Narrow Results

In this paper, we conduct a study on the scalar field obtained from $f(R)$ gravity via Weyl transformation of the spacetime metric $g_{\mu \nu }$ from the Jordan frame to the Einstein frame. The scalar field is obtained as a result of the modification in the geometrical part of Einstein’s field equation of General Relativity. For the Hu–Sawicki model of $f(R)$ gravity, we find the effective potential of the scalar field and calculate its mass. Our study shows that the scalar field (also named as scalaron) obtained from this model has the chameleonic property, i.e. the scalaron becomes light in the low-density region, while it becomes heavy in the high-density region of matter. Then it is found that the scalaron can be regarded as a dark matter (DM) candidate since the scalaron mass is found to be quite close to the mass of ultralight axions, a prime DM candidate. Thus, the scalaron in the Hu–Sawicki model of $f(R)$ gravity behaves as DM. Further, a study on the evolution of the scalaron mass with the redshift is also carried out, which depicts that scalaron becomes light with expansion of the Universe and with different rates at different stages of the Universe.

The conventional Friedmann cosmology is known to be in tension with the existence of stable particles having interaction strength typical for supersymmetry and heavier than several TeV. A possible way to save life of such particles may be a modification of the standard cosmological expansion law in such a way that the density of these heavy relics would be significantly reduced. We study particle creation in the Starobinsky inflationary model for different decay channels of the scalaron. It is shown that the process of thermalization superheavy stable particles with the coupling strength typical for the GUT SUSY could be created with the density equal to the observed density of dark matter.

In this paper, the modified $F(R)$ gravity theory with the function $F(R)=-(1/\beta )ln(1-\beta R)$ is studied. The action at small coupling $\beta$ becomes Einstein–Hilbert action. The bound on the parameter $\beta$ from local tests is $\beta \le 2\times 10^{-6}$ cm². We find the constant curvature solutions and it was shown that the de Sitter space is unstable but a solution with zero Ricci scalar is stable. The potential and the mass of the scalar field (scalaron) are obtained in Einstein’s frame. The slow-roll cosmological parameters are studied and e-folds number is evaluated. The critical points of autonomous equations are analyzed. The function $m(r)$ that describes the deviation from the $\mathrm{\Lambda }$CDM model is calculated.

The fixed points for the dynamical system in the phase space have been calculated with dark matter in the $f(R)$ gravity models. The stability conditions of these fixed points are obtained in the ongoing accelerated phase of the universe, and the values of the Hubble parameter and Ricci scalar are obtained for various evolutionary stages of the universe. We present a range of some modifications of general relativistic action consistent with the $\mathrm{\Lambda }$CDM model. We elaborate upon the fact that the upcoming cosmological observations would further constrain the bounds on the possible forms of $f(R)$ with greater precision that could in turn constrain the search for dark matter in colliders.

The cosmology has made enormous progress after the construction of General Relativity (GR) in 1915. The theoretical predictions of GR — such as the existence of black holes and gravitational waves — have been directly/indirectly confirmed by observations. Now, we know that GR is sufficiently dependable to describe the gravitational law in the solar system.