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Optimal extraction of cosmological information from observations of the Cosmic Microwave Background critically relies on our ability to accurately undo the distortions caused by weak gravitational lensing. In this work, we demonstrate the use of denoising diffusion models in performing Bayesian lensing reconstruction. We show that score-based generative models can produce accurate, uncorrelated samples from the CMB lensing convergence map posterior, given noisy CMB observations. To validate our approach, we compare the samples of our model to those obtained using established Hamiltonian Monte Carlo methods, which assume a Gaussian lensing potential. We then go beyond this assumption of Gaussianity, and train and validate our model on non-Gaussian lensing data, obtained by ray-tracing N-body simulations. We demonstrate that in this case, samples from our model have accurate non-Gaussian statistics beyond the power spectrum. The method provides an avenue towards more efficient and accurate lensing reconstruction, that does not rely on an approximate analytic description of the posterior probability. The reconstructed lensing maps can be used as an unbiased tracer of the matter distribution, and to improve delensing of the CMB, resulting in more precise cosmological parameter inference., Comment: 12 pages, 10 figures. v2: typo in one of the equations fixed, references added

By measuring, modeling and interpreting cosmological datasets, one can place strong constraints on models of the Universe. Central to this effort are summary statistics such as power spectra and bispectra, which condense the high-dimensional dataset into low-dimensional representations. In this work, we introduce a modern set of estimators for computing such statistics from three-dimensional clustering data, and provide a flexible Python implementation; PolyBin3D. Working in a maximum-likelihood formalism, we derive general estimators for the two- and three-point functions, which yield unbiased spectra regardless of the survey mask, weighting scheme, and presence of holes in the window function. These can be directly compared to theory without the need for mask-convolution. Furthermore, we present a numerical scheme for computing the optimal (minimum-variance) estimators for a given survey, which is shown to reduce error-bars on large-scales. Our Python package includes both general "unwindowed'' estimators and idealized equivalents (appropriate for simulations), each of which are efficiently implemented using fast Fourier transforms and Monte Carlo summation tricks, and additionally supports GPU acceleration. These are extensively validated in this work, with Monte Carlo convergence (relevant for masked data) achieved using only a small number of iterations (typically $<10$ for bispectra). This will allow for fast and unified measurement of two- and three-point functions from current and upcoming survey data., Comment: 32 pages, 8 figures, submitted to Phys. Rev. D. Code available at https://github.com/oliverphilcox/PolyBin3D

As a counterpart to the four-fermion interaction, which describes massive vector exchange at low energies, we investigate the low energy effective action of photons under exchange of a massive graviton. We show how integrating out a massive graviton leads to the most general duality-invariant vector interactions in 4D or, vice versa, how any such interactions have a natural interpretation within massive gravity. Moreover, we demonstrate how the special case of Born-Infeld theory arises from arguably the simplest graviton potential within ghost-free dRGT massive gravity., Comment: 7 pages. v2 matches version accepted for JHEP

The 21-cm brightness temperature fluctuation from the Dark Ages ($z \simeq 30-100$) will allow us to probe the inflationary epoch on very small scales ($>0.1 \, \mbox{Mpc}^{-1}$), inaccessible to cosmic microwave background experiments. Combined with the possibility to collect information from different redshift slices, the 21-cm bispectrum has the potential to significantly improve constraints on primordial non-Gaussianity. However, recent work has shown secondary effects source off-diagonal terms in the covariance matrix which can significantly affect forecasted constraints, especially in signals that peak in the squeezed configuration, such as the local bispectrum. In this paper we propose the three-point $\langle 21-21-\rm CMB \rangle$ bispectrum cross-correlation as a new independent observational channel sensitive to local primordial non-Gaussianity. We find that, contrary to the 21-cm bispectrum, secondary contributions are subdominant to the primordial signal for values $f_{\rm NL}^{\rm loc} \sim 1$, resulting in negligible effects from off-diagonal terms in the covariance matrix. We forecast that CMB $T$ and $E$ modes cross-correlated with an ideal cosmic variance-limited 21-cm experiment with a $0.1$ MHz frequency and $0.1$ arc-minute angular resolution could reach $f_{\rm NL}^{\rm loc} \sim 6 \times 10^{-3}$. This forecast suggests cross-correlation between CMB and 21-cm experiments could provide a viable alternative to 21-cm auto-spectra in reaching unprecedented constraints on primordial local non-Gaussianities., Comment: 38 pages, 14 figures, code available at https://github.com/GiorgioOrlando/21cm_CMB_cross

We study the use of U-Nets in reconstructing the linear dark matter density field and its consequences for constraining cosmological parameters, in particular primordial non-Gaussianity. Our network is able to reconstruct the initial conditions of redshift $z=0$ density fields from N-body simulations with $90\%$ accuracy out to $k \leq 0.4$ h/Mpc, competitive with state-of-the-art reconstruction algorithms at a fraction of the computational cost. We study the information content of the reconstructed $z=0$ density field with a Fisher analysis using the QUIJOTE simulation suite, including non-Gaussian initial conditions. Combining the pre- and post-reconstructed power spectrum and bispectrum data up to $k_{\rm max} = 0.52$ h/Mpc, we find significant improvements on all parameters. Most notably, we find a factor $3.65$ (local), $3.54$ (equilateral) and $2.90$ (orthogonal) improvement on the marginalized errors of $f_{\rm NL}$ as compared to only using the pre-reconstructed data. We show that these improvements can be attributed to a combination of reduced data covariance and parameter degeneracy. The results constitute an important step towards more optimal inference of primordial non-Gaussianity from non-linear scales., Comment: 22 pages, 8 figures, 3 tables, codes available at https://github.com/tsfloss/URecon and https://github.com/tsfloss/DensityFieldTools. v2 matches version accepted for JCAP

In the pursuit of primordial non-Gaussianities, we hope to access smaller scales across larger comoving volumes. At low redshift, the search for primordial non-Gaussianities is hindered by gravitational collapse, to which we often associate a scale $k_{\rm NL}$. Beyond these scales, it will be hard to reconstruct the modes sensitive to the primordial distribution. When forecasting future constraints on the amplitude of primordial non-Gaussianity, $f_{\rm NL}$, off-diagonal components are usually neglected in the covariance because these are small compared to the diagonal. We show that the induced non-Gaussian off-diagonal components in the covariance degrade forecast constraints on primordial non-Gaussianity, even when all modes are well within what is usually considered the linear regime. As a testing ground, we examine the effects of these off-diagonal components on the constraining power of the matter bispectrum on $f_{\rm NL}$ as a function of $k_{\rm max}$ and redshift, confirming our results against N-body simulations out to redshift $z=10$. We then consider these effects on the hydrogen bispectrum as observed from a PUMA-like 21-cm intensity mapping survey at redshifts $2

We investigate tomography of 21-cm brightness temperature fluctuations during the Dark Ages as a probe for constraining primordial non-Gaussianity. We expand the 21- cm brightness temperature up to cubic order in perturbation theory and improve previous models of the signal by including the effect of the free electron fraction. Using modified standard perturbation theory methods that include baryonic pressure effects we derive an improved secondary bispectrum and for the first time derive the secondary trispectrum of 21-cm brightness temperature fluctuations. We then forecast the amount of information available from the Dark Ages to constrain primordial non-Gaussianity, including the imprints of massive particle exchange during inflation and we determine how much signal is lost due to secondary non-Gaussianity. We find that although secondary non-Gaussianity swamps the primordial signal, primordial non-Gaussianity can still be extracted with signal-to-noise ratios that surpass current and future CMB experiments by several orders of magnitude, depending on the experimental setup. Furthermore, we conclude that for the bi- and trispectra of massive particle exchange marginalizing over other primordial shapes affects signal-to-noise ratios more severely than secondary shapes. Baryonic pressure effects turn out to have a negligible impact on our forecasts, even at scales close to the Jeans scale. The results of this work reinforce the prospects of 21-cm brightness temperature fluctuations from the Dark Ages as the ultimate probe for primordial non-Gaussianity., Comment: 47 pages, 20 figures, code available at https://github.com/tsfloss/21-cm-Dark-Ages-Fisher-Forecast. v2: minor typos corrected. v3: matches published version