Late time cosmology in f(R,G)- gravity with interacting fluids

Cosmological models are obtained in a $f(R)$ modified gravity with a coupled Gauss-Bonnet (GB) terms in the gravitational action. The dynamical role of the GB terms is explored with a coupled dilaton field in two different cases (I) $f(R)= R + \gamma R^2- \lambda \left( \frac{R}{3m_s^2} \right)^{\delta}$ where $\gamma$, $\lambda$ and $\delta$ are arbitrary constants and (II) $f(R)=R$ and estimate the constraints on the model parameters. In the first case we choose GB terms coupled with a free scalar field in the presence of interacting fluid and in the second case GB terms coupled with scalar field in a self interacting potential to compare the observed universe. The evolutionary scenario of the universe is obtained adopting a numerical technique as the field equations are highly non-linear. Defining a new density parameter $\Omega_{H}$, a ratio of the dark energy density to the present energy density of the non-relativistic matter, we look for a late accelerating universe. The state finder parameters $\Omega_{H}$, deceleration parameter ($q$), jerk parameter ($j$) are plotted. It is noted that a non-singular universe with oscillating cosmological parameters for a given strength of interactions is admitted in Model-I. The gravitational coupling constant $\lambda$ is playing an important role. The Lagrangian density of $f(R)$ is found to dominate over the GB terms when oscillating phase of dark energy arises. In Model-II, we do not find oscillation of the cosmological parameters as the universe evolves. In the presence of interaction the energy from radiation sector of matter cannot flow to the other two sectors of fluid. The range of values of the strengths of interaction of the fluids are estimated for a stable universe assuming the primordial gravitational wave speed equal to unity.

The Black Hole Mass Function Across Cosmic Times. I. Stellar Black Holes and Light Seed Distribution

This is the first paper in a series aimed at modeling the black hole (BH) mass function, from the stellar to the intermediate to the (super)massive regime. In the present work, we focus on stellar BHs and provide an ab initio computation of their mass function across cosmic times; we mainly consider the standard, and likely dominant, production channel of stellar-mass BHs constituted by isolated single/binary star evolution. Specifically, we exploit the state-of-the-art stellar and binary evolutionary code SEVN, and couple its outputs with redshift-dependent galaxy statistics and empirical scaling relations involving galaxy metallicity, star formation rate and stellar mass. The resulting relic mass function dN / dVd log m • as a function of the BH mass m • features a rather flat shape up to m • ≈ 50 M ⊙ and then a log-normal decline for larger masses, while its overall normalization at a given mass increases with decreasing redshift. We highlight the contribution to the local mass function from isolated stars evolving into BHs and from binary stellar systems ending up in single or binary BHs. We also include the distortion on the mass function induced by binary BH mergers, finding that it has a minor effect at the high-mass end. We estimate a local stellar BH relic mass density of ρ • ≈ 5 × 107 M ⊙ Mpc−3, which exceeds by more than two orders of magnitude that in supermassive BHs; this translates into an energy density parameter Ω• ≈ 4 × 10−4, implying that the total mass in stellar BHs amounts to ≲1% of the local baryonic matter. We show how our mass function for merging BH binaries compares with the recent estimates from gravitational wave observations by LIGO/Virgo, and discuss the possible implications for dynamical formation of BH binaries in dense environments like star clusters. We address the impact of adopting different binary stellar evolution codes (SEVN and COSMIC) on the mass function, and find the main differences to occur at the high-mass end, in connection with the numerical treatment of stellar binary evolution effects. We highlight that our results can provide a firm theoretical basis for a physically motivated light seed distribution at high redshift, to be implemented in semi-analytic and numerical models of BH formation and evolution. Finally, we stress that the present work can constitute a starting point to investigate the origin of heavy seeds and the growth of (super)massive BHs in high-redshift star-forming galaxies, that we will pursue in forthcoming papers.

Nuclear level densities away from line of β-stability

The variation of total nuclear level densities (NLDs) and level density parameters with proton number Z are studied around the β-stable isotope, Z0, for a given mass number. We perform our analysis for a mass range A=40 to 180 using the NLDs from popularly used databases obtained with the single-particle energies from two different microsopic mass-models. These NLDs which include microscopic structural effects such as collective enhancement, pairing and shell corrections, do not exhibit inverted parabolic trend with a strong peak at Z0 as predicted earlier. We also compute the NLDs using the single-particle energies from macroscopic-microscopic mass-model. Once the collective and pairing effects are ignored, the inverted parabolic trends of NLDs and the corresponding level density parameters become somewhat visible. Nevertheless, the factor that governs the (Z-Z0) dependence of the level density parameter, leading to the inverted parabolic trend, is found to be smaller by an order of magnitude. We further find that the (Z-Z0) dependence of NLDs is quite sensitive to the shell effects.

Standardizing Dainotti-correlated gamma-ray bursts, and using them with standardized Amati-correlated gamma-ray bursts to constrain cosmological model parameters

We show that each of the three Dainotti-correlated gamma-ray burst (GRB) data sets recently compiled by Wang et al. and Hu et al., that together probe the redshift range 0.35 ≤ z ≤ 5.91, obey cosmological-model-independent Dainotti correlations and so are standardizable. We use these GRB data in conjunction with the best currently-available Amati-correlated GRB data, that probe 0.3399 ≤ z ≤ 8.2, to constrain cosmological model parameters. The resulting cosmological constraints are weak, providing lower limits on the non-relativistic matter density parameter, mildly favoring non-zero spatial curvature, and largely consistent with currently accelerated cosmological expansion as well as with constraints determined from better-established data.

Performance analysis of brushless DC motor with optimum magnetic energy for bicycle application

<span lang="EN-US">Brushless DC (BLDC) motor is widely used for various applications such as transportation. BLDC motor has many advantages compared to brush motor such as more compact, high robustness and simplest construction. The maintenance of this motor also low compared to brush motor due to absent of the brush inside the motor. For electric bicycle application, the conventional motor has low electromagnetic torque because not properly designed. It faces low torque density as the motor in full load condition especially during climb uphill. In this research, an optimum magnetic energy is being determine by proper selection of permanent magnet size. In addition, this research also increases the input current in dynamic condition into the designed BLDC motor. Finite element method (FEM) is used to analyze other performance characteristic of improved motor such as back electromotive force (EMF), electromagnetic torque, flux linkage, and stator flux density. Parameter for improve the current motor are selected and varied based on the required specification. In conclusion, the research proposed the new motor specification that has highest electromagnetic torque of brushless DC motor. Finally, this research provides guidelines, suggestions and proposes a better improved structure in optimize the magnetic energy in BLDC motor.</span>

Shell-structure and asymmetry effects in level densities

Level density [Formula: see text] is derived for a nuclear system with a given energy [Formula: see text], neutron [Formula: see text], and proton [Formula: see text] particle numbers, within the semiclassical extended Thomas–Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain [Formula: see text], where [Formula: see text] is the modified Bessel function of the entropy [Formula: see text], and [Formula: see text] is related to the number of integrals of motion, except for the energy [Formula: see text]. For small shell structure contribution one obtains within the micro–macroscopic approximation (MMA) the value of [Formula: see text] for [Formula: see text]. In the opposite case of much larger shell structure contributions one finds a larger value of [Formula: see text]. The MMA level density [Formula: see text] reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA [Formula: see text] to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter [Formula: see text], which differs significantly from that of neutron resonances.

Interacting Rényi holographic dark energy with parametrization on the interaction term

In this work, we study the Rényi holographic dark energy (RHDE) model in a flat FRW Universe where the infrared cut-off is taken care by the Hubble horizon and also by taking three different parametrizations of the interaction term between the dark matter and the dark energy. Analyzing graphically, the behavior of some cosmological parameters in particular deceleration parameter, equation of state (EoS) parameter, energy density parameter and squared speed of sound, in the process of the cosmic evolution, is found to be leading towards the late-time accelerated expansion of the RHDE model. Also, we find the departure for the derived models from the standard [Formula: see text]CDM model according to the evolution of jerk parameter. Moreover, we compare the model parameters by considering the observational Hubble data which consist of 51 points in the redshift range [Formula: see text].

Imprints of Gravitational Millilensing on the Light Curve of Gamma-Ray Bursts

In this work, we search for signatures of gravitational millilensing in gamma-ray bursts (GRBs) in which the source−lens−observer geometry produces two images that manifest in the GRB light curve as superimposed peaks with identical temporal variability (or echoes), separated by the time delay between the two images. According to the sensitivity of our detection method, we consider millilensing events due to point-mass lenses in the range of 105 − 107 M ⊙ at lens redshift about half that of the GRB, with a time delay on the order of 10 s. Current GRB observatories are capable of resolving and constraining this lensing scenario if the above conditions are met. We investigated the Fermi/GBM GRB archive from the year 2008 to 2020 using the autocorrelation technique and found one millilensed GRB candidate out of 2137 GRBs searched, which we use to estimate the optical depth of millilensed GRBs by performing a Monte Carlo simulation to find the efficiency of our detection method. Considering a point-mass model for the gravitational lens, where the lens is a supermassive black hole, we show that the density parameter of black holes (ΩBH) with mass ≈ 106 M ⊙ is about 0.007 ± 0.004. Our result is one order of magnitude larger compared to previous work in the lower mass range of 102 − 103 M ⊙, which gave a density parameter ΩBH ≈ 5 × 10−4, and recent work in the mass range of 102 − 107 M ⊙, which reported ΩBH ≈ 4.6 × 10−4. The mass fraction of black holes in this mass range to the total mass of the universe would be f = ΩBH/Ω M ≈ 0.027 ± 0.016.

Constraints on Non-Flat Starobinsky f(R) Dark Energy Model

We study the viable Starobinsky f(R) dark energy model in spatially non-flat FLRW backgrounds, where f(R)=R−λRch[1−(1+R2/Rch2)−1] with Rch and λ representing the characteristic curvature scale and model parameter, respectively. We modify CAMB and CosmoMC packages with the recent observational data to constrain Starobinsky f(R) gravity and the density parameter of curvature ΩK. In particular, we find the model and density parameters to be λ−1<0.283 at 68% C.L and ΩK=−0.00099−0.0042+0.0044 at 95% C.L, respectively. The best χ2 fitting result shows that χf(R)2≲χΛCDM2, indicating that the viable f(R) gravity model is consistent with ΛCDM when ΩK is set as a free parameter. We also evaluate the values of AIC, BIC and DIC for the best fitting results of f(R) and ΛCDM models in the non-flat universe.

Primordial black holes formation in the inflationary model with field-dependent kinetic term for quartic and natural potentials

Within the framework of inflationary model with field-dependent kinetic term for quartic and natural potentials, we investigate generation of the primordial black holes (PBHs) and induced gravitational waves (GWs). In this setup, we consider a kinetic function as $$G(\phi )=g_I(\phi )\big (1+g_{II}(\phi )\big )$$ G ( ϕ ) = g I ( ϕ ) ( 1 + g II ( ϕ ) ) and show that in the presence of first term $$g_I(\phi )$$ g I ( ϕ ) both quartic and natural potentials, in contrast to the standard model of inflation, can be consistent, with the 68% CL of Planck observations. Besides, the second term $$g_{II}(\phi )$$ g II ( ϕ ) can cause a significant enhancement in the primordial curvature perturbations at the small scales which results the PBHs formation. For the both potentials, we obtain an enhancement in the scalar power spectrum at the scales $$k\sim 10^{12}~{\mathrm{Mpc}}^{-1}$$ k ∼ 10 12 Mpc - 1 , $$10^{8}~{\mathrm{Mpc}}^{-1}$$ 10 8 Mpc - 1 , and $$10^{5}~{\mathrm{Mpc}}^{-1}$$ 10 5 Mpc - 1 , which causes PBHs production in mass scales around $$10^{-13}M_{\odot }$$ 10 - 13 M ⊙ , $$10^{-5}M_{\odot }$$ 10 - 5 M ⊙ , and $$10 M_{\odot }$$ 10 M ⊙ , respectively. Observational constraints confirm that PBHs with a mass scale of $$10^{-13}M_{\odot }$$ 10 - 13 M ⊙ can constitute the total of dark matter in the universe. Furthermore, we estimate the energy density parameter of induced GWs which can be examined by the observation. Also we conclude that it can be parametrized as a power-law function $$\Omega _{\mathrm{GW}}\sim (f/f_c)^n$$ Ω GW ∼ ( f / f c ) n , where the power index equals $$n=3-2/\ln (f_c/f)$$ n = 3 - 2 / ln ( f c / f ) in the infrared limit $$f\ll f_{c}$$ f ≪ f c .