Dark spinor inflation -- theory primer and dynamics

Inflation driven by a single dark spinor field is discussed. We define the notion of a dark spinor field and derive the cosmological field equations for such a matter source. The conditions for inflation are determined and an exactly solvable model is presented. We find the power spectrum of the quantum fluctuation of this field and compare the results with scalar field inflation.Comment: 13 pages; typo in Eq. (12) corrected, minor improvement

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

On the relation between mass of pion, fundamental physical constants and cosmological parameters

In this article we reconsider the old mysterious relation, advocated by Dirac and Weinberg, between the mass of the pion, the fundamental physical constants, and the Hubble parameter. By introducing the cosmological density parameters, we show how the corresponding equation may be written in a form that is invariant with respect to the expansion of the Universe and without invoking a varying gravitational "constant", as was originaly proposed by Dirac. It is suggest that, through this relation, Nature gives a hint that virtual pions dominante the "content" of the quantum vacuum

Einstein static universes are unstable in generic f(R) models

We study Einstein static universes in the context of generic f(R) models. It is shown that Einstein static solutions exist for a wide variety of modified gravity models sourced by a barotropic perfect fluid with equation of state w=p/rho, but these solutions are always unstable to either homogeneous or inhomogeneous perturbations. Our general results are in agreement with specific models investigated in that past. We also discuss how our techniques can be applied to other scenarios in f(R) gravity.Comment: 7 pages, 2 figures. Minor corrections. Minor changes and references added to match version accepted by Phys. Rev.

Stability of the Einstein static universe in f(R) gravity

We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are parameterized by a linear equation of state parameter w=p/rho. Contrary to classical general relativity, it is found that in f(R) gravity a stable Einstein cosmos with a positive cosmological constant does indeed exist. Thus, we are lead to conclude that, in principle, modifications in f(R) gravity stabilize solutions which are unstable in general relativity.Comment: 7 pages, 2 figures, 2 tables; references adde

A new two-sphere singularity in general relativity

The Florides solution, proposed as an alternative to the interior Schwarzschild solution, represents a static and spherically symmetric geometry with vanishing radial stresses. It is regular at the center, and is matched to an exterior Schwarzschild solution. The specific case of a constant energy density has been interpreted as the field inside an Einstein cluster. In this work, we are interested in analyzing the geometry throughout the permitted range of the radial coordinate without matching it to the Schwarzschild exterior spacetime at some constant radius hypersurface. We find an interesting picture, namely, the solution represents a three-sphere, whose equatorial two-sphere is singular, in the sense that the curvature invariants and the tangential pressure diverge. As far as we know, such singularities have not been discussed before. In the presence of a large negative cosmological constant (anti-de Sitter) the singularity is removed.Comment: 17 pages, 3 figure

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

Debye relaxation and 250 K anomaly in glass forming monohydroxy alcohols

A previous dielectric, near-infrared (NIR), and nuclear magnetic resonance study on the hydrogen-bonded liquid 2-ethyl-1-hexanol [C. Gainaru et al., Phys. Rev. Lett. 107, 118304 (2011)] revealed anomalous behavior in various static quantities near 250 K. To check whether corresponding observations can be made for other monohydroxy alcohols as well, these experimental methods were applied to such substances with 5, 6, 7, 8, and 10 carbon atoms in their molecular backbone. All studied liquids exhibit a change of behavior near 250 K which is tentatively ascribed to effects of hydrogen bond cooperativity. By analyzing the NIR band intensities, a linear cluster size is derived that agrees with estimates from dielectric spectroscopy. All studied alcohols, except 4-methyl-3-heptanol, display a dominant Debye-like peak. Furthermore, neat 2-ethyl-1-butanol exhibits a well resolved structural relaxation in its dielectric loss spectrum which so far has only been observed for diluted monohydroxy alcohols.Comment: 39 pages including 12 figure

NMR Study of the New Magnetic Superconductor CaK(Fe$0.951Ni0.049)4As4: Microscopic Coexistence of Hedgehog Spin-vortex Crystal and Superconductivity

Coexistence of a new-type antiferromagnetic (AFM) state, the so-called hedgehog spin-vortex crystal (SVC), and superconductivity (SC) is evidenced by $^{75}$As nuclear magnetic resonance study on single-crystalline CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$. The hedgehog SVC order is clearly demonstrated by the direct observation of the internal magnetic induction along the $c$ axis at the As1 site (close to K) and a zero net internal magnetic induction at the As2 site (close to Ca) below an AFM ordering temperature $T_{\rm N}$ $\sim$ 52 K. The nuclear spin-lattice relaxation rate 1/$T_1$ shows a distinct decrease below $T_{\rm c}$ $\sim$ 10 K, providing also unambiguous evidence for the microscopic coexistence. Furthermore, based on the analysis of the 1/$T_1$ data, the hedgehog SVC-type spin correlations are found to be enhanced below $T$ $\sim$ 150 K in the paramagnetic state. These results indicate the hedgehog SVC-type spin correlations play an important role for the appearance of SC in the new magnetic superconductor.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. B rapid communicatio

Extra force in f(R)f(R) modified theories of gravity

The equation of motion for test particles in $f(R)$ modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, $R$, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak field limit. Connections with MOND and with the Pioneer anomaly are further discussed.Comment: Revtex4 file, 5 pages. Version to appear in Physical Review