We present the results of a novel type of numerical simulation that realizes a rotating Universe with a shear-free, rigid body rotation inspired by a Gödel-like metric. We run cosmological simulations of unperturbed glasses with various degrees of rotation in the Einstein-de Sitter and the ΛCDM cosmologies. To achieve this, we use the StePS N-body code capable of simulating the infinite Universe, overcoming the technical obstacles of classical toroidal (periodic) topologies that would otherwise prevent us from running such simulations. Results show a clear anisotropy between the polar and equatorial expansion rates with more than 1% deviation from the isotropic case for maximal rotation without closed timeline curves within the horizon, ω0≈10−3 Gyr−1; a considerable effect in the era of precision cosmology.
We establish that regular black holes can form from gravitational collapse. Our model builds on a recent construction that realized regular black holes as exact solutions to purely gravitational theories that incorporate an infinite tower of higher curvature corrections in any dimension D≥5 [arXiv:2403.04827]. We identify a two-dimensional Horndeski theory that captures the spherically symmetric dynamics of the theories in question and use this to prove a Birkhoff theorem and obtain the generalized Israel junction conditions. Armed with these tools, we consider the collapse of thin shells of pressureless matter, showing that this leads generically to the formation of regular black holes. The interior dynamics we uncover is intricate, consisting of shell bounces and white hole explosions into a new universe. The result is that regular black holes are the unique spherically symmetric solutions of the corresponding theories and also the endpoint of gravitational collapse of matter. Along the way, we establish evidence for a solution-independent upper bound on the curvature, suggestive of Markov's limiting curvature hypothesis.
We develop a quantum theory of inflaton and its decay product of various gauge boson pairs to investigate the preheating towards thermalized universe. The inflaton decay into gauge-boson pairs is shown to be inevitably accompanied by tachyon-mass-like correction to inflation potential that ultimately leads to an inflaton escape out of trapped local potential minimum towards the field infinity. This gives rise to a conversion mechanism of early inflationary acceleration to a quintessence dark energy acceleration at late stages of cosmic evolution. The success of the escape depends on how standard particles are incorporated into a scheme of extended Jordan-Brans-Dicke gravity. New types of super-radiance mechanism that enhance the ending of preheating are identified and compared with the Dicke model.
We study the eigenmodes of the spin-2 Laplacian in orientable Euclidean manifolds and their implications for the tensor-induced part of the cosmic microwave background (CMB) temperature and polarization anisotropies. We provide analytic expressions for the correlation matrices of Fourier-mode amplitudes and of spherical harmonic coefficients. We demonstrate that non-trivial spatial topology alters the statistical properties of CMB tensor anisotropies, inducing correlations between harmonic coefficients of differing ℓ and m and across every possible pair of temperature and E- and B-modes of polarization. This includes normally forbidden TB and EB correlations. We compute the Kullback-Leibler (KL) divergence between the pure tensor-induced CMB fluctuations in the usual infinite covering space and those in each of the non-trivial manifolds under consideration, varying both the size of the manifolds and the location of the observer. We find that the amount of information about the topology of the Universe contained in tensor-induced anisotropies does not saturate as fast as its scalar counterpart; indeed, the KL divergence continues to grow with the inclusion of higher multipoles up to the largest ℓ we have computed. Our results suggest that CMB polarization measurements from upcoming experiments can provide new avenues for detecting signatures of cosmic topology, motivating a full analysis where scalar and tensor perturbations are combined and noise is included.