Gábor Rácz, László Dobos, Róbert Beck, István Szapudi, István Csabai

According to the general relativistic Birkhoff's theorem, spherically symmetric regions in an isotropic universe behave like mini-universes with their own cosmological parameters. We estimate local expansion rates for a large number of such regions, and use the volume-averaged increment of the scale parameter at each time step in an otherwise standard cosmological $N$-body simulation. The particle mass, corresponding to a coarse graining scale, is an adjustable parameter. This mean field approximation neglects tidal forces and boundary effects, but it is the first step towards a non-perturbative statistical backreaction calculation. We show that a volume-averaged simulation with the $\Omega_m=1$ Einstein--de~Sitter setting in each region closely tracks the expansion and structure growth history of a $\Lambda$CDM cosmology, and confirm the numerical results with analytic calculations as well. The very similar expansion history guarantees consistency with the concordance model and, due to the small but characteristic differences, our model can be distinguished from the standard $\Lambda$CDM model by future precision observations. Furthermore, our model naturally resolves the emerging tension between the local Hubble constant and the Planck best-fitting cosmology.

Stephon Alexander, Sam Cormack

We explore the possibility that fermionic dark matter undergoes a BCS transition to form a superfluid. This requires an attractive interaction between fermions and we describe a possible source of this interaction induced by torsion. We describe the gravitating fermion system with the Bogoliubov-de Gennes formalism in the local density approximation. We solve the Poisson equation along with the equations for the density and gap energy of the fermions to find a self-gravitating, superfluid solution for dark matter halos. In order to produce halos the size of dwarf galaxies, we require a particle mass of $\sim 200\mathrm{eV}$. We find a maximum attractive coupling strength before the halo becomes unstable. If dark matter halos do have a superfluid component, this raises the possibility that they contain vortex lines which may be detectable via gravitational lensing.

Christoph Schmid

We show that Einstein's $R^{\hat{0} \hat{0}}$ equation for nonrelativistic matter and strong gravitational fields is identical with Newton's equation for relative radial acceleration of neighbouring freefalling particles, spherically averaged. These laws are explicitely identical with primary observer's (1) space-time slicing by radial 4-geodesics, (2) radially parallel Local Ortho-Normal Bases, LONBs, (3) Riemann normal 3-coordinates. Hats on indices denote LONBs. General relativity follows from Newton's law of relative acceleration, Einstein's inertial motion, Lorentz covariance, and energy-momentum conservation combined with Bianchi identity. The gravitational field equation of Newton-Gauss and Einstein's $R^{\hat{0} \hat{0}}$ equation are identical and linear in gravitational field for an inertial primary observer.--- Einstein's equivalence between fictitious forces and gravitational forces is formulated as equivalence theorem in the equations of motion. With this, the gravitational field equation of 19th-century Newtonian physics and Einstein's equation for $R^{\hat{0} \hat{0}}$ are identical and bilinear in the gravitational forces for non-inertial primary observers.--- $R^{\hat{0} \hat{0}} = - div \vec{E}_g$ and $2 R^{\hat{i} \hat{0}} = - (curl \vec{B}_g)^{\hat{i}}$ hold exactly for inertial primary observers, if one uses our LONB's. The gravitational $\vec{E}_g, \vec{B}_g $ are measured exactly with quasistatic particles via $(d/dt) p_{\hat{i}}$ and $(d/dt) S_{\hat{i}}$ in correspondence with the electromagnetic $\vec{E}$ and $\vec{B}$. The $(\vec{E}_g, \vec{B}_g)$ are identical with the observer's Ricci connection along his worldline, $(\omega_{\hat{a} \hat{b}})_{\hat{0}}$.

J. W. Moffat

An alternative to the postulate of dark energy required to explain the accelerated expansion of the universe is to adopt an inhomogeneous cosmological model to explain the supernovae data without dark energy. We adopt a void cosmology model, based on the inhomogeneous Lema\^{i}tre-Tolman-Bondi solution of Einstein's field equations. The model can resolve observational anomalies in the $\Lambda CDM$ model, such as the discrepancy between the locally measured value of the Hubble constant, $H_0=73.24\pm 1.74\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$, and the $H_0=66.93\pm 0.62\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ determined by the Planck satellite data and the $\Lambda CDM$ model, and the lithium $^{7}{\rm Li}$ problem, which is a $5\sigma$ mismatch between the theoretical prediction for the $^{7}{\rm Li}$ from big bang nucleosynthesis and the value that we observe locally today at $z=0$. The void model can also resolve the tension between the number of massive clusters derived from the Sunyaev-Zel'dovich effect by the Planck satellite and the number expected from the CMB anisotropies, and the CMB weak lensing anomaly observed in the Planck data. The cosmological Copernican principle and the time and position today coincidence conundrums in the $\Lambda CDM$ and void cosmological models are discussed.