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A simple and natural extension of the standard $\Lambda$CDM model is to allow relic neutrinos to have non-zero degeneracy. We confront this $\Lambda$CDM$\xi$ model, $\Lambda$CDM with neutrino mass $M_\nu$ and degeneracy $\xi_3$ as additional parameters, with the \textit{Planck} TT, lowT, plik--lensing, BAO, and DES datasets, and we observe a strong preference (Bayes factor $\log_{10}B=1.9$) for it over the standard $\Lambda$CDM model. Both the $H_0$ and $S_8$ tensions are resolved to within 1$\sigma$ with the same set of neutrino parameters, along with 3$\sigma$ evidence for nonzero neutrino mass ($M_\nu=0.58^{+0.17}_{-0.13}\ \mathrm{eV}$) and degeneracy ($\xi_3=1.27^{+0.42}_{-0.22}$). Furthermore, our analysis favors the scalar index $n_s$ to be slightly larger than 1, compatible with some hybrid inflation models, as well as a significantly larger optical depth $\tau$ than the standard Planck value, indicating an earlier onset of reionization., Comment: 11 pages, 4 main + 2 appendix figures

Neutrinos are believed to be the most abundant fermions in the Universe, but their masses are unknown, except for being non-zero but much smaller than other fermions. Cosmological relic neutrinos could also have non-zero chemical potentials (or asymmetries). Using neutrino-involved N-body simulations, we investigate the neutrino effects on the matter pairwise velocity, which itself is an interesting probe of cosmology. We find that for light-halo ($[10^{11},10^{13}]\ M_\odot$) mean pairwise velocity, in the transition range ($[4,15]\ \mathrm{Mpc}$), the effects of neutrino masses overwhelm the effects of neutrino asymmetries, while in the two-halo-group range ($[25,50]\ \mathrm{Mpc}$), for both light and heavy haloes ($[10^{13},10^{15}]\ M_\odot$), the effects of neutrino asymmetries dominate, making it possible to disentangle the two effects. We provide fitting formulae to quantify the effects of neutrino mass and asymmetry on halo-halo pairwise velocities., Comment: 15 pages, 4 main + 3 appendix figures, accepted for publication in MNRAS

The Cosmological Principle (CP) -- the notion that the Universe is spatially isotropic and homogeneous on large scales -- underlies a century of progress in cosmology. It is conventionally formulated through the Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies as the spacetime metric, and culminates in the successful and highly predictive $\Lambda$-Cold-Dark-Matter ($\Lambda$CDM) model. Yet, tensions have emerged within the $\Lambda$CDM model, most notably a statistically significant discrepancy in the value of the Hubble constant, $H_0$. Since the notion of cosmic expansion determined by a single parameter is intimately tied to the CP, implications of the $H_0$ tension may extend beyond $\Lambda$CDM to the CP itself. This review surveys current observational hints for deviations from the expectations of the CP, highlighting synergies and disagreements that warrant further study. Setting aside the debate about individual large structures, potential deviations from the CP include variations of cosmological parameters on the sky, discrepancies in the cosmic dipoles, and mysterious alignments in quasar polarizations and galaxy spins. While it is possible that a host of observational systematics are impacting results, it is equally plausible that precision cosmology may have outgrown the FLRW paradigm, an extremely pragmatic but non-fundamental symmetry assumption., Comment: extended contents and references, 73 pages (excluding references), 30 figures, version accepted for publication in Class. Quant. Grav. "Focus issue on the Hubble constant tension"

Recent observations suggest that there are violations of the isotropy of the universe at large scales, an important part of the cosmological principle. In this paper, we use the Cosmic Microwave Background (CMB) data to search for spatial variations of the cosmological parameters in the $\Lambda\mathrm{CDM}$ model. We fit the Planck temperature angular power spectrum $\mathcal{C}^{TT}_\ell$ for 48 different half-skies, centering on 48 different directions, to search for directional dependences of the standard cosmological parameters. There are $3(2)\sigma$-level directional variations in $\Omega_bh^2$, $\Omega_ch^2$, $n_s$, $100\theta_\mathrm{MC}$, and $H_0$ $(\tau$ and $\ln(10^{10}A_s))$. Furthermore, the directional distributions of the parameters follow a dipole form to good approximation. The Bayes factor between the isotropic and anisotropic hypotheses is $0.0041$, strongly disfavouring the former. The best-fit dipole axes for $\Omega_bh^2$, $\Omega_ch^2$, $n_s$, $100\theta_\mathrm{MC}$, and $A_s e^{-2\tau}$ all generally align with the mean direction of $\boldsymbol{V} \equiv (b = -5.6^{+17.0{\circ}}_{-17.4}, l = 48.8^{+14.3{\circ}}_{-14.4})$, which is roughly perpendicular to the dipole of the variation in fine structure constant, and is about $45^{\circ}$ to the directions of the CMB kinematic dipole, CMB parity asymmetry, and polarization of QSOs. Our results suggest either significant violation of the cosmological principle, or previously unknown systematic errors in the standard CMB analysis., Comment: 18 pages, 7 figures, accepted to Phys. Rev. D

In the standard $\Lambda$CDM model, neutrinos are treated as radiation, with their masses and possible degeneracy ignored. In this paper, we compute the impact of a finite relic neutrino degeneracy $\xi$ on the CMB angular power spectra, and obtain constraints on $\xi$ using current cosmological data sets. We find that $\xi \approx O(1)$ is still allowed. We also study the correlations between $\xi$, the Hubble parameter $H_0$, and the spectral index $n_s$. Due to these correlations, the CMB constraints on inflation models are loosened when $\xi$ is fitted together with other cosmological parameters, such that some models excluded at 95% confidence level by standard fittings without $\xi$ could be revived. Furthermore, the tension in CMB and local measurements of $H_0$ is slightly alleviated. Our results suggest that $\xi$ is a non-negligible physical parameter for cosmological analyses., Comment: 21 pages, 10 figures; minor changes to match the published JCAP version

Light but massive cosmological neutrinos do not cluster significantly on small scales, due to their high thermal velocities. With finite masses, cosmological neutrinos become part of the total matter field and contribute to its smoothing. Structure formation in the presence of massive neutrinos is therefore impeded compared to that in the standard $\Lambda$CDM cosmology with massless neutrinos. Neutrinos' masses also distort the anisotropy power spectrum of cosmic microwave background (CMB). Furthermore, a finite chemical potential $\mu$ for cosmological neutrinos, still allowed by current data, would have a non-negligible impact on CMB and structure formation. We consistently evaluate effects of neutrino masses and chemical potentials on the matter power spectrum by use of a neutrino-involved N-body simulation, with cosmological parameters obtained from a Markov-Chian Moonte-Carlo (MCMC) refitting of CMB data. Our results show that while a finite averaged neutrino mass $m_\nu$ tends to suppress the matter power spectrum in a range of wave numbers, the neutrino degeneracy parameters ${\xi_i \equiv \mu_i /T}$ ($i=$1, 2, 3) enhance the latter, leading to a large parameter degeneracy between $m_\nu$ and $\xi_i$. We provide an empirical formula for the effects on the matter power spectrum in a selected range of wave numbers induced by $m_\nu$ and $\eta \equiv \sqrt{\sum_i \xi^2_i}$. Observing a strong correlation between $m_\nu$ and $\eta$, we propose a single redshift-independent parameter $m_\nu - \frac{4}{3}\eta^2$ to characterize the neutrino effects on the matter power spectrum., Comment: 31 pages, 17 figures, matched the JCAP published version

The clustering amplitude of 7143 clusters from the Sloan Digital Sky Survey (SDSS) is found to increase with cluster mass, closely agreeing with the Gaussian random field hypothesis for structure formation. The amplitude of the observed cluster correlation exceeds the predictions from pure cold dark matter (CDM) simulation by $\simeq 6\%$ for the standard Planck-based values of the cosmological parameters. We show that this excess can be naturally accounted for by free streaming of light neutrinos, which opposes gravitational growth, so clusters formed at fixed mass are fewer and hence more biased than for a pure CDM density field. An enhancement of the cluster bias by 7\% matches the observations, corresponding to a total neutrino mass, $m_{\nu} = 0.119 \pm 0.034$ eV at 67\% confidence level, for the standard relic neutrino density. If ongoing laboratory experiments favor a normal neutrino mass hierarchy then we may infer a somewhat larger total mass than the minimum oscillation based value, $\sum m_{\nu} \simeq 0.056eV$, with 90\% confidence. Much higher precision can be achieved by applying our method to a larger sample of more distant clusters with weak lensing derived masses., Comment: 7 pages, 3 figures, Major improvement: Simulations results and MCMC analysis added