In this paper, we have introduced a new f(R) gravity model as an attempt to have a model with more parametric control, so that the model can be used to explain the existing problems as well as to explore new directions in physics of gravity, by properly constraining it with recent observational data. Here basic aim is to study the properties of Gravitational Waves (GWs) in this new model. In f(R) gravity metric formalism, the model shows the existence of scalar degree of freedom as like other f(R) gravity models. Due to this reason, there is a scalar mode of polarization of GWs present in the theory. This polarization mode exists in a mixed state, of which one is transverse massless breathing mode with non-vanishing trace and the other is massive longitudinal mode. The longitudinal mode being massive, travels at speed less than the usual tensor modes found in General Relativity (GR). Moreover, for a better understanding of the model, we have studied the potential and mass of scalar graviton in both Jordan frame and Einstein frame. This model can pass the solar system tests and can explain primordial and present dark energy. Also, we have put constraints on the model. It is found that the correlation function for the third mode of polarization under certain mass scale predicted by the model agrees well with the recent data of Pulsar Timing Arrays. It seems that this new model would be useful in dealing with different existing issues in the areas of astrophysics and cosmology.

The links between the deformation parameter $$\beta $$β of the generalized uncertainty principle (GUP) to the two free parameters $$\hat{\omega }$$ω^ and $$\gamma $$γ of the running Newtonian coupling constant of the Asymptotic Safe gravity (ASG) program, has been conducted recently in [Phys. Rev. D 105 (2022) 12, 124054. https://doi.org/10.1103/PhysRevD.105.124054] In this paper, we test these findings by calculating and examining the shadow and quasinormal modes of black holes, and demonstrate that the approach provides a theoretical framework for exploring the interplay between quantum gravity and GUP. Our results confirm the consistency of ASG and GUP, and offer new insights into the nature of black holes and their signatures. The implications of these findings for future studies in quantum gravity are also discussed.

In this work, we have studied the quasinormal modes of a black hole in a model of the type $$f(Q)=\underset{n}{\sum }a_{n}\left( Q-Q_{0}\right) ^{n} $$f ( Q ) = ∑ n a n Q - Q 0 n in f(Q) gravity by using a recently introduced method known as Bernstein spectral method and confirmed the validity of the method with the help of well known Padé averaged higher order WKB approximation method. Here we have considered scalar perturbation and electromagnetic perturbation in the black hole spacetime and obtained the corresponding quasinormal modes. We see that for a non-vanishing nonmetricity scalar $$Q_0$$Q 0 , quasinormal frequencies in scalar perturbation are greater than those in electromagnetic perturbation scenarios. On the other hand, the damping rate of gravitational waves is higher for electromagnetic perturbation. To confirm the quasinormal mode behaviour, we have also investigated the time domain profiles for both types of perturbations.

We study the tideless traversable wormholes in the f(R) gravity metric formalism. First we consider three shape functions of wormholes and study their viabilities and structures. The connection between the f(R) gravity model and wormhole shape function has been studied and the dependency of the f(R) gravity model with the shape function is shown. We also obtain a wormhole solution in the f(R) gravity Starobinsky model surrounded by a cloud of strings. In this case, the wormhole shape function depends on both the Starobinsky model parameter and the cloud of strings parameter. The structure and height of the wormhole is highly affected by the cloud of strings parameter, while it is less sensitive to the Starobinsky model parameter. The energy conditions have been studied and we found the ranges of the null energy condition violation for all wormhole structures. The quasinormal modes from these wormhole structures for the scalar and Dirac perturbations are studied using higher order WKB approximation methods. The quasinormal modes for the toy shape functions depend highly on the model parameters. In case of the Starobinsky model's wormhole the quasinormal frequencies and the damping rate increase with an increase in the Starobinsky model parameter in scalar perturbation. Whereas in Dirac perturbation, with an increase in the Starobinsky model parameter the quasinormal frequencies decrease and the damping rate increases. The cloud of strings parameter also impacts prominently and differently the quasinormal modes from the wormhole in the Starobinsky model.