Narrow Results

Using the observed time and spatial intervals defined originally by Einstein and the observational frame in the vierbein formalism, we propose that in curved space–time, for a wave received in laboratories, the observed frequency is the changing rate of the phase of the wave relative to the local observable time scale and the momentum is the changing rate of the phase relative to the local observable spatial length scale. The case of Robertson–Walker universe is especially considered and the application to de Sitter universe results in a cosmological constant in perfect agreement with the observational data.

In this work, Friedmann–Robertson–Walker (FRW) universe filled with dark matter (DM) (perfect fluid with negligible pressure) along with dark energy (DE) in the background of Galileon gravity is considered. Four DE models with different equation of state (EoS) parametrizations have been employed namely, linear, Chevallier–Polarski–Lindler (CPL), Jassal–Bagla–Padmanabhan (JBP) and logarithmic parametrizations. From Stern, Stern+Baryonic Acoustic Oscillation (BAO) and Stern+BAO+Cosmic Microwave Background (CMB) joint data analysis, we have obtained the bounds of the arbitrary parameters ${\omega }_0$ and ${\omega }_1$ by minimizing the ${\chi }^2$ test. The best fit values and bounds of the parameters are obtained at 66%, 90% and 99% confidence levels which are shown by closed confidence contours in the figures. For the logarithmic model unbounded confidence contours are obtained and hence the model parameters could not be finitely constrained. The distance modulus $\mu$(z) against redshift $z$ has also been plotted for our predicted theoretical models for the best fit values of the parameters and compared with the observed Union2 data sample and SNe Type Ia 292 data and we have shown that our predicted theoretical models permits the observational datasets. From the data fitting it is seen that at lower redshifts $(z<0.3)$ the SNe Type Ia 292 data gives a better fit with our theoretical models compared to the Union2 data sample. So, from the data analysis, SNe Type Ia 292 data is the more favored data sample over its counterpart given the present choice of free parameters. From the study, it is also seen that the logarithmic parametrization model is less supported by the observational data. Finally, we have generated the plot for the deceleration parameter against the redshift parameter for all the theoretical models and compared the results with the work of Farooq et al., (2013).

The inner structure of compact stars is checked from theoretical as well as observational points of view. In this paper, we determine the possible radii of six compact stars: two binary millisecond pulsars, namely PSR J1614-2230 and PSR J1903+327, studied by [P. B. Demorest, T. Pennucci, S. M. Ransom, M. S. E. Roberts and W. T. Hessels, Nature467, 1081 (2010)] and four X-ray binaries, namely Cen X-3, SMC X-1, Vela X-1 and Her X-1 studied by [M. L. Rawls et al., Astrophys. J.730, 25 (2011)]. Interestingly, we see that density of the star does not vanishes at the boundary though it is maximum at the center which implies that these compact stars may be treated as strange stars rather than neutron stars. We propose a stiff equation of state (EoS) relating to pressure with matter density. We also obtain compactness (u) and surface redshift (Z${}_s$) for the above-mentioned stars and compare it with the recent observational data.

In this paper, we study the inner structure of some neutron stars from theoretical as well as observational points of view. We calculate the probable radii, compactness (u) and surface redshift (Z${}_s$) of five neutron stars (X-ray binaries) namely 4U 1538-52, LMC X-4, 4U 1820-30, 4U 1608-52, EXO 1745-248. Here, we propose a stiff equation of state (EoS) of matter distribution which relates pressure with matter density. Finally, we check the stability of such kind of theoretical structure.

We investigate whether compact stars having Tolman-like interior geometry admit conformal symmetry. Taking anisotropic pressure along the two principal directions within the compact object, we obtain physically relevant quantities such as transverse and radial pressure, density and redshift function. We study the equation of state (EOS) for the matter distribution inside the star. From the relation between pressure and density function of the constituent matter, we explore the nature and properties of the interior matter. The redshift function and compactness parameter are found to be physically reasonable. The matter inside the star satisfies the null, weak and strong energy conditions. Finally, we compare the masses and radii predicted from the model with corresponding values in some observed stars.

Recent observations of Stephan’s Quintet (SQ) gave new indications on its formation scenario. Older formation and role of NCG 7317 should be considered in revised numerical models of the compact group. Velocities of group members to recreate are estimated from redshift measurements. Several effects contribute to observed redshifts and a new effect is predicted to be the result of the gravitational interaction between photons and constant magnetic fields creating gravitational waves. The energy carried by these waves is manifested as redshifts of the photons. Cosmological simulation data are used to prove the significant contribution of our effect. The analysis of synthetic observations created from those simulations has shown that redshifts of SQ members could be misinterpreted as caused only from Doppler Effect. The revised models of the group should consider a new method to recreate the formation scenario based on redshift patterns and not mis-estimated velocities.

A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorentzian isometries of our new de Sitter relativity [I. I. Cotăescu, Eur. Phys. J. C 77, 485 (2017)]. This formula combines in a nontrivial manner the well-known cosmological contribution given by Lamaître’s law with that of the relative motion of the source with respect to a fixed observer as in de Sitter relativity instead of special relativity. Other related quantities as the dispersion relation, the propagation time of the photon and the real distance between the source and observer at the moment of observation are discussed pointing out their specific features in the de Sitter relativity.

We derive for the first time the form of the spiral null geodesics around the photon sphere of the Reissner–Nordstrom black hole in the de Sitter expanding universe. Moreover, we obtain the principal parameter we need for deriving, according to our method [I. I. Cotăescu, Eur. Phys. J. C 81, 32 (2021)], the black hole shadow and the related redshift as measured by a remote observer situated in the asymptotic zone. We obtain thus a criterion of detecting charged black holes without peculiar velocities when one knows the mass, redshift and the black hole shadow.

We propose a new method for calculating the redshift in galaxies, according to which the amount of redshift in the spectrum of each galaxy consists of two parts: about 2/3 of the redshift is due to the speed of the galaxy moving away from us, and about 1/3 is due to the fact that photons moving in the expanding Universe acquire an additional (non-Doppler) redshift. The additional reddening of photons in the spectrum of the galaxy is due to photons coming to us from the past, when the gravitational potential of the universe was lower, and consequently, the frequencies of atomic spectra were also lower than at present. A scheme of a laboratory experiment is proposed that will allow direct measurement of a non-Doppler (additional) part of the cosmological redshift and demonstrate the very fact of the expansion of the universe in real time in about 15 min. The experiment also makes it possible to measure the expansion rate of the universe and its current gravitational potential. These results will help to significantly refine modern ideas about the age of the universe, and about the amount of dark energy and dark matter in it.

A dark matter field fluid model is proposed. This model assumes that interstellar space is uniformly filled with dark matter, which possesses a fluid property and a field property; the fluid property follows general fluid mechanics, the interaction of the field with an ordinary baryonic object is proportional to the mass of the object, it also has a force opposing gravity. The data of the Moon-Earth gravitational system agrees with this model very well and the average dark matter field fluid constant is 4.39 × 10^-22s^-1m^-(1-n). This is the first proof that the motion of celestial objects can be treated in a fluid medium. The cosmological redshift formula derived from this model describes the observed redshifts very well. A huge redshift from a distant celestial object may not necessarily indicate that it is quickly receding from us. The universe may not expand as rapidly as thought.

A half-metal diluted magnetic semiconductor (DMS) can be formed in heavy V-doped TiO₂. Contradictory experimental results in the literature have reported about the absorption spectra blueshift and redshift results in heavy V-doped TiO₂. This study aims to reveal the mechanism of half-metal DMS in heavy V-doped TiO₂ and solve the problem of absorption spectra blueshift and redshift in the doping system. In this study, models of the unit cells of pure anatase TiO₂ and two V heavy-doped supercells of Ti${}_{0.96875}$V${}_{0.03125}$O₂ and Ti${}_{0.9375}$V${}_{0.0625}$O₂ were constructed based on density functional theory, which uses the first-principles plane-wave ultrasoft pseudopotential method. All models were obtained through geometry optimization. Local density approximation $(\mathrm{\text{LDA}})+U$ was used to calculate the band structure, density of states (DOS), orbital charge and absorption spectrum of the doping system. The calculated results under the condition of electron spin showed that in the heavy doping concentration range, the volume of supercells increases, the total energy and formation energy decrease and the stability of the supercells increases as V doping concentration increases. Furthermore, the interaction of $p$–$p$ states is weaker than that of $p$–$d$ states, which results in the valence band maximum shifting toward the low-energy region, and also the optical bandgap becomes narrower as well as the redshift and intensity of the absorption spectrum become more notable. Noticeably, the hybrid coupling effect of Ti-3$d$ and V-3$d$ states becomes stronger, and the magnetic moment increases. The Fermi levels of spin-up band structure within the conduction band, which form the $n$-type degenerate semiconductors, and the Fermi levels of spin-down band structure within the bandgap indicate that the doping system has semiconductor features. Therefore, V-doped anatase TiO₂ is an extremely promising DMS because of its high electron polarizability of nearly 100%. The calculation results are consistent with the experimental data; these results explain the problems reasonably and adequately. Therefore, the research findings can help solve the contradiction of the redshift and blueshift in the preparation of photocatalysts and half-metal diluted magnetic semiconductors of V heavy-doped anatase TiO₂.

Titanium dioxide (TiO₂) is one of the most promising photocatalysts for photoelectrochemical applications due to its high chemical as well as photochemical stability. Its efficiency in practical applications is limited due to its wide bandgap, a high rate of recombination of electron–hole pairs and the weak photo-carriers separation efficiency. In this computational study, a path was followed to find out the redshift of the TiO₂ light absorption edge via lead (Pb) doping. The density functional theory (DFT) results revealed that the doped TiO₂ bandgap was decreased to the lower edge (2.1 eV) in the visible region resulting in a relatively better optical absorption of the material. Furthermore, doped TiO₂ was found to absorb a large part of the solar spectrum. The improvement in optical absorption resulted in good photo response. The calculated results also showed a redshift in optical properties produced through the doping of Pb in TiO₂.

The InAs/GaAs quantum dots (QDs) with a baselength of less than 10 nm are studied by the excitation-, temperature-dependent and magneto-photoluminescence (PL). The baselengths of the QDs, calculated by the PL ground state transition energy and estimated by magneto-PL spectra, are in agreement with the result of atomic force microscopy measurements. By means of the excitation-dependent PL, we demonstrate that only the ground electron and hole states exist when the baselength of the QDs is smaller than about 7.3 nm, whereas the larger dots with a baselength of about 8.7 nm will give rise to one excited hole state. The measured energy separation between the ground and the excited hole states is in good agreement with the theoretical calculation. The transition energy in temperature-dependent PL spectra shows a rapid redshift as the temperature is higher than the critical temperature. The redshift rate is about 2.8 and 2.5 times larger than the values calculated by Varshni's law for small and large dots respectively. The higher redshift rate can be explained by the stronger tunneling effect. In addition, the PL linewidths show a V-shape dependence with the temperature. This behavior could be well described as a tunneling and electron-phonon scattering effect.

Anatase TiO₂ supercells were studied by first-principles, in which one was undoped and another three were high N-doping. Partial densities of states, band structure, population and absorption spectrum were calculated. The calculated results indicated that in the condition of TiO_2-xN_x (x = 0.0625, 0.125, 0.25), the higher the doping concentration is, the shorter will be the lattice parameters parallel to the direction of c-axis. The strength of covalent bond significantly varied. The formation energy increases at first, and then decreases. The doping models become less stable as N-doping concentration increases. Meanwhile, the narrower the band gap is, the more significant will be the redshift, which is in agreement with the experimental results.

In this theoretical study, a path was adapted to investigate the redshifting of the TiO₂ absorption edge by molybdenum (Mo), yttrium (Y) and nitrogen (N) doping. The geometrical model, band gap and photo response were noted in the developed model of anatase TiO₂. The tri-doped model showed very small modification in the structure as compared to a reference TiO₂ model. The 3d states of Mo mix up with the 3d states of Ti, resulting in the reduction of band gap. The Y 2p states were introduced around the middle of the band gap of Y-doped TiO₂. Good reduction was found in the gap of tri-doped TiO₂ model and the created states were occupied. The doping of N via oxygen (O) substitution in tri-doped model resulted in the band gap reduction by introducing states in the band gap due to the mixing of N 2p and O 2p states.

The cosmological problem is studied here starting from a metric with a variable scale factor for time and two different ones for space, noted R for ordinary space and S for the extra dimensions. Once R has been obtained from physical principles, one is left for S with a differential equation which can be solved through Lie group analysis and dynamical systems theory, and a frequent use of computer algebra has been made in the ensuing calculations. This leads to a good agreement with the recent observational results relating to distant supernovae. However, the solution obtained for S is particularly simple if spacetime has a dimension at least equal to ten, a result to be compared with those given by superstring or M theories.

We study the structure formation by investigating the spherical collapse model in the context of new agegraphic dark energy (NADE) model in flat FRW cosmology. We compute the perturbational quantities $g(a)$, ${\delta }_c(z_c)$, $\lambda (z_c)$, $\xi (z_c)$, ${\mathrm{\Delta }}_{\mathrm{\text{vir}}}(z_c)$, $log[\nu f(\nu )]$ and $log[n(k)]$ for the NADE model and compare the results with those of EdS and $\mathrm{\Lambda }\mathrm{\text{CDM}}$ models. We find that there is a dark energy-dominated universe at low redshifts and a matter-dominated universe at high redshifts in agreement with the observations. Also, the size of structures, the overdense spherical region, and the halo size in the NADE model are found to be smaller, denser, and larger than those of EdS and $\mathrm{\Lambda }\mathrm{\text{CDM}}$ models. We compare our results with the results of tachyon scalar field and holographic dark energy models.

In this methodological paper, we consider two problems an astronaut faces under the black hole horizon in the Schwarzschild metric. (1) How to maximize the survival proper time. (2) How to make a visible part of the outer universe as large as possible before hitting the singularity. Our consideration essentially uses the concept of peculiar velocities based on the “river model.” Let an astronaut cross the horizon from the outside. We reproduce from the first principles the known result that point (1) requires that an astronaut turn off the engine near the horizon and follow the path with the momentum equal to zero. We also show that point (2) requires maximizing the peculiar velocity of the observer. Both goals (1) and (2) require, in general, different strategies inconsistent with each other that coincide at the horizon only. The concept of peculiar velocities introduced in a direct analogy with cosmology and its application for the problems studied in this paper can be used in advanced general relativity courses.

Equilibrium sequences were developed for rotating neutron stars in the relativistic mean-field interaction framework using four density-dependent equations of state (EOSs) for the neutron star matter. These sequences were constructed for the observed rotation frequencies of 25, 317, 346, 716 and 1122Hz. The bounds of sequences, the secular axisymmetric instability, static and Keplerian sequences were calculated in each model to determine the stability region. The gravitational mass, quadrupole moment, polar, forward and backward redshifts, and Kerr parameter were calculated according to this stability region, and the allowable range of these quantities was then determined for each model. According to the results, DDF and DD-ME$\delta$ were unable to properly describe the low-frequency neutron stars, PSR J0348+432, PSR J1614-2230 and PSR J0740+6620 rotate at a frequency of 25, 317 and 346Hz, respectively. On the other hand, all the selected EOSs properly described the rotation of PSR J1748-244ad and PSR J1739-285 at a frequency of 716 and 1122Hz, respectively. The mass of these stars was, therefore, in the range of $[0.68,2.14]M_{\odot }$ and $[1.67,2.24]M_{\odot }$, respectively. The polar, forward and backward redshifts, and the quadrupole moment were calculated in all the selected rotating frequencies and the Keplerian sequence. The results were consistent with observations. Confirming the mass of $1.5_{-1.0}^{+0.4}{M}_{\odot }$ for EXO 0748-676, our result, $Z_P\approx 0.3$, will be close to the observed value, and the EOSs used in this study properly describe this star. Interestingly, the extremum of Kerr parameter, polar, forward and backward redshifts in all models reached constant values of, $a/M\approx 0.7$, $Z_p\approx 0.8$, $Z_{\mathrm{\text{eq}}}^f\approx -0.3$ and $Z_{\mathrm{\text{eq}}}^b\approx 2.2$, respectively. These behaviors of redshifts and Kerr parameter are approximately independent of EOS. The observed behaviors must evaluate by other EOSs to find universal relations for these quantities. Also, a limit value was found for each of these parameters. In this case where these parameters are greater than the limit value, the star can rotate at a frequency equal to or greater than $\nu =1122$Hz.

The evolution of the baryon distribution in different phases, derived from cosmological simulations, are here reported. These computations indicate that presently most of baryons are in a warm-hot intergalactic (WHIM) medium (about 43%) while at z = 2.5 most of baryons constitute the diffuse medium (about 74%). Stars and the cold gas in galaxies represent only 14% of the baryons at z = 0. For z < 4 about a half of the metals are locked into stars while the fraction present in the WHIM and in the diffuse medium increases with a decreasing redshift. In the redshift range 0 ≤ z ≤ 2.5, the amount of metals in the WHIM increases from 4% to 22% while in the diffuse medium it increases from 0.6% to 4%. This enrichment process is due essentially to a turbulent diffusion mechanism associated to mass motions driven by supernova explosions. At z = 0, simulated blue (late type) galaxies show a correlation of the oxygen abundance present in the cold gas with the luminosity of the considered galaxy that agrees quite well with data derived from HII regions.