Dipole Cosmology: Revisiting Our Universe with a Flow

Abstract

In this thesis, we explore an ansatz alternative to the FLRW classes of spacetimes for our Universe, in light of observations that exhibit anisotropies at late times. Despite the existence of these anisotropies beyond the scope of the ΛCDM model remain under debate, we study the possibility of the existence of a global dynamical flow in our Universe. We introduce a dynamical flow into our cosmological model in a systematic manner, guided by the Copernican principle, which asserts that we do not occupy a special or preferred position in the Universe. Observations from the CMB and large-scale structure (LSS) indicate that the Universe evolves with time. The FLRW class of spacetimes emerges from imposing maximal spatial symmetry on constant-time hypersurfaces, consistent with this observation. In our context, we have an additional prior that the Universe has a global flow in the matter sector. It is intuitively plausible that if there is a flow and therefore a preferred spatial direction, the isotropy group can at most be U(1) – the group of axial rotations around the flow direction. Furthermore, this leads us to the Locally Rotationally symmetric (L.R.S) tilted Bianchi models. We looked at its solution space for different classes of Equations of State (EoS) parameters. We specifically showed that for a class of dynamical EoS, referred to as the flowing dark energy, the geometry asymptotes to FLRW classes of spacetimes, whereas the anisotropy in the matter sector can increase for a robust set of initial conditions. The CMB exhibits a high degree of isotropy and homogeneity at the time of recombination, despite some evidence for large-scale anomalies reported by WMAP and Planck. Motivated by this, we investigate whether a very small matter anisotropy present in the early Universe can evolve into a sizeable bulk flow at late times. We find that even in presence of a cosmological constant (Λ) the anisotropies associated with matter flow induce only small backreactions on the background geometry, thereby keeping the shear evolution consistent with Wald’s cosmic no-hair theorem. Notably, we observe that flow instabilities can arise even in backgrounds that are nearly FLRW, which may have important physical implications. A small tilt perturbation introduced during cosmic evolution can result in a significant bulk flow or an enhanced cosmic dipole. Such a scenario would suggest that the dipole observed in the sky may not arise solely from our local motion, but could instead be a manifestation of a large-scale, global flow between us and the CMB rest frame or other cosmological sources Since these sources lie at different redshifts, the corresponding dipole signatures need not be identical, offering a potential explanation for observed dipole anomalies across different datasets. Our realistic Universe is composed primarily of matter and radiation, each playing a distinct role in its evolution. To make our paradigm more physically relevant, we extend our analysis by introducing multiple fluid components into the system—specifically, radiation and matter—each with its own independent dynamical flow. To capture realistic cosmological conditions, we define a class of models referred to as dipole ΛCDM models, where the boundary conditions are chosen such that a suitably defined notion of dimensionless energy densities for matter and radiation match the present-day Planck values of Ωm,0 and Ωr,0. Within this framework, we explore the evolution of the relative velocity (or “tilt") between the two fluids and find that it can grow significantly over time for a broad and robust set of initial conditions. This dynamical growth of relative flow can contribute to a non-kinematical component of the observed CMB dipole, suggesting that part of the dipole may originate from large-scale structure or global flow patterns, rather than purely from our peculiar motion with respect to the CMB rest frame due to our local inhomogeneity. We further investigate the behaviour of both single- and multi-fluid systems in the asymptotic regime near the initial cosmological singularity. Unlike the FLRW spacetimes, where the singularity is point-like, our anisotropic background geometry admits a richer singularity structure. In particular, we observe the emergence of pancake- and filament-type singularities arising due to anisotropic collapse along specific spatial directions. These singularities reflect the influence of shear and flow anisotropies on the early-time dynamics of the spacetime. In the context of the dipole ΛCDM model incorporating matter and radiation, we extend this analysis to show how the presence of multiple fluids and their respective flow fields influence the nature of the singularity. We demonstrate that different classes of singularities correspond to distinct asymptotic behaviour of key dynamical quantities such as expansion rates, tilt velocities, and anisotropic stresses. This classification provides deeper insight into how initial conditions and fluid interactions shape the global structure of the early Universe within non-FLRW frameworks.