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-Lemaître-Robertson-Walker (FLRW) cosmologies as the spacetime metric, and culminates in the successful and highly predictive Λ-Cold-Dark-Matter (ΛCDM) model. Yet, tensions have emerged within the ΛCDM model, most notably a statistically significant discrepancy in the value of the Hubble constant,H₀. Since the notion of cosmic expansion determined by a single parameter is intimately tied to the CP, implications of theH₀tension may extend beyond ΛCDM 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.

Recent Wilkinson Microwave Anisotropy Probe (WMAP) data confirm the cosmic microwave background (CMB) quadrupole anomaly. We further elaborate our previous proposal that the quadrupole power can be naturally suppressed in axis-symmetric universes. In particular, we discuss in greater detail the CMB quadrupole anisotropy and considerably improve our analysis. As a result, we obtain tighter constraints on the direction of the axis of symmetry as well as on the eccentricity at decoupling. We find that the quadrupole amplitude can be brought in accordance with observations with an eccentricity at decoupling of about $0.64\times {10}^{-2}$. Moreover, our determination of the direction of the symmetry axis is in reasonable agreement with recent statistical analyses of cleaned CMB temperature fluctuation maps obtained by means of improved internal linear combination methods as galactic foreground subtraction technique.

The recent 3 yr Wilkinson Microwave Anisotropy Probe data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit $\Lambda$–cold dark matter prediction. We show that by allowing the large-scale spatial geometry of our universe to be plane symmetric with eccentricity at decoupling or order ${10}^{-2}$, the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.

We analyze the magnitude-redshift data of type Ia supernovae included in the Union and Union2 compilations in the framework of an anisotropic Bianchi type I cosmological model and in the presence of a dark-energy fluid with anisotropic equation of state. We find that the amount of deviation from isotropy of the equation of state of dark energy, the skewness $\delta${}, and the present level of anisotropy of the large-scale geometry of the Universe, the actual shear $\Sigma${}0, are constrained in the ranges -0.16$\lesssim${}$\delta${}$\lesssim${}0.12 and -0.012$\lesssim${}$\Sigma${}0$\lesssim${}0.012 (1$\sigma${} C.L.) by Union2 data. Supernova data are then compatible with a standard isotropic universe ($\delta${}=$\Sigma${}0=0), but a large level of anisotropy, both in the geometry of the Universe and in the equation of state of dark energy, is allowed.

We determine the (pseudo)critical lines of QCD with two degenerate staggered fermions at nonzero temperature and quark or isospin density, in the region of imaginary chemical potentials; analytic continuation is then used to prolongate to the region of real chemical potentials. We obtain an accurate determination of the curvatures at zero chemical potential, quantifying the deviation between the case of finite quark and of finite isospin chemical potential. Deviations from a quadratic dependence of the pseudocritical lines on the chemical potential are clearly seen in both cases: we try different extrapolations and, for the case of nonzero isospin chemical potential, confront them with the results of direct Monte~Carlo simulations. Finally we find that, as for the finite quark density case, an imaginary isospin chemical potential can strengthen the transition until turning it into strong first order.

We determine the continuum limit of the curvature of the pseudocritical line of QCD with $n_f=2+1$ staggered fermions at nonzero temperature and quark density. We perform Monte Carlo simulations at imaginary baryon chemical potentials with Highly Improved Staggered Quarks (HISQ), adopting the HISQ/tree action discretization as implemented in the code by the MILC Collaboration. Couplings are adjusted so as to move on a line of constant physics, as determined in Ref. [1], with the strange quark mass $m_s$ fixed at its physical value and a light-to-strange mass ratio $m_l/m_s=1/20$. The chemical potential is set at the same value for the three quark species, ${\mu }_l={\mu }_s\equiv \mu$. We attempt an extrapolation to the continuum using the results on lattices with temporal size up to $L_t=12$. Our estimate for the continuum value of the curvature $\kappa$ at zero baryon density, $\kappa =0.020(4)$, is compared with recent lattice results and with experimental determinations of the freeze-out curve.