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The standard cosmological model, which assumes statistical isotropy and parity invariance, predicts the absence of correlations between even-parity and odd-parity observables of the cosmic microwave background (CMB). Contrary to these predictions, large-angle CMB temperature anomalies generically involve correlations between even-$\ell$ and odd-$\ell$ angular power spectrum $C_\ell$, while recent analyses of CMB polarization have revealed non-zero equal-$\ell$ $EB$ correlations. These findings challenge the conventional understanding, suggesting deviations from statistical isotropy, violations of parity, or both. Cosmic topology, which involves changing only the boundary conditions of space relative to standard cosmology, offers a compelling framework to potentially account for such parity-violating observations. Topology inherently breaks statistical isotropy, and can also break homogeneity and parity, providing a natural paradigm for explaining observations of parity-breaking observables without the need to add parity violation to the underlying microphysics. Our investigation delves into the harmonic space implications of topology for CMB correlations, using as an illustrative example $EB$ correlations generated by tensor perturbations under both parity-preserving and parity-violating scenarios. Consequently, these findings not only challenge the foundational assumptions of the standard cosmological model but also open new avenues for exploring the topological structure of the Universe through CMB observations., Comment: 20 pages, 4 figures

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave background in the test case of Euclidean $E_1$ topology (the 3-torus) with a cubic fundamental domain of a size scale significantly smaller than the diameter of the last scattering surface. Different machine learning approaches are capable of classifying the harmonic-space realizations with accuracy greater than 99% if the topology scale is half of the diameter of the last-scattering surface and orientation of the topology is known. For distinguishing random rotations of these sky realizations from realizations of the covering space, the extreme gradient boosting classifier algorithm performs best with an accuracy of 88%. Slightly lower accuracies of 83% to 87% are obtained with the random forest classifier along with one- and two-dimensional convolutional neural networks. The techniques presented here can also accurately classify non-rotated cubic $E_1$ topology realizations with a topology scale slightly larger than the diameter of the last-scattering surface, if provided enough training data. This work identifies the prospects and the main challenges for developing machine learning techniques that are capable of accurately classifying observationally viable topologies., Comment: 32 pages, 12 figures, 4 tables

If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. We present formulas for eigenmodes in orientable Euclidean manifolds with the topologies $E_{1}-E_{6}$, $E_{11}$, $E_{12}$, $E_{16}$, and $E_{18}$ that encompass the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the observed CMB sky. We find that topologies where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB give a correlation signal that is larger than cosmic variance noise in the CMB. This implies that if cosmic topology is the explanation of large-angle anomalies in the CMB, then the distance to our nearest clone is not much larger than the diameter of the last scattering surface. We argue that the topological information is likely to be better preserved in three-dimensional data, such as will eventually be available from large-scale structure surveys., Comment: 79 pages, 9 figures. v3: version published in JCAP

Polarization of the cosmic microwave background (CMB) is sensitive to new physics violating parity symmetry, such as the presence of a pseudoscalar "axionlike" field. Such a field may be responsible for early dark energy (EDE), which is active prior to recombination and provides a solution to the so-called Hubble tension. The EDE field coupled to photons in a parity-violating manner would rotate the plane of linear polarization of the CMB and produce a cross-correlation power spectrum of $E$- and $B$-mode polarization fields with opposite parities. In this paper, we fit the $EB$ power spectrum predicted by the photon-axion coupling of the EDE model with a potential $V(\phi)\propto [1-\cos(\phi/f)]^3$ to polarization data from Planck. We find that the unique shape of the predicted $EB$ power spectrum is not favored by the data and obtain a first constraint on the photon-axion coupling constant, $g=(0.04\pm 0.16)M_{\text{Pl}}^{-1}$ (68% CL), for the EDE model that best fits the CMB and galaxy clustering data. This constraint is independent of the miscalibration of polarization angles of the instrument or the polarized Galactic foreground emission. Our limit on $g$ may have important implications for embedding EDE in fundamental physics, such as string theory., Comment: 7 pages, 3 figures, 1 table. Accepted for publication in Physical Review Letters. The stacked EB power spectrum is publicly available at https://github.com/LilleJohs/Observed-EB-Power-Spectrum

The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within $\Lambda$CDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. This result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients., Comment: 22 pages, 7 figures. v3: Corrected Figs. 3, 4, and 5 as published in Erratum

The shortest distance around the Universe through us is unlikely to be much larger than the horizon diameter if microwave background anomalies are due to cosmic topology. We show that observational constraints from the lack of matched temperature circles in the microwave background leave many possibilities for such topologies. We evaluate the detectability of microwave background multipole correlations for sample cases. Searches for topology signatures in observational data over the large space of possible topologies pose a formidable computational challenge., Comment: 7 pages, 4 figures. v4: version published in PRL

The observed pattern of linear polarization of the cosmic microwave background (CMB) photons is a sensitive probe of physics violating parity symmetry under inversion of spatial coordinates. A new parity-violating interaction might have rotated the plane of linear polarization by an angle $\beta$ as the CMB photons have been traveling for more than 13 billion years. This effect is known as "cosmic birefringence." In this paper, we present new measurements of cosmic birefringence from a joint analysis of polarization data from two space missions, Planck and WMAP. This dataset covers a wide range of frequencies from 23 to 353 GHz. We measure $\beta = 0.342^{\circ\,+0.094^\circ}_{\phantom{\circ\,}-0.091^\circ}$ (68% C.L.) for nearly full-sky data, which excludes $\beta=0$ at 99.987% C.L. This corresponds to the statistical significance of $3.6\sigma$. There is no evidence for frequency dependence of $\beta$. We find a similar result, albeit with a larger uncertainty, when removing the Galactic plane from the analysis., Comment: 9 pages, 5 figures, 1 table. The code to reproduce the results of this paper is available at https://github.com/LilleJohs/Cosmic_Birefringence. Accepted for publication in Physical Review D

This is a solicited whitepaper for the Snowmass 2021 community planning exercise. The paper focuses on measurements and science with the Cosmic Microwave Background (CMB). The CMB is foundational to our understanding of modern physics and continues to be a powerful tool driving our understanding of cosmology and particle physics. In this paper, we outline the broad and unique impact of CMB science for the High Energy Cosmic Frontier in the upcoming decade. We also describe the progression of ground-based CMB experiments, which shows that the community is prepared to develop the key capabilities and facilities needed to achieve these transformative CMB measurements., Comment: contribution to Snowmass 2021

We numerically and analytically explore the background cosmological dynamics of multifield dark energy with highly nongeodesic or "spinning" field-space trajectories. These extensions of standard single-field quintessence possess appealing theoretical features and observable differences from the cosmological standard model. At the level of the cosmological background, we perform a phase-space analysis and identify approximate attractors with late-time acceleration for a wide range of initial conditions. Focusing on two classes of field-space geometry, we derive bounds on parameter space by demanding viable late-time acceleration and the absence of gradient instabilities, as well as from the de Sitter swampland conjecture., Comment: 19 pages, 12 figures. v2: Improved and published version

By converting conventional spin-singlet Cooper pairs to polarized spin-triplet pairs, it is possible to sustain long-ranged spin-polarized supercurrents flowing through strongly polarized ferromagnets. Obtaining such a conversion via spin-orbit interactions, rather than magnetic inhomogeneities, has recently been explored in the literature. A challenging aspect with regard to experimental detection has been that in order for Rashba spin-orbit interactions, present e.g. at interfaces due to inversion symmetry breaking, to generate such long-ranged supercurrents, an out-of-plane component of the magnetization is required. This limits the choice of materials and can induce vortices in the superconducting region complicating the interpretation of measurements. Therefore, it would be desirable to identify a way in which Rashba spin-orbit interactions can induce long-ranged supercurrents for purely in-plane rotations of the magnetization. Here, we show that this is possible in a lateral Josephson junction where two superconducting electrodes are placed in contact with a ferromagnetic film via two thin, heavy normal metals. The magnitude of the supercurrent in such a setup becomes tunable by the in-plane magnetization angle when using only a single magnetic layer. These results could provide a new and simpler way to generate controllable spin-polarized supercurrents than previous experiments which utilized complicated magnetically textured Josephson junctions., Comment: 9 pages, 5 figures