Inflation from the Symmetry of the Generalized Cosmological Model

It is shown that the inflationary model is the result of the symmetry of the generalized F(R,T,X,φ)-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case of cosmological models F(R,X,φ) and F(T,X,φ) the Monge–Ampère equation is still obtained, one of the solutions including the Starobinsky model. For these models, it is shown that one can obtain both power-law and exponential solutions for the scale factor from the Euler–Lagrange equations. In this case, the scalar field φ has similar time dependences, exponential and exponential. The resulting form of the Lagrangian of the model allows us to consider it as a model with R2 or X2. However, it is also shown that previously less studied models with a non-minimal relationship between R and X are important, as one of the possible models. It is shown that in this case the power-law model can have a limited evolutionary period with a negative value of the kinetic term.

Compact objects by gravitational decoupling in f(R) gravity

The objective of this paper is to discuss anisotropic solutions representing static spherical self-gravitating systems in f(R) theory. We employ the extended gravitational decoupling approach and transform temporal as well as radial metric potentials which decomposes the system of non-linear field equations into two arrays: one set corresponding to seed source and the other one involves additional source terms. The domain of the isotropic solution is extended in the background of f(R) Starobinsky model by employing the metric potentials of Krori–Barua spacetime. We determine two anisotropic solutions by employing some physical constraints on the extra source. The values of unknown constants are computed by matching the interior and exterior spacetimes. We inspect the physical viability, equilibrium and stability of the obtained solutions corresponding to the star Her X-I. It is observed that one of the two extensions satisfies all the necessary physical requirements for particular values of the decoupling parameter.

Note on the reheating temperature in Starobinsky-type potentials

The relation between the reheating temperature, the number of e-folds and the spectral index is shown for the Starobinsky model and some of its descendants through a very detailed calculation of these three quantities. The conclusion is that for viable temperatures between 1 MeV and $$10^9$$ 10 9 GeV the corresponding values of the spectral index enter perfectly in its $$2\sigma $$ 2 σ C.L., which shows the viability of this kind of models.

Viability tests of f(R)-gravity models with Supernovae Type 1A data

In this work, we will be testing four different general f(R)-gravity models, two of which are the more realistic models (namely the Starobinsky and the Hu–Sawicki models), to determine if they are viable alternative models to pursue a more vigorous constraining test upon them. For the testing of these models, we use 359 low- and intermediate-redshift Supernovae Type 1A data obtained from the SDSS-II/SNLS2 Joint Light-curve Analysis (JLA). We develop a Markov Chain Monte Carlo (MCMC) simulation to find a best-fitting function within reasonable ranges for each f(R)-gravity model, as well as for the Lambda Cold Dark Matter ($$\varLambda $$ΛCDM) model. For simplicity, we assume a flat universe with a negligible radiation density distribution. Therefore, the only difference between the accepted $$\varLambda $$ΛCDM model and the f(R)-gravity models will be the dark energy term and the arbitrary free parameters. By doing a statistical analysis and using the $$\varLambda $$ΛCDM model as our “true model”, we can obtain an indication whether or not a certain f(R)-gravity model shows promise and requires a more in-depth view in future studies. In our results, we found that the Starobinsky model obtained a larger likelihood function value than the $$\varLambda $$ΛCDM model, while still obtaining the cosmological parameters to be $$\varOmega _{m} = 0.268^{+0.027}_{-0.024}$$Ωm=0.268-0.024+0.027 for the matter density distribution and $${\bar{h}} = 0.690^{+0.005}_{-0.005}$$h¯=0.690-0.005+0.005 for the Hubble uncertainty parameter. We also found a reduced Starobinsky model that are able to explain the data, as well as being statistically significant.

Dynamics of collapsing stellar filament and exotic matter

This paper studies the collapse of stellar filaments in the presence of dark matter (DM). We use [Formula: see text] gravity to involve DM in the collapse. We apply Darmois junction conditions (DJCs) on the surface of collapsing boundary [Formula: see text] and obtain the collapse equation. The radial pressure associated with the seen matter is found to be nonzero at [Formula: see text]. We then use Starobinsky model, [Formula: see text], as a candidate of DM to obtain stability criteria (SC) of the collapsing body. It is found that the stability of filamentary structure relates radial pressure of baryonic directly with the gravitational effects of DM. Stability of polytropic family of filaments are studied by applying polytropic equation of state to baryonic contribution. For all polytropic stable filaments, it turns out that the visible matter density is exponentially linked to effects of DM. Finally, we discuss connection between exotic terms and gravitational waves (GW). It is theoretically indicated that the presence of DM can affect the GW propagation.

Supergravity as the Dark Side of the Universe

The Dark Side of the Universe, which includes the cosmological inflation in the early Universe, the current dark energy and dark matter, can be theoretically described by supergravity, though it is non-trivial. We recall the arguments pro and contra supersymmetry and supergravity, and define the viable supergravity models describing the Dark Side of the Universe in agreement with all current observations. Our approach to inflation is based on the Starobinsky model, the dark energy is identified with the positive cosmological constant (de Sitter vacuum), and the dark matter particle is given by the lightest superparticle identified with the supermassive gravitino. The key role is played by spontaneous supersymmetry breaking.