Rotating Neutron Stars in F(R) Gravity with Axions

We investigate equilibrium configurations of uniformly rotating neutron stars in $R^2$ gravity with axion scalar field for GM1 equation of state (EoS) for nuclear matter. The mass-radius diagram, mass-central energy density are presented for some frequencies in comparison with static stars. We also compute equatorial and polar radii and moment of inertia for stars. For axion field $\phi$ the coupling in the form $\sim R^2\phi$ is assumed. Several interesting results follow from our consideration. Maximal possible star mass with given EoS increases due to the contribution of coupling term. We discovered the possibility to increase maximal frequency of the rotation in comparison with General Relativity. As a consequence the lower bound on mass of the fast rotating stars decreases. For frequency $f=700$ Hz neutron stars with masses $\sim M_\odot$ can exist for some choice of parameters (in General Relativity for same EoS this limit is around $1.2 M_{\odot}$). Another feature of our solutions is relatively small increase of stars radii for high frequencies in comparison with static case. Thus, eventually the new class of neutron stars in $R^2$ gravity with axions is discovered namely fast rotating compact stars with intermediate masses.Comment: to appear in MNRAS; 8 pp., 4 figure

Supermassive Neutron Stars in Axion F(R)F(R) Gravity

We investigated realistic neutron stars in axion $R^{2}$ gravity. The coupling between curvature and axion field $\phi$ is assumed in the simple form $\sim R^2\phi$. For the axion mass in the range $m_{a}\sim 10^{-11}-10^{-10}$ eV the solitonic core within neutron star and corresponding halo with size $\sim 100$ km can exist. Therefore the effective contribution of $R^2$ term grows inside the star and it leads to change of star parameters (namely, mass and radius). We obtained the increase of star mass independent from central density for wide range of masses. Therefore, maximal possible mass for given equation of state grows. At the same time, the star radius increases not so considerably in comparison with GR. {Hence, our model may predict possible existence of supermassive compact stars with masses $M\sim 2.2-2.3M_\odot$ and radii $R_{s}\sim 11$ km for realistic equation of state (we considered APR equation of state). In General Relativity one can obtain neutron stars with such characteristics only for unrealistic, extremely stiff equations of state.} Note that this increase of mass occurs due to change of solution for scalar curvature outside the star. In GR curvature drops to zero on star surface where $\rho=p=0$. In the model under consideration the scalar curvature dumps more slowly in comparison with vacuum $R^2$ gravity due to axion "galo" around the star.Comment: to appear in MNRAS, 9pp., 6 figure

Chandrasekhar Mass Limit of White Dwarfs in Modified Gravity

We investigate the Chandrasekhar mass limit for white dwarfs in various models of $f(R)$ gravity. Two equations of state for stellar matter are used: simple relativistic polytropic equation with polytropic index $n=3$ and the realistic Chandrasekhar equation of state. For calculations it is convenient to use the equivalent scalar-tensor theory in the Einstein frame and then to return in the Jordan frame picture. For white dwarfs we can neglect terms containing relativistic effects from General Relativity and we consider the reduced system of equations. Its solution for any model of $f(R)=R+\beta R^{m}$ ($m\geq 2$, $\beta>0$) gravity leads to the conclusion that the stellar mass decreases in comparison with standard General Relativity. For realistic equations of state we find that there is a value of the central density for which the mass of white dwarf peaks. Therefore, in frames of modified gravity there is lower limit on the radius of stable white dwarfs and this minimal radius is greater than in General Relativity.Comment: 9 pp., 4 figure

Analysis of scalar perturbations in cosmological models with a non-local scalar field

We develop the cosmological perturbations formalism in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field in the presence of the arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We carry out the general analysis related to the curvature and entropy perturbations and consider the most specific example of perturbations when important quantities in the model become complex.Comment: LaTeX, 25 pages, 1 figure, v2: Subsection 3.2 and Section 5 added, references added, accepted for publication in Class. Quant. Grav. arXiv admin note: text overlap with arXiv:0903.517

Conference on the occasion of the 60th Birthday of Professor Emilio Elizalde

Some major developments of physics in the last three decades are addressed by highly qualified specialists in different specific fields. They include renormalization problems in QFT, vacuum energy fluctuations and the Casimir effect in different configurations, and a wealth of applications. A number of closely related issues are also considered. The cosmological applications of these theories play a crucial role and are at the very heart of the book; in particular, the possibility to explain in a unified way the whole history of the evolution of the Universe: from primordial inflation to the present day accelerated expansion. Further, a description of the mathematical background underlying many of the physical theories considered above is provided. This includes the uses of zeta functions in physics, as in the regularization problems in QFT already mentioned, specifically in curved space-time, and in Casimir problems as