Probing Parity-Violation with the Four-Point Correlation Function of BOSS Galaxies

Parity-violating physics in the early Universe can leave detectable traces in late-time observables. Whilst vector- and tensor-type parity-violation can be observed in the $B$-modes of the cosmic microwave background, scalar-type signatures are visible only in the four-point correlation function (4PCF) and beyond. This work presents a blind test for parity-violation in the 4PCF of the BOSS CMASS sample, considering galaxy separations in the range $[20,160]h^{-1}\mathrm{Mpc}$. The parity-odd 4PCF contains no contributions from standard $\Lambda$CDM physics and can be efficiently measured using recently developed estimators. Data are analyzed using both a non-parametric rank test (comparing the BOSS 4PCFs to those of realistic simulations) and a compressed $\chi^2$ analysis, with the former avoiding the assumption of a Gaussian likelihood. These find similar results, with the rank test giving a detection probability of $99.6\%$ ($2.9\sigma$). This provides significant evidence for parity-violation, either from cosmological sources or systematics. We perform a number of systematic tests: although these do not reveal any observational artefacts, we cannot exclude the possibility that our detection is caused by the simulations not faithfully representing the statistical properties of the BOSS data. Our measurements can be used to constrain physical models of parity-violation. As an example, we consider a coupling between the inflaton and a $U(1)$ gauge field and place bounds on the latter's energy density, which are several orders of magnitude stronger than those previously reported. Upcoming probes such as DESI and Euclid will reveal whether our detection of parity-violation is due to new physics, and strengthen the bounds on a variety of models.Comment: 30 pages, 11 figures, accepted by Phys. Rev. D. Code available at https://github.com/oliverphilcox/Parity-Odd-4PC

Optimal Estimation of the Binned Mask-Free Power Spectrum, Bispectrum, and Trispectrum on the Full Sky: Scalar Edition

We derive optimal estimators for the two-, three-, and four-point correlators of statistically isotropic scalar fields defined on the sphere, such as the Cosmic Microwave Background temperature fluctuations, allowing for arbitrary (linear) masking and inpainting schemes. In each case, we give the optimal unwindowed estimator (obtained via a maximum-likelihood prescription, with an associated Fisher deconvolution matrix), and an idealized form, and pay close attention to their efficient computation. For the trispectrum, we include both parity-even and parity-odd contributions, as allowed by symmetry. The estimators can include arbitrary weighting of the data (and remain unbiased), but are shown to be optimal in the limit of inverse-covariance weighting and Gaussian statistics. The normalization of the estimators is computed via Monte Carlo methods, with the rate-limiting steps (involving spherical harmonic transforms) scaling linearly with the number of bins. An accompanying code package, PolyBin, implements these estimators in Python, and we demonstrate the estimators' efficacy via a suite of validation tests.Comment: 33 pages, 10 figures, code available at https://github.com/oliverphilcox/PolyBin. Accepted by Phys. Rev.

Do the CMB Temperature Fluctuations Conserve Parity?

Observations of the Cosmic Microwave Background (CMB) have cemented the notion that the large-scale Universe is both statistically homogeneous and isotropic. But is it invariant also under reflections? To probe this we require parity-sensitive statistics: for scalar observables, the simplest is the trispectrum. We make the first measurements of the parity-odd scalar CMB, focusing on the large-scale ($2<\ell<510$) temperature anisotropies measured by Planck. This is facilitated by new quasi-maximum-likelihood estimators for binned correlators, which account for mask convolution and leakage between even- and odd-parity components, and achieve ideal variances within $\approx 20\%$. We perform a blind test for parity violation by comparing a $\chi^2$ statistic from Planck to theoretical expectations, using two suites of simulations to account for the possible likelihood non-Gaussianity and residual foregrounds. We find consistency at the $\approx 0.4\sigma$ level, yielding no evidence for novel early-Universe phenomena. The measured trispectra allow for a wealth of new physics to be constrained; here, we use them to constrain eight primordial models, including Ghost Inflation, Cosmological Collider scenarios, and Chern-Simons gauge fields. We find no signatures of new physics, with a maximal detection significance of $2.0\sigma$. Our results also indicate that the recent parity excesses seen in the BOSS galaxy survey are not primordial in origin, given that the CMB dataset contains roughly $250\times$ more primordial modes, and is far easier to interpret, given the linear physics, Gaussian statistics, and accurate mocks. Tighter CMB constraints can be wrought by including smaller scales and adding polarization data.Comment: 7+13 pages, 4+5 figures, accepted by Phys. Rev. Lett. Code available at https://github.com/oliverphilcox/PolyBin/tree/main/planck_publi

Efficient Computation of NN-point Correlation Functions in DD Dimensions

We present efficient algorithms for computing the $N$-point correlation functions (NPCFs) of random fields in arbitrary $D$-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences, and provide a natural tool to describe a range of stochastic processes. Typically, NPCF estimators have $\mathcal{O}(n^N)$ complexity (for a data set containing $n$ particles); their application is thus computationally infeasible unless $N$ is small. By projecting onto a suitably-defined angular basis, we show that the estimators can be written in separable form, with complexity $\mathcal{O}(n^2)$, or $\mathcal{O}(n_{\rm g}\log n_{\rm g})$ if evaluated using a Fast Fourier Transform on a grid of size $n_{\rm g}$. Our decomposition is built upon the $D$-dimensional hyperspherical harmonics; these form a complete basis on the $(D-1)$-sphere and are intrinsically related to angular momentum operators. Concatenation of $(N-1)$ such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. In particular, isotropic correlation functions require only states with zero combined angular momentum. We provide explicit expressions for the NPCF estimators as applied to both discrete and gridded data, and discuss a number of applications within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.Comment: 12 pages, 2 figures, submitted to PNAS. Comments welcome

Testing Parity Symmetry with the Polarized Cosmic Microwave Background

New physics in the early Universe could lead to parity-violation in the late Universe, sourcing statistics whose sign changes under point reflection. The best constraints on such phenomena have come from the Planck temperature fluctuations; however, this is already cosmic-variance-limited down to relatively small scales, thus only small improvements are expected in the future. Here, we search for signatures of parity-violation in the polarized CMB, using the Planck PR4 $T$- and $E$-mode data. We perform both a simulation-based blind test for any parity-violating signal at $\ell<518$, and a targeted search for primordial $U(1)$ gauge fields (and the amplitudes of a generic collapsed model) at $\ell<2000$. In all cases, we find no evidence for new physics, with the model-independent test finding consistency with the FFP10/NPIPE simulation suite at $(-)0.4\sigma$, and the gauge field test constraining the fractional amplitude of gauge fields during inflation to be below $6\times 10^{-19}$ at $95\%$ confidence level for a fiducial model. The addition of polarization data can significantly improve the constraints, depending on the particular model of primordial physics, and the bounds will tighten significantly with the inclusion of smaller-scale information.Comment: 15 pages, 9 figures. Submitted to Phys. Rev.

Combining Full-Shape and BAO Analyses of Galaxy Power Spectra: A 1.6% CMB-independent constraint on H0

We present cosmological constraints from a joint analysis of the pre- and post-reconstruction galaxy power spectrum multipoles from the final data release of the Baryon Oscillation Spectroscopic Survey (BOSS). Geometric constraints are obtained from the positions of BAO peaks in reconstructed spectra, analyzed in combination with the unreconstructed spectra in a full-shape (FS) likelihood using a joint covariance matrix, giving stronger parameter constraints than FS-only or BAO-only analyses. We introduce a new method for obtaining constraints from reconstructed spectra based on a correlated theoretical error, which is shown to be simple, robust, and applicable to any flavor of density-field reconstruction. Assuming $\Lambda$CDM with massive neutrinos, we analyze data from two redshift bins $z_\mathrm{eff}=0.38,0.61$ and obtain $1.6\%$ constraints on the Hubble constant $H_0$, using only a single prior on the current baryon density $\omega_b$ from Big Bang Nucleosynthesis (BBN) and no knowledge of the power spectrum slope $n_s$. This gives $H_0 = 68.6\pm1.1\,\mathrm{km\,s}^{-1}\mathrm{Mpc}^{-1}$, with the inclusion of BAO data sharpening the measurement by $40\%$, representing one of the strongest current constraints on $H_0$ independent of cosmic microwave background data. Restricting to the best-fit slope $n_s$ from Planck (but without additional priors on the spectral shape), we obtain a $1\%$ $H_0$ measurement of $67.8\pm 0.7\,\mathrm{km\,s}^{-1}\mathrm{Mpc}^{-1}$. We find strong constraints on the cosmological parameters from a joint analysis of the FS, BAO, and Planck data. This sets new bounds on the sum of neutrino masses $\sum m_\nu < 0.14\,\mathrm{eV}$ (at $95\%$ confidence) and the effective number of relativistic degrees of freedom $N_\mathrm{eff} = 2.90^{+0.15}_{-0.16}$, though contours are not appreciably narrowed by the inclusion of BAO data.Comment: 42 pages, 12 figures, accepted by JCAP, likelihoods available at https://github.com/Michalychforever/lss_montepython (minor typo corrected