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.

Local determinations of the Hubble constant $H_0$ favor a higher value than Planck based on cosmic microwave background and $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$). Through a model-independent expansion, we show that low redshift ($z\lesssim 0.7$) data comprising baryon acoustic oscillations, cosmic chronometers, and Type Ia supernovae have a preference for quintessence models that lower $H_0$ relative to $\mathrm{\Lambda }\mathrm{CDM}$. In addition, we confirm that an exponential coupling to dark matter cannot alter this conclusion in the same redshift range. Our results leave open the possibility that a coupling in the matter-dominated epoch, potentially even in the dark ages, may yet save $H_0$ from sinking in the string theory swampland.

The tension between early and late Universe probes of the Hubble constant has motivated various new FLRW cosmologies. Here, we reanalyse the Hubble tension with a recent age of the Universe constraint. This allows us to restrict attention to matter and a dark energy sector that we treat without assuming a specific model. Assuming analyticity of the Hubble parameter H ( z ), and a generic low redshift modification to flat ΛCDM, we find that low redshift data ( z ≲ 2.5) and well-motivated priors only permit a dark energy sector close to the cosmological constant Λ. This restriction rules out late Universe modifications within FLRW. We show that early Universe physics that alters the sound horizon can yield an upper limit of H ₀ ∼ 71 ± 1 km s ⁻¹ Mpc ⁻¹ . Since various local determinations may be converging to H ₀ ∼ 73 km s ⁻¹ Mpc ⁻¹ , a breakdown of the FLRW framework is a plausible resolution. We outline how future data, in particular strongly lensed quasar data, could also provide further confirmations of such a resolution.

Hubble tension is routinely presented as a mismatch between the Hubble constant $H_0$ determined locally and a value inferred from the flat $\mathrm{\Lambda }\mathrm{CDM}$ cosmology. In essence, the tension boils down to a disagreement between two numbers. Here, assuming the tension is cosmological in origin, we predict that within flat $\mathrm{\Lambda }\mathrm{CDM}$ there should be other inferred values of $H_0$, and that a “running of $H_0$ with redshift” can be expected. These additional determinations of $H_0$ may be traced to a difference between the effective equation of state (EoS) of the Universe within the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology framework and the current standard model. We introduce a diagnostic that flags such a running of $H_0$.

We consider a low redshift ($z<0.7$) cosmological data set comprising megamasers, cosmic chronometers, type Ia supernovae and baryon acoustic oscillations, which we bin according to their redshift. For each bin, we read the value of $H_0$ by fitting directly to the flat $\mathrm{\Lambda }\mathrm{CDM}$ model. Doing so, we find that $H_0$ descends with redshift, allowing one to fit a line with a nonzero slope of statistical significance $2.1\sigma$. Our analysis rests on the use of cosmic chronometers to break a degeneracy in baryon acoustic oscillations data and it will be imperative to revisit this feature as data improves. Nevertheless, our results provide the first independent indication of the descending trend reported by the H0LiCOW Collaboration. If substantiated going forward, early Universe solutions to the Hubble tension will struggle explaining this trend.

We present an analytic solution of a charged black hole with hyperscaling violating factor in an Einstein-Maxwell-Dilaton model where the scalar potential is key to the existence of a solution. This solution provides a candidate gravitational description of theories with hyperscaling violation at both finite temperature and finite charge density. Using this background we explore certain features of these theories via AdS/CFT correspondence. Finally, we discuss embeddings based on the well-known sphere reductions of ten and eleven-dimensional supergravity.