We study several extensions of the Starobinsky model of inflation, which obey all observational constraints on the inflationary parameters, by demanding that both the inflaton scalar potential in the Einstein frame and the F(R) gravity function in the Jordan frame have the explicit dependence upon fields and parameters in terms of elementary functions. Our models are continuously connected to the original Starobinsky model via changing the parameters. We modify the Starobinsky (R + R²) model by adding an R³-term, an R⁴-term, and an R^3/2-term, respectively, and calculate the scalar potentials, the inflationary observables and the allowed limits on the deformation parameters by using the latest observational bounds. We find that the tensor-to-scalar ratio in the Starobinsky model modified by the R^3/2-term significantly increases with raising the parameter in front of that term. On the other side, we deform the scalar potential of the Starobinsky model in the Einstein frame in powers of y = exp(-√(2/3)ϕ/M_Pl), where ϕ is the canonical inflaton (scalaron) field, calculate the corresponding F(R) gravity functions in the two new cases, and find the restrictions on the deformation parameters in the lowest orders with respect to the variable y that is physically small during slow-roll inflation.

This talk is based on the paper [1].

[1] Vsevolod R. Ivanov, Sergei V. Ketov, Ekaterina O. Pozdeeva, and Sergey Yu Vernov. Analytic extensions of starobinsky model of inflation. Journal of Cosmology and Astroparticle Physics, 2022(03):058, 2022.

In this paper we present the flowchart of the Gamma-Ray Burst (GRB) afterglows, to create a numerical FORTRAN code. In the context of several proposed models, the hydrodynamic evolution describing the external shock of the jet with the environment surrounding of the GRB source or the Interstellar medium is discussed. A comparison of the results with data by considering the synchrotron emission as a basic mechanism for the radiation part was also made.

The formation of the large structures of the Universe results from gravitational instability, which pushes dark matter to collapse, forming a network (called the cosmic web) of dense voids, sheets, filaments, and knots. Each element of the cosmic web is based on the local dimensionality of the gravitational collapse, which is equal to the number of positive eigenvalues of the tidal field. Thus, a point is part of a knot, filament or wall if it has respectively 3, 2 or 1 positive eigenvalue, if it has no positive eigenvalue, it is part of a void.

Using 2000 different ΛCDM model of the Quijote suite of N-Body simulations, we studied the properties of non-linearity and non-Gaussianity of the cosmic web by distinguishing each element and according to the cosmological model. Several observables have been calculated, for each category individually, namely: i) Mass and volume filling fractions, ii) the probability distribution function P (δ) and its first 4 moments iii) The power spectrum P (k). We also calculated the cross-correlations between the 4 categories, as well as the cross-correlations between each category and the matter field.

Our results show that each category has its own non-linear and non-Gaussian characteristics for a given cosmological model, and that the geometric and dynamical properties of each category depend differently on the cosmological parameters, in particular on Ω_m and σ₈. We were also able to constrain the n_s and Ω_b parameters by isolating respectively the walls and filaments properties.
We finally show that, instead of relying only on the matter field, the use of the cosmic web information allows a finer understanding of the origin of the nonlinear and non-Gaussian properties of the gravitational instability according to cosmological models, and much better inference of all cosmological parameters.

At finite isospin chemical potential μI, the tension between measured decays and partial branching ratios of neutral and charged bosons as functions of dimuon mass squared and the SM isospin asymmetry shall be analyzed in the nonperturbative QCD-effective model, the Polyakov linear sigma-model. With the derivation of the explicit symmetry-breaking term h3, the QCD phase structure could be mapped out to finite μB and μI. We conclude the critical temperatures Tχ decrease with increasing μB and μI and the (Tχ-μI) boundary could be extended to the (Tχ-μB) plane.

Inflationary cosmology is the dominant perspective in explaining the early physics of the universe. Along with solving the flatness, homogeneity, and unwanted relics problems, inflationary cosmology interprets inhomogeneities in the Cosmic Microwave Background Radiation. Three models of inflation are considered in this study: Natural inflation, Power-law inflation, and inflationary model based on variations of the strong coupling constant. Unfortunately, in Einstein's gravity, these three models did not match current observational constraints represented by Planck2018 (TT, EE, TE), BK18, and other experiments (lowE, lensing) separately or combined. However, our study demonstrates that by modifying the gravitational sector, represented by F(R) gravity with/without non-minimal coupling between the inflaton field and gravity, the models can be rescued and accommodate the observations. Moreover, the study is conducted within Palatini's formalism of gravity rather than one based on metric formulation. Finally, we demonstrate that the models can produce inherently different results when analyzed within different inflationary scenarios like warm slow-roll inflation, cold constant-roll inflation, or non-canonical inflation. The talk is based on:
M.AlHallak, A.AlRakik, N.Chamoun and M.S.El-Daher, Universe 8 (2022) no.2, 126 doi:10.3390/universe8020126 [arXiv:2111.05075 [astro-ph.CO]].
M.AlHallak, N.Chamoun and M.S.Eldaher, JCAP 10 (2022), 001 doi:10.1088/1475-7516/2022/10/001 [arXiv:2202.01002 [astro-ph.CO]].
M.AlHallak, K.K.A Said, N.CHAMOUN and M.S.El-Daher, [arXiv:2211.07775 [gr-qc]].
And current studies.

In this presentation, we have studied an anisotropic Bianchi type-I cosmological model within the framework of f(R, T) gravity. Our motivation to study an anisotropic model is the following. Observations seem to indicate that the universe is flat, but they do not rule out some small measure of anisotropy.
To obtain exact solutions of the field equations, we have used the condition that σ/θ, where  is σ is the anisotropy, and θ is the expansion scalar, be a function of the scale factor [IJTP, 54, (2015), 2740-2757]. Our model possesses an initial singularity and during early times, exhibits decelerating
expansion. Later, the universe transits to accelerating expansion at late times. We have analyzed the cosmological parameters, both with time and redshift, and illustrated their evolution by means of pictorial representations. The energy conditions are analysed in detail, and illustrated by means of
diagrams. Statefinder diagnostics are carried out as well. We confront the models against observational data by using the 57 data point measurements of the Hubble parameter. It is found that our model fits the observed data well. Finally, we plot the higher order derivatives of the scale factor, viz., the jerk, snap and lerk parameters. These parameters show the deviation of our models from the standard ΛCDM model.

In the framework of geometric optics, which sufficiently describes the effects in the near-earth environment, Faraday rotation is purely a reference frame effect. A simple encoding procedure could mitigate the Faraday phase error. However, geometric optics approximation is not sufficient to describe the propagation of waves of large but finite frequencies. So, we outline the technique to solve the equations for the propagation of an electromagnetic wave up to the subleading order geometric optics expansion in curved spacetimes. This could be achieved in two nontrivial steps. First, we need to construct a set of parallel propagated null tetrads in curved spacetimes. A general procedure exists for solving the parallel transport equations in Petrov-D spacetimes, which contain an extra constant of motion, also called the Carter constant. Two of the components of such tetrad give the propagation and polarization of an electromagnetic wave in geometric optics approximation. Then we should use the parallel propagated tetrad to solve the modified trajectory equation in curved spacetimes. The wavelength-dependent deviation of the electromagnetic waves is observed, which gives the mathematical description of the gravitational Faraday effect in curved spacetimes.

Neutron stars are nuclear physics laboratories, providing a unique opportunity to apply and search for new physics. In that spirit, we explored few new concepts of nuclear physics studied in a neutron star environment: In the first concept, the reported 17 MeV boson, which has been proposed as an explanation to the ⁸Be ,⁴He and ¹²C reported anomalies, is investigated in the context of its possible influence in the neutron star structure, defining a universal Equation of State as well. In the second concept, the synthesis of hyper-heavy elements is investigated under conditions, simulating the neutron star environment.

Motivated by recently explored examples, we undertake a systematic study of conformal invariance in one-dimensional sigma models where an isometry group has been gauged. Perhaps surprisingly, we uncover classes of sigma models which are only scale invariant in their ungauged form and become fully conformally invariant only after gauging. In these cases the target space of the gauged sigma model satisfies a deformation of the well-known conformal geometry constraints. We consider bosonic models as well as their N = 1,2,4 supersymmetric extensions. We solve the quantum ordering ambiguities in implementing (super-) conformal symmetry on the physical Hilbert space. Examples of our general results are furnished by the D(2,1;0)-invariant Coulomb branch quiver models relevant for black hole physics.

Much has been written on the vacuum catastrophe and cosmological constant problem where we have the worst discrepancy between theory and measurement of about a factor of 120 orders of magnitude. In this paper, we improve this discrepancy by more than half which still remains very high, but also propose 3 avenues, one of which is an exciting prediction of a missing bosonic particle, that can help resolve the vacuum catastrophe. The paper builds on the standard theoretical calculation of the vacuum energy density using a quantum harmonic oscillator model and then sums the contributions of all the Standard Model's quantum fields vacuum states. The basis for this calculation is a new Zeta function regularization method used to tame the infinities present in the improper integrals of power functions. The paper also presents a few other findings in the area of vacuum energy.