arXiv subjects

Ricardo G. Rodrigues

Publications and source records attributed to Ricardo G. Rodrigues.

3 recordsLinked to original sources

arXiv2026

Cosmic topology. Part Va. Information content of the observable Universe

If the Universe possesses a compact spatial topology with characteristic scale not much larger than the diameter of the observable Universe, then the associated symmetry transformations imprint specific statistical correlations on density perturbations. We derive the covariance between perturbation modes in the full topology volume and compute the induced covariance between modes in the observable subvolume. We then use this covariance to estimate the available information about topology contained in the full set of observable linear perturbations. For two sample Euclidean examples - the cubic three-torus ($E_1$) and a three-torus with a quarter turn ($E_3$) - the three-dimensional density field carries enough information to detect topology on scales up to 25 percent larger than those accessible from the two-dimensional cosmic microwave background anisotropies alone. Future probes of the cosmic density field using deep galaxy surveys or neutral-hydrogen 21-cm intensity mapping, combined with computationally intensive searches over the large parameter space of admissible topologies, thus offer a plausible avenue to extending the range of detectable cosmic topologies.

astro-ph.CO↗

arXiv2026

Multipolar structure of the local expansion rate from incomplete sky data

Using the Cosmicflows-4 data, we reconstruct the first multipolar moments of a general function describing the local expansion rate. In addition to the conventional harmonic approach, we employ a basis of symmetric and trace-free tensors to characterize the anisotropies of the expansion rate, allowing us to identify all directions associated with each of its multipoles. Focusing on objects in $z\in[0.01,0.05]$ in the CMB rest frame, we derive all $2\ell+1$ degrees of freedom in the multipoles $\ell=1,2$ and 3, which are split into one amplitude and $\ell$ unit vectors per multipole. To mitigate anisotropies induced by incomplete sky coverage, we introduce a pixel-based mask that removes poorly sampled pixels. The full-sky expansion rate is reconstructed using two independent approaches: a pseudo-inverse of the multipole-coupling kernel induced by the mask, and a maximum-likelihood estimate of the underlying full-sky field. These approaches are validated through simulations that explore different mask resolutions, cosmic variance and statistical noise. We find that the quadrupole and octupole amplitudes are consistent (at $95\%$ C.L.) with the expectations of a $Λ$CDM universe with linear and mild nonlinear perturbations, where the anisotropies of the expansion rate result from small peculiar velocities. The dipole amplitude, however, is inconsistent with $Λ$CDM predictions at 3.3$σ$, with a direction $(l, b) = (290^\circ, -4^\circ) \pm 5^\circ$ consistent with a bulk flow. This signal comes predominantly from sources in $z\in[0.03,0.05]$. Finally, we conduct alignment tests between the dipole, quadrupole, and octupole vectors. We confirm recent findings showing that the maxima of these multipoles are approximately located at $(290^\circ,-4^\circ)$. However, detailed tests using the complete vector structure of these multipoles reveal no evidence of alignments.

astro-ph.CO↗

arXiv2025

Fréchet Vectors as sensitive tools for blind tests of CMB anomalies

Cosmological data collected on a sphere, such as CMB anisotropies, are typically represented by the spherical harmonic coefficients, denoted as $a_{\ell m}$. The angular power spectrum, or $C_\ell$, serves as the fundamental estimator of the variance in this data. Alternatively, spherical data and their variance can also be characterized using Multipole Vectors (MVs) and the Fréchet variance. The vectors that minimize this variance, known as Fréchet Vectors (FVs), define the center of mass of points on a compact space, and are excellent indicators of statistical correlations between different multipoles. We demonstrate this using both simulations and real data. Through simulations, we show that FVs enable a blind detection and reconstruction of the location associated with a mock Cold Spot anomaly introduced in an otherwise isotropic sky. Applying these tools to the 2018 Planck maps, we implement several improvements on previous null tests of Gaussianity and statistical isotropy, down to arc-minute scales. Planck's MVs appear consistent with these hypotheses at scales $2 \leq\ell \leq 1500$ when the common mask is applied, whereas the same test using the FVs rejects them with significances between 5.3 and 8.2$σ$. The inclusion of anisotropic noise simulations render the FVs marginally consistent ($\geq 2σ$) with the null hypotheses at the same scales, but still rejects them at $3.5-3.7σ$ when we consider scales above $\ell=1500$, where the signal-to-noise is small. Limitations of the noise and/or foregrounds modeling may account for these deviations from the null hypothesis.

astro-ph.CO↗