There is growing interest in testing alternative gravity theories using the subtle gravitational redshifts in clusters of galaxies. However, current models all neglect a transverse Doppler redshift of similar magnitude, and some models are not self-c
onsistent. An equilibrium model would fix the gravitational and transverse Doppler velocity shifts to be about 6sigma^2/c and 3sigma^2/2c in order to fit the observed velocity dispersion sigma self-consistently. This result comes from the Virial Theorem for a spherical isotropic cluster, and is insensitive to the theory of gravity. A gravitational redshift signal also does not directly distinguish between the Einsteinian and f(R) gravity theories, because each theory requires different dark halo mass function to keep the clusters in equilibrium. When this constraint is imposed, the gravitational redshift has no sensitivity to theory. Indeed our N-body simulations show that the halo mass function differs in f(R), and that the transverse Doppler effect is stronger than analytically predicted due to non-equilibrium.
We derive a simple analytical expression for the two-body force in a sub-class of MOND-like theories and make testable predictions in the modification to the two-body orbital period, shape, and precession rate, and escape speed etc. We demonstrate th
e applications of the modified Keplers law in the timing of satellite orbits around the Milky Way, and checking the feasibility of MOND in the orbit of Large Magellanic Cloud, the M31 galaxy, and the merging Bullet Clusters. MOND appears to be consistent with satellite orbits although with a tight margin. Our results on two-bodies are also generalized to restricted three-body, many-body problems, rings and shells.
Modern astronomical data on galaxy and cosmological scales have revealed powerfully the existence of certain dark sectors of fundamental physics, i.e., existence of particles and fields outside the standard models and inaccessible by current experime
nts. Various approaches are taken to modify/extend the standard models. Generic theories introduce multiple de-coupled fields A, B, C, each responsible for the effects of DM (cold supersymmetric particles), DE (Dark Energy) effect, and MG (Modified Gravity) effect respectively. Some theories use adopt vanilla combinations like AB, BC, or CA, and assume A, B, C belong to decoupled sectors of physics. MOND-like MG and Cold DM are often taken as opposite frameworks, e.g. in the debate around the Bullet Cluster. Here we argue that these ad hoc divisions of sectors miss important clues from the data. The data actually suggest that the physics of all dark sectors is likely linked together by a self-interacting oscillating field, which governs a chameleon-like dark fluid, appearing as DM, DE and MG in different settings. It is timely to consider an interdisciplinary approach across all semantic boundaries of dark sectors, treating the dark stress as one identity, hence accounts for several coincidences naturally.
First principles study of structural, elastic, and electronic properties of the cubic perovskitetype BaHfO$_3$ has been performed using the plane wave ultrasoft pseudo-potential method based on density functional theory with revised Perdew-Burke-Ernz
erhof exchange-correlation functional of the generalized gradient approximation (GGA-RPBE). The calculated equilibrium lattice constant of this compound is in good agreement with the available experimental and theoretical data reported in the literatures. The independent elastic constants (emph{C}$_{11}$, emph{C}$_{12}$, and emph{C}$_{44}$), bulk modules emph{B} and its pressure derivatives $B^{prime}$, compressibility $beta$, shear modulus emph{G}, Youngs modulus emph{Y}, Poissons ratio $ u$, and Lam{e} constants ($mu, lambda$) are obtained and analyzed in comparison with the available theoretical and experimental data for both the singlecrystalline and polycrystalline BaHfO$_3$. The band structure calculations show that BaHfO$_3$ is a indirect bandgap material (R-$Gamma$ = 3.11 eV) derived basically from the occupied O 2emph{p} and unoccupied Hf 5emph{d} states, and it still awaits experimental confirmation. The density of states (total, site-projected, and emph{l}-decomposed) and the bonding charge density calculations make it clear that the covalent bonds exist between the Hf and O atoms and the ionic bonds exist between the Ba atoms and HfO$_3$ ionic groups in BaHfO$_3$. From our calculations, it is shown that BaHfO$_3$ should be promising as a candidate for synthesis and design of superhard materials due to the covalent bonding between the transition metal Hf 5emph{d} and O 2emph{p} states.
The tight correlation between galaxy bulges and their central black hole masses likely emerges in a phase of rapid collapse and starburst at high redshift, due to the balance of gravity on gas with the feedback force from starbursts and the wind from
the black hole; the average gravity on per unit mass of gas is ~ 2 x 10^-10 m/sec^2 during the star burst phase. This level of gravity could come from the real r^{-1} cusps of Cold Dark Matter (CDM) halos, but the predicted gravity would have a large scatter due to dependence on cosmological parameters and formation histories. Better agreement is found with the gravity from the scalar field in some co-varia
Several rare coincidences of scales in standard particle physics are needed to explain (i) why neutrinos have mass, (ii) why the negative pressure of the cosmological dark energy (DE) coincides with the positive pressure of random motion of dark matt
er (DM) in bright galaxies, (iii) why Dark Matter in galaxies seems to have a finite phase-space density, and to follow the Tully-Fisher-Milgrom relation of galaxy rotation curves. The old idea of self-interacting DM is given a new spin: we propose that the neutrino spin-gravity coupling could lead to a cosmic neutrino dark fluid with a an internal energy density varying as function of the local acceleration of the neutrino fluid with respect the CMB background. We link the Tully-Fisher-Milgrom relation of spiral galaxies (or MOND) with the relativistic pressure of the neutrino dark fluid without modifying Einsteinian gravity.
Empirical theories of Dark Matter like MOND gravity and of Dark Energy like f(R) gravity were motivated by astronomical data. But could these theories be branches rooted from a more general hence natural framework? Here we propose the natural Lagrang
ian of such a framework based on simple dimensional analysis and co-variant symmetry requirements, and explore various outcomes in a top-down fashion. Our framework preserves the co-variant formulation of GR, but allows the expanding physical metric be bent by a single new species of Dark Fluid flowing in space-time. Its non-uniform stress tensor and current vector are simply functions of a vector field of variable norm, resembling the 4-vector electromagnetic potential description for the photon fluid, but is dark (e.g., by very early decoupling from the baryon-radiation fluid). The Dark Fluid framework naturally branches into a continuous spectrum of theories with Dark Energy and Dark Matter effects, including the $f(R)$ gravity, TeVeS-like theories, Einstein-Aether and $ uLambda$ theories as limiting cases. When the vector field degenerates into a pure Higgs-like scalar field, we obtain the physics for inflaton and quintessence. In this broad setting we emphasize the non-constant dynamical field behind the cosmological constant effect, and highlight plausible corrections beyond the classical MOND predictions. Choices of parameters can be made to pass BBN, PPN, and causality constraints. The Dark Fluid is inspired to unify/simplify the astronomically successful ingredients of previous constructions: the desired effects of inflaton plus quintessence plus Cold DM particle fields or MOND-like scalar field(s) are shown largely achievable by one vector field only.
Various TeVeS-inspired and f(R)-inspired theories of gravity have added an interesting twist to the search for dark matter and vacuum energy, modifying the landscape of astrophysics day by day. These theories can be together called a {bf N}on-{bf u}n
iform Dark Energy fluid (a Nu-Lambda fluid or a ${mathbf VLambda}$ fluid); a common thread of these theories, according of an up-to-date summary by HZL cite{Halle}, is a non-uniform vector field, describing an uneven vacuum energy fluid. The so-called alternative gravity theories are in fact in the standard GR gravity framework except that the cosmological constant is replaced by a non-trivial non-uniform vacuum energy, which couples the effects of Dark Matter and Dark Energy together by a single field. Built initially bottom-up rather than top-down as most gravity theories, TeVeS-inspired theories are healthily rooted on empirical facts. Here I attempt a review of some sanity checks of these fast-developing theories from galaxy rotation curves, gravitational lensing and cosmic acceleration. I will also discuss some theoretical aspects of the vacuum energy, and point out some analogies with electromagnetism and the Casimir effect.
We propose a unified single-field description of the galactic Dark Matter and various uniform scalar fields for the inflation and cosmological constant. The two types of effects could originate from a fluid of both spatially and temporally varying Va
cuum Energy if the vacuum has an uneven pressure caused by a photon-like vector field (of perhaps an unstable massive boson). We propose a most general Lagrangian with a {bf N}on-{bf u}niform Cosmological Constant for this vacuum fluid (dubbed as a Nu-Lambda fluid), working within the framework of Einsteinian gravity. This theory includes a continuous spectrum of plausible dark energy theories and gravity theories, e.g., inflation, quintessence, k-essence, f(R), Generalized Einstein-Aether f(K), MOND, TeVeS, BSTV etc. theories. It also suggests new models such as a certain f(K+R) model, which suggests intriguing corrections to MOND depending of redshift and density. Some specific constructions of the Nu-Lambda fluid (e.g., Zhaos V-$Lambda$ model) closely resemble the $Lambda$CDM cosmology on large scale, but fit galaxy rotation curves as good as MOND. Perturbed Einstein Equations in a simple $f(K_4)$ model are solvable and show effects of a DM coupled to DE. Incorporating the perturbation equations here into standard simulations for cosmological structure growth offers a chance to falsify examples of the Nu-Lambda theories.
A rare coincidence of scales in standard particle physics is needed to explain why $Lambda$ or the negative pressure of cosmological dark energy (DE) coincides with the positive pressure $P_0$ of random motion of dark matter (DM) in bright galaxies.
Recently Zlosnik et al. (2007) propose to modify the Einsteinian curvature by adding a non-linear pressure from a medium flowing with a four-velocity vector field $U^mu$. We propose to check whether a smooth extension of GR with a simple kinetic Lagrangian of $U^mu$ can be constructed, and whether the pressure can bend space-time sufficiently to replace the roles of a $w=-1$ DE, $w=0$ Cold DM and heavy neutrinos in explaining anomalous accelerations at all scales. As a specific proof of concept we find a Vector-for-$Lambda$ model (${mathbf VLambda}$-model) and its variants. With essentially {it no free parameters}, these appear broadly consistent with the solar system, gravitational potentials in dwarf spiral galaxies and the bullet cluster of galaxies, early universe with inflation, structure formation and BBN, and late acceleration with a 1:3 ratio of DM:DE.
