Physics of dark energy particles

We consider the astrophysical and cosmological implications of the existence of a minimum density and mass due to the presence of the cosmological constant. If there is a minimum length in nature, then there is an absolute minimum mass corresponding to a hypothetical particle with radius of the order of the Planck length. On the other hand, quantum mechanical considerations suggest a different minimum mass. These particles associated with the dark energy can be interpreted as the ``quanta'' of the cosmological constant. We study the possibility that these particles can form stable stellar-type configurations through gravitational condensation, and their Jeans and Chandrasekhar masses are estimated. From the requirement of the energetic stability of the minimum density configuration on a macroscopic scale one obtains a mass of the order of 10^55 g, of the same order of magnitude as the mass of the universe. This mass can also be interpreted as the Jeans mass of the dark energy fluid. Furthermore we present a representation of the cosmological constant and of the total mass of the universe in terms of `classical' fundamental constants.Comment: 10 pages, no figures; typos corrected, 4 references added; 1 reference added; reference added; entirely revised version, contains new parts, now 14 page

Zero Energy of Plane-Waves for ELKOs

We consider the ELKO field in interaction through contorsion with its own spin density, and we investigate the form of the consequent autointeractions; to do so we take into account the high-density limit and find plane wave solutions: such plane waves give rise to contorsional autointeractions for which the Ricci metric curvature vanishes and therefore the energy density is equal to zero identically. Consequences are discussed.Comment: 7 page

Spin Fluids in Homogeneous and Isotropic Space-times

We consider a Weyssenhoff fluid assuming that the space-time is homogeneous and isotropic, therefore being relevant for cosmological considerations of gravity theories with torsion. It is explicitly shown that theWeyssenhoff fluids obeying the Frenkel condition or the Papapetrou–Corinaldesi condition are incompatible with the cosmological principle which restricts the torsion tensor to have only the vector and axial vector components. Moreover, it turns out that the Weyssenhoff fluid obeying the Tulczyjew condition is also incompatible with the cosmological principle. This condition has not been analyzed so far in this context. Based on this result, we propose to reconsider a number of previous works that analyzed cosmological solutions of the Einstein–Cartan theory, since their spin fluids did not obey usually the cosmological principle.Розглянуто рiдину Вiссенхофа у припущеннi, що простiр-час є однорiдним та iзотропним i тому придатний для космологiчного розгляду теорiй гравiтацiї з крученням. Показано, що рiдини Вiссенхофа, для яких виконується умова Френкеля або умова Папапетроу–Корiналдезi, є несумiсними з космологiчним принципом, згiдно з яким тензор кручення має тiльки векторну i аксiальну векторну компоненти. Бiльше того, виявилося, що рiдина Вiссенхофа, що задовольняє умову Тульчiєва, також несумiсна з космологiчним принципом. Але цю умову не було проаналiзовано повнiстю в цьому контекстi. Ґрунтуючись на цих результатах, запропоновано переглянути деякi попереднi роботи, в яких проаналiзовано космологiчнi розв’язки теорiї Ейнштейна–Картана, оскiльки їхнi спiновi рiдини звичайно не задовольняють космологiчний принцип

Minimum mass-radius ratio for charged gravitational objects

We rigorously prove that for compact charged general relativistic objects there is a lower bound for the mass-radius ratio. This result follows from the same Buchdahl type inequality for charged objects, which has been extensively used for the proof of the existence of an upper bound for the mass-radius ratio. The effect of the vacuum energy (a cosmological constant) on the minimum mass is also taken into account. Several bounds on the total charge, mass and the vacuum energy for compact charged objects are obtained from the study of the Ricci scalar invariants. The total energy (including the gravitational one) and the stability of the objects with minimum mass-radius ratio is also considered, leading to a representation of the mass and radius of the charged objects with minimum mass-radius ratio in terms of the charge and vacuum energy only.Comment: 19 pages, accepted by GRG, references corrected and adde

Galactic cold dark matter as a Bose-Einstein condensate of WISPs

We propose here the dark matter content of galaxies as a cold bosonic fluid composed of Weakly Interacting Slim Particles (WISPs), represented by spin-0 axion-like particles and spin-1 hidden bosons, thermalized in the Bose-Einstein condensation state and bounded by their self-gravitational potential. We analyze two zero-momentum configurations: the polar phases in which spin alignment of two neighbouring particles is anti-parallel and the ferromagnetic phases in which every particle spin is aligned in the same direction. Using the mean field approximation we derive the Gross-Pitaevskii equations for both cases, and, supposing the dark matter to be a polytropic fluid, we describe the particles density profile as Thomas-Fermi distributions characterized by the halo radii and in terms of the scattering lengths and mass of each particle. By comparing this model with data obtained from 42 spiral galaxies and 19 Low Surface Brightness (LSB) galaxies, we constrain the dark matter particle mass to the range $10^{-6}-10^{-4} eV$ and we find the lower bound for the scattering length to be of the order $10^{-14} fm$.Comment: 13 pages; 6 figures; references added; v.3: typo corrected in the abstract, published in JCA

A few provoking relations between dark energy, dark matter and pions

I present three relations, striking in their simplicity and fundamental appearance. The first one connects the Compton wavelength of a pion and the dark energy density of the Universe; the second one connects Compton wavelength of a pion and the mass distribution of non-baryonic dark matter in a Galaxy; the third one relates mass of a pion to fundamental physical constants and cosmological parameters. All these relations are in excellent numerical agreement with observations

Torsion, an alternative to dark matter?

We confront Einstein-Cartan's theory with the Hubble diagram. An affirmative answer to the question in the title is compatible with today's supernovae data.Comment: 14 pp, 3 figures. Version 2 matches the version published in Gen. Rel. Grav., references added. Version 3 corrects a factor 3 in Cartan's equations to become

Sharp bounds on the critical stability radius for relativistic charged spheres

In a recent paper by Giuliani and Rothman \cite{GR}, the problem of finding a lower bound on the radius $R$ of a charged sphere with mass M and charge Q<M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M\leq 4R/9, has been found. In this paper we derive the surprisingly transparent inequality $$\sqrt{M}\leq\frac{\sqrt{R}}{3}+\sqrt{\frac{R}{9}+\frac{Q^2}{3R}}.$$ The inequality is shown to hold for any solution which satisfies $p+2p_T\leq\rho,$ where $p\geq 0$ and $p_T$ are the radial- and tangential pressures respectively and $\rho\geq 0$ is the energy density. In addition we show that the inequality is sharp, in particular we show that sharpness is attained by infinitely thin shell solutions.Comment: 20 pages, 1 figur

Stability of the Einstein static universe in IR modified Ho\v{r}ava gravity

Recently, Horava proposed a power counting renormalizable theory for (3+1)-dimensional quantum gravity, which reduces to Einstein gravity with a non-vanishing cosmological constant in IR, but possesses improved UV behaviors. In this work, we analyze the stability of the Einstein static universe by considering linear homogeneous perturbations in the context of an IR modification of Horava gravity, which implies a `soft' breaking of the `detailed balance' condition. The stability regions of the Einstein static universe are parameterized by the linear equation of state parameter w=p/\rho and the parameters appearing in the Horava theory, and it is shown that a large class of stable solutions exists in the respective parameter space.Comment: 9 pages, 5 figures; references adde

Classical and quantum properties of a 2-sphere singularity

Recently Boehmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein-Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.Comment: 10 pages, 1 figure, minor corrections, final versio