Modern Physics Letters A

Accelerating cosmic expansion is a challenging issue faced by cosmology in the present times. Modified gravity could present a promising choice in order to understand and explain it in its framework. In this context, $f(R)$ models of modified gravity look apparently the most compatible and viable scenario. In this work, we investigate the cosmic dynamics of the late times using a dynamical system approach in $f(R)$ cosmology. The properties associated with the critical points are investigated to understand the system stability by analyzing the dynamical system which describes the cosmological evolution from the perspective of the model under consideration. It is observed that the accelerated cosmic expansion following the phase of matter domination is arrived at in a particular model $f(R)=R^{p}exp(\frac{q}{R})$ under discussion. The geometric curve $m(r)$ also helps figure out some significant properties of the model upon plotting in the $(r,m)$ plane. It also assists substantially to form the dynamical system for the model in question. The analysis of system stability is carried out by finding out the critical points of the dynamical system whose dynamic characteristics are responsible for the stability of the model. It is extended afterward by considering the cosmological constant as dark energy, which proves, however, redundant from the viewpoint of modified gravity in $f(R)$ models. Two cases regarding linear and nonlinear interactions between cosmic fluids are also discussed. At some points, as the analysis shows, we see that accelerated expansion is attained by yielding a viable epoch of matter domination. The results which came out through stability analysis show that the universe is currently subject to accelerating expansion regardless of the dark energy to remain in existence.

Quantum cryptography was proposed as a counter to the capacity of quantum computers to break classical cryptosystems. A broad subclass of quantum cryptography, called quantum key distribution (QKD), relies on quantum mechanical process for secure distribution of the keys. Quantum channels are inherently noisy, and therefore these protocols will be susceptible to noise as well. In this paper, we study the performance of two QKD protocols — BB84 and E91 under amplitude damping error. We show that while E91 protocol loses its security immediately due to loss of entanglement, the performance of BB84 protocol reduces to random guessing with increasing time. Next, we consider the action of an Eve on the BB84 protocol under amplitude damping noise, who is restricted to guessing the outcome of the protocol only. Under this restriction, we show that Eve can still do better than random guessing when equipped with the characteristics of the noisy channel. Finally, we propose a modification of the BB84 protocol which retains the security of the original protocol, but ensures that Eve cannot get any advantage in guessing the outcome, even with complete channel information.

In this paper, we discussed the multiple vector fields during the inflation era and the inflationary magnetogenesis with multiple vector fields. Instead of a single coupling function in single vector field models, the coupling matrix between vector fields and scalar field which drive the inflation is introduced. The dynamical equations for multiple vector fields are obtained and applied to the inflation era. We discussed three cases for the double-field model. In the no mutual-coupling case, one can find that both electric and magnetic spectrum can be scale-invariant at the end of inflation, meanwhile, the strong coupling problem can be avoided. The effect of mutual coupling between different vector fields is also discussed. We found that weak mutual coupling can lead to a slightly blue spectrum of the magnetic field. On the other hand, in the strong mutual-coupling case, the scale-invariant magnetic spectrum can also be obtained but the energy density of electromagnetic fields either leads to the backreaction problem or is diluted by inflation.

If there is a population of black holes distributed randomly in space, light rays passing in their vicinity will acquire random phases. In the “two-slit” model of an interferometer this can, for a high density of black holes, lead to a diffusion in the phase difference between the two arms of the interferometer and thus to a loss of coherence or “visibility” in interferometric observations. Hence the existence of “fringe contrast” or “visibility” in interferometric observations can be used to put a limit on the possible presence of black holes along the flight path. We give a formula for this effect and consider its application, particularly for observations in cosmology. Under the assumption that the dark matter consists of primordial black holes, we consider sources at high $z$, up to the CMB. While the strongest results are for the CMB as the most remote source, more nearby sources at high $z$ lead to similar effects. The effect increases with the baseline, and in the limiting case of the CMB we find that with earth-size baselines a nonzero “visibility” would limit the mass of possible primordial black holes, to approximately $M∕M_{\odot }\le 10^{-1}$. Although such limits would not appear to be as strong as those obtained, say from microlensing, they involve a much different methodology and are dominated by very early times (see Table ). Longer baselines lead to more stringent limits and in principle with extreme lengths, the method could possibly find positive evidence for primordial black holes. In this case, however, all other kinds of phase averaging would have to be constrained or eliminated.

Locally Rotationally Symmetric (LRS) Bianchi type-I metric is examined in the presence of perfect fluid. Exact solutions of Einstein’s field equations (EFE) have been studied by taking into account a hyperbolic scale factor. We observed that the model has initial singularity. It is found that the Universe approaches isotropy at late times. Through state finder pair $\{r,s\}$, it is observed that at late cosmic time, the model behaves analogous to $\mathrm{\Lambda }$CDM model. Energy conditions of the model are studied and it is found that null energy condition (NEC), weak energy condition (WEC) and dominant energy conditions (DEC) are satisfied for our model while SEC is violated. We investigate some physically and geometrically realistic models in order to develop a viable cosmological model.

In this paper, we present an analysis of the circular motion of test particles around a Schwarzschild-MOG black hole. Initially, our focus lies on studying the shadow cast by the spherically symmetric black hole within the framework of MOG gravity. Notably, we observe that the presence of MOG influences both the photon-sphere and the black hole’s shadow, causing them to increase in size. Furthermore, our research reveals that the characteristic radii of massive particles in circular orbits around the Schwarzschild-MOG black hole, specifically the innermost stable circular orbits (ISCO) and marginally bound orbits, are greater than those observed in the Schwarzschild metric alone. Additionally, we examine the electromagnetic field structure when a black hole is subjected to an external uniform magnetic field. Our findings demonstrate that in the vicinity of the Schwarzschild-MOG black hole, the magnetic field exhibits non-uniform behavior, with field lines becoming more densely distributed. Lastly, we delve into the motion of charged particles around the Schwarzschild-MOG black hole in the presence of an external magnetic field. Our investigation highlights that the ISCO position for charged particles is consistently less than that for neutral particles, indicating a significant distinction between the two scenarios.

In this work, the analysis of the behavior of an interior solution in the frame of Einstein’s general theory of relativity is reported. Given the possibility that, for greater densities than the nuclear density, the matter presents anisotropies in the pressures and that these are the orders of density present in the interior of the compact stars, the solution that is discussed considers that the interior region contains an anisotropic fluid, i.e. $P_r\ne P_t$. The compactness value, where $u=\frac{GM}{c^{2}R}$, for which the solution is physically acceptable is $u\le 0.23577$ as such the graphic analysis of the model is developed for the case in which the mass $M=(0.85\pm 0.15)M_{\odot }$ and the radius $R=8.1\pm 0.41\mathrm{\text{km}}$ which corresponds to the star Her X-1, with maximum compactness $u_{max}=0.1919$, although for other values of compactness $u\le 0.23577$ the behavior is similar. The functions of density and pressures are positive, finite and monotonically decreasing, also the solution is stable according to the cracking criteria and the range of values is consistent with what is expected for these type of stars.

The current paper corrects an error that occurred in a previously published paper. The error starts from Sec. , Eq. () whereby the scalar value of the wave-vector needs to be corrected. The net result is that the final formulas for the relativistic Doppler effect and for aberration get simplified. The source of the error is an extra multiplication factor by “$c$”. We need to replace the incorrect $k=C^{\prime }\cdot k^{\prime }c+a_{44}{k}^{\prime }$ in [A. Sfarti, MPLA 37, 2250238 (2022)] with the correct expression $k=C^{\prime }\cdot k^{\prime }+a_{44}{k}^{\prime }$.