmic infrared background from Planck as well as galaxy density maps from the LSST survey. We construct a likelihood for constraining the tensor-to-scalar ratio r that contains auto and cross spectra between observed B modes and the lensing B-mode template. We test our delensing analysis pipeline on map-based simulations containing survey nonidealities, but that, for this initial exploration, does not include contamination from Galactic and extragalactic foregrounds. We find that the SO survey masking and inhomogeneous and atmospheric noise have very little impact on the delensing performance, and the r constraint becomes σ(r)≈0.0015 which is close to that obtained from the idealized forecasts in the absence of the Galactic foreground and is nearly a factor of 2 tighter than without delensing. We also find that uncertainties in the external large-scale structure tracers used in our multitracer delensing pipeline lead to bias much smaller than the 1σ statistical uncertainties. [ABSTRACT FROM AUTHOR]

We propose a new reionization probe that uses cosmic microwave background (CMB) observations; the cross-correlation between fluctuations in the CMB optical depth which probes the integrated electron density, δτ, and the Compton y-map which probes the integrated electron pressure. This cross-correlation is much less contaminated than the y-map power spectrum by late-time cluster contributions. In addition, this cross-correlation can constrain the temperature of ionized bubbles while the optical-depth fluctuations and kinetic Sunyaev Zel'dvich effect can not. We measure this new observable using a Planck y-map as well as a map of optical-depth fluctuations that we reconstruct from Planck CMB temperature data. We use our measurements to derive a first CMB only upper limit on the temperature inside ionized bubbles, Tb≲7.0×105 K (2σ). We also present future forecasts, assuming a fiducial model with characteristic reionization bubble size Rb=5 Mpc and Tb=5×104 K. The signal-to-noise ratio of the fiducial cross-correlation using a signal dominated y-map from the Probe of Inflation and Cosmic Origins (PICO) becomes ≃7 with CMB-S4 δτ and ≃13 with CMB-HD δτ. For the fiducial model, we predict that the CMB-HD--PICO cross-correlation should achieve an accurate measurement of the reionization parameters; Tb≃49800-5100+4500 K and Rb≃5.09-0.79+0.66 Mpc. Since the power spectrum of the electron density fluctuations is constrained by the δτ autospectrum, the temperature constraints should be only weakly model dependent on the details of the electron distributions and should be statistically representative of the temperature in ionized bubbles during reionization. This cross-correlation could, therefore, become an important observable for future CMB experiments. [ABSTRACT FROM AUTHOR]

We present new constraints on anisotropic birefringence of the cosmic microwave background polarization using two seasons of data from the Atacama Cosmology Telescope covering 456 square degrees of sky. The birefringence power spectrum, measured using a curved-sky quadratic estimator, is consistent with zero. Our results provide the tightest current constraint on birefringence over a range of angular scales between 5 arc minutes and 9°. We improve previous upper limits on the amplitude of a scale-invariant birefringence power spectrum by a factor of between 2 and 3. Assuming a nearly massless axion field during inflation, our result is equivalent to a 2σ upper limit on the Chern-Simons coupling constant between axions and photons of gαγ<4.0×10-2/HI, where HI is the inflationary Hubble scale. [ABSTRACT FROM AUTHOR]

We present robust constraints on the stochastic gravitational waves (GWs) at Mpc scales from the cosmic microwave background (CMB) data. CMB constraints on GWs are usually characterized as the tensor-to-scalar ratio, assuming specifically a power-law form of the primordial spectrum, and are obtained from the angular spectra of CMB. Here, we relax the assumption of the power-law form, and consider to what extent one can constrain a monochromatic GW at shorter wavelengths. Previously, such a constraint has been derived at the wavelengths larger than the resolution scale of the CMB measurements, typically above 100 Mpc (below 10-16 Hz in frequency). However, GWs whose wavelength is much shorter than 100 Mpc can imprint a small but non-negligible signal on CMB anisotropies at observed angular scales, ℓ < 1000. Here, using the CMB temperature, polarization, and lensing data set, we obtain the best constraints to date at 10-16 - 10-14 Hz of the GWs produced before the time of decoupling, which are tighter than those derived from the astrometric measurements and upper bounds on extra radiations. In the future, the constraints on GWs at Mpc scales will be further improved by several orders of magnitude with the precision B -mode measurement on large scales, ℓ < 100. [ABSTRACT FROM AUTHOR]

Cosmic microwave background (CMB) lensing is an integrated effect whose kernel is greater than half the peak value in the range 1

We study the impact of the nonlinear growth of the large-scale structure (LSS) on the removal of the gravitational lensing effect (delensing) in cosmic microwave background (CMB) B modes. The importance of the nonlinear growth of the LSS in the gravitational lensing analysis of CMB has been recently recognized by several works, while its impact on delensing is not yet explored. The delensing using mass tracers such as galaxies and cosmic infrared background could be also affected by the nonlinear growth. We find that the nonlinear growth of the LSS leads to ~0.3% corrections to the B-mode spectrum after delensing with a high-z mass tracer (zm~2) at l=1000-2000. The off-diagonal correlation coefficients of the lensing B-mode template spectrum become significant for delensing with low-z tracers (zm0.5), but are negligible with high-z tracers (such as cosmic infrared background). On the other hand, the power spectrum covariance of the delensed B mode is not significantly affected by the nonlinear growth of the LSS, and the delensing efficiency is not significantly changed even if we use low-z tracers. The CMB B-mode internal delensing is also not significantly affected by the nonlinear growth. [ABSTRACT FROM AUTHOR]

Cosmological structures grow differently in theories of gravity which are modified as compared to Einstein's general relativity (GR). Cosmic microwave background (CMB) fluctuation patterns at the last scattering surface are lensed by these structures along the photon path to the observer. The observed CMB pattern therefore keeps trace of the growth history of structures. We show that observations of the CMB lensing bispectrum offer an interesting way to constrain deviations from GR in a broad class of scalar-tensor theories of gravity called "beyond Horndeski". We quantify how the constraints on generic parameters describing the deviations from GR depend on the effective multipole range of the analysis. Our results further indicate that an accurate nonlinear correction of the matter bispectrum in the modified gravity considered is necessary when the bispectrum is used to probe scales beyond a multipole ℓmax≳1500. We also found that the results are insensitive to details of the implementation of the screening mechanism, at very small scales. We finally demonstrate the potential of the lensing bispectrum to provide a blind reconstruction of the redshift evolution of our modified gravity parameters by combining the analysis of CMB and low-z source lensing data. [ABSTRACT FROM AUTHOR]

We present constraints on the patchy reionization by measuring the trispectrum of the Planck 2015 cosmic microwave background (CMB) temperature anisotropies. The patchy reionization leads to anisotropies in the CMB optical depth, and the statistics of the observed CMB anisotropies is altered. We estimate the trispectrum of the CMB temperature anisotropies to constrain spatial variation of the optical depth. We show that the measured trispectrum is consistent with that from the standard lensed CMB simulation at 2σ. While no evidence of the patchy reionization is found in the Planck 2015 temperature trispectrum, the CMB constraint on the patchy reionization is significantly improved from previous works. Assuming the analytic bubble-halo model of Wang and Hu (2006), the constraint obtained in this work rules out the typical bubble size at the ionization fraction of ∼0.5 as R≳10 Mpc. Further, our constraint implies that large-scale B-modes from the patchy reionization are not a significant contamination in detecting the primordial gravitational waves of r≳0.001 if the B mode induced by the patchy reionization is described by Dvorkin et al. (2009). The CMB trispectrum data starts to provide meaningful constraints on the patchy reionization. [ABSTRACT FROM AUTHOR]

We present a new method for delensing B modes of the cosmic microwave background (CMB) using a lensing potential reconstructed from the same realization of the CMB polarization (CMB internal delensing). The B -mode delensing is required to improve sensitivity to primary B modes generated by, e.g., the inflationary gravitational waves, axionlike particles, modified gravity, primordial magnetic fields, and topological defects such as cosmic strings. However, the CMB internal delensing suffers from substantial biases due to correlations between observed CMB maps to be delensed and that used for reconstructing a lensing potential. Since the bias depends on realizations, we construct a realization-dependent (RD) estimator for correcting these biases by deriving a general optimal estimator for higher-order correlations. The RD method is less sensitive to simulation uncertainties. Compared to the previous l -splitting method, we find that the RD method corrects the biases without substantial degradation of the delensing efficiency. [ABSTRACT FROM AUTHOR]

We study the reconstruction of the cosmic rotation power spectrum produced by parity-violating physics, with an eye to ongoing and near future cosmic microwave background (CMB) experiments such as BICEP Array, CMBS4, LiteBIRD and Simons Observatory. In addition to the inflationary gravitational waves and gravitational lensing, measurements of other various effects on CMB polarization open new window into the early Universe. One of these is anisotropies of the cosmic polarization rotation which probes the Chern-Simons term generally predicted by string theory. The anisotropies of the cosmic rotation are also generated by the primordial magnetism and in the Standard Model extention framework. The cosmic rotation anisotropies can be reconstructed as quadratic in CMB anisotropies. However, the power of the reconstructed cosmic rotation is a CMB four-point correlation and is not directly related to the cosmic-rotation power spectrum. Understanding all contributions in the four-point correlation is required to extract the cosmic rotation signal. Assuming inflationary motivated cosmic-rotation models, we employ simulation to quantify each contribution to the four-point correlation and find that (1) a secondary contraction of the trispectrum increases the total signal-to-noise, (2) a bias from the lensing-induced trispectrum is significant compared to the statistical errors in, e.g., LiteBIRD and CMBS4-like experiments, (3) the use of a realization-dependent estimator decreases the statistical errors by 10%-20%, depending on experimental specifications, and (4) other higher-order contributions are negligible at least for near future experiments. [ABSTRACT FROM AUTHOR]

We present constraints on a cosmic string network with a measurement of weak gravitational lensing from CMB temperature map. The cosmic string network between the observer and last scattering surface of CMB photons generates vector and/or tensor metric perturbations, and the deflection of CMB photons by these gravitational fields has a curl mode which is not produced by the scalar metric perturbations. In this paper, we use the power spectrum of curl mode obtained from Planck to constrain the string tension, Gμ, and the reconnection probability, P. In demonstrating the parameter constraints with Planck curl mode, we also measure the lensing power spectrum from the Atacama Cosmology Telescope (ACT) 2008 season data, which have better angular resolution with lower instrumental noise on a much smaller chunk of the sky. Assuming P=1, the upper bound on tension is Gμ=6.6×10-5 with 2σ (95% C.L.), using curl mode from Planck, which is weaker than that from the small-scale temperature power spectrum. For small values of P, however, the constraint from curl mode becomes tighter compared to that from the temperature power spectrum. For P≲10-2, we obtain the constraint on the combination of the string parameters as GμP-1=3.4×10-5 at more than 2σ (95% C.L.). [ABSTRACT FROM AUTHOR]

We investigate the impact of non-Gaussian lensing deflections on measurements of the CMB lensing power spectrum. We find that the false assumption of their Gaussianity significantly biases these measurements in current and future experiments at the percent level. The bias is detected by comparing CMB lensing reconstructions from simulated CMB data lensed with Gaussian deflection fields to reconstructions from simulations lensed with fully non-Gaussian deflection fields. The non-Gaussian deflections are produced by ray tracing through snapshots of an N-body simulation and capture both the non-Gaussianity induced by nonlinear structure formation and by multiple correlated deflections. We find that the amplitude of the measured bias can be modeled with analytic expressions for a lensing bispectrum-induced bias derived by Böhm et al. in 2016 when post-Born corrections are included in the lensing bispectrum model. The bias is largest in temperature-based measurements, where it is detected with a significance of 2.84σ in the power spectrum of reconstructed convergence fields. Cross-correlating the reconstruction with the noiseless input convergence fields results in a 5.21σ detection. We do not find evidence for the bias in measurements from a combination of polarization fields (EB,EB). We argue that this non-Gaussian bias should be even more important for measurements of cross-correlations of CMB lensing with low-redshift tracers of large-scale structure. [ABSTRACT FROM AUTHOR]