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Register a new userNeutron stars in $f(R)$ gravity and scalar-tensor theories
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In $f(R)$ gravity and Brans-Dicke theory with scalar potentials, we study the structure of neutron stars on a spherically symmetric and static background for two equations of state: SLy and FPS. In massless BD theory, the presence of a scalar coupling $Q$ with matter works to change the star radius in comparison to General Relativity, while the maximum allowed mass of neutron stars is hardly modified for both SLy and FPS equations of state. In Brans-Dicke theory with the massive potential $V(phi)=m^2 phi^2/2$, where $m^2$ is a positive constant, we show the difficulty of realizing neutron star solutions with a stable field profile due to the existence of an exponentially growing mode outside the star. As in $f(R)$ gravity with the $R^2$ term, this property is related to the requirement of extra boundary conditions of the field at the surface of star. For the self-coupling potential $V(phi)=lambda phi^4/4$, this problem can be circumvented by the fact that the second derivative $V_{,phi phi}=3lambdaphi^2$ approaches 0 at spatial infinity. In this case, we numerically show the existence of neutron star solutions for both SLy and FPS equations of state and discuss how the mass-radius relation is modified as compared to General Relativity.
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The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in $f(R)$ gravity and Horndeski theory, both containing scalar modes. These theories predict that in addition to the familiar $+$ and $times$ polarizations, there are transverse breathing and longitudinal polarizations excited by the massive scalar mode and the new polarization is a single mixed state. It would be very difficult to detect the longitudinal polarization by interferometers, while pulsar timing array may be the better tool to detect the longitudinal polarization.
In this work we study a modified version of vacuum $f(R)$ gravity with a kinetic term which consists of the first derivatives of the Ricci scalar. We develop the general formalism of this kinetic Ricci modified $f(R)$ gravity and we emphasize on cosmological applications for a spatially flat cosmological background. By using the formalism of this theory, we investigate how it is possible to realize various cosmological scenarios. Also we demonstrate that this theoretical framework can be treated as a reconstruction method, in the context of which it is possible to realize various exotic cosmologies for ordinary Einstein-Hilbert action. Finally, we derive the scalar-tensor counterpart theory of this kinetic Ricci modified $f(R)$ gravity, and we show the mathematical equivalence of the two theories.
We study the screening mechanism in the most general scalar-tensor theories that leave gravitational waves unaffected and are thus compatible with recent LIGO/Virgo observations. Using the effective field theory of dark energy approach, we consider the general action for perturbations beyond linear order, focussing on the quasi-static limit. When restricting to the subclass of theories that satisfy the gravitational wave constraints, the fully nonlinear effective Lagrangian contains only three independent parameters. One of these, $beta_1$, is uniquely present in degenerate higher-order theories. We compute the two gravitational potentials for a spherically symmetric matter source and we find that for $beta_1 ge 0$ they decrease as the inverse of the distance, as in standard gravity, while the case $beta_1 < 0$ is ruled out. For $beta_1 > 0$, the two potentials differ and their gravitational constants are not the same on the inside and outside of the body. Generically, the bound on anomalous light bending in the Solar System constrains $beta_1 lesssim 10^{-5}$. Standard gravity can be recovered outside the body by tuning the parameters of the model, in which case $beta_1 lesssim 10^{-2}$ from the Hulse-Taylor pulsar.
In literature there is a model of modified gravity in which the matter Lagrangian is coupled to the geometry via trace of the stress-energy momentum tensor $T=T_{mu}^{mu}$. This type of modified gravity is called as $f(R,T)$ in which $R$ is Ricci scalar $R=R_{mu}^{mu}$. We extend manifestly this model to include the higher derivative term $Box R$. We derived equation of motion (EOM) for the model by starting from the basic variational principle. Later we investigate FLRW cosmology for our model. We show that de Sitter solution is unstable for a generic type of $f(R,Box R, T)$ model. Furthermore we investigate an inflationary scenario based on this model. A graceful exit from inflation is guaranteed in this type of modified gravity.
We focus on a series of $f(R)$ gravity theories in Palatini formalism to investigate the probabilities of producing the late-time acceleration for the flat Friedmann-Robertson-Walker (FRW) universe. We apply statefinder diagnostic to these cosmological models for chosen series of parameters to see if they distinguish from one another. The diagnostic involves the statefinder pair ${r,s}$, where $r$ is derived from the scale factor $a$ and its higher derivatives with respect to the cosmic time $t$, and $s$ is expressed by $r$ and the deceleration parameter $q$. In conclusion, we find that although two types of $f(R)$ theories: (i) $f(R) = R + alpha R^m - beta R^{-n}$ and (ii) $f(R) = R + alpha ln R - beta$ can lead to late-time acceleration, their evolutionary trajectories in the $r-s$ and $r-q$ planes reveal different evolutionary properties, which certainly justify the merits of statefinder diagnostic. Additionally, we utilize the observational Hubble parameter data (OHD) to constrain these models of $f(R)$ gravity. As a result, except for $m=n=1/2$ of (i) case, $alpha=0$ of (i) case and (ii) case allow $Lambda$CDM model to exist in 1$sigma$ confidence region. After adopting statefinder diagnostic to the best-fit models, we find that all the best-fit models are capable of going through deceleration/acceleration transition stage with late-time acceleration epoch, and all these models turn to de-Sitter point (${r,s}={1,0}$) in the future. Also, the evolutionary differences between these models are distinct, especially in $r-s$ plane, which makes the statefinder diagnostic more reliable in discriminating cosmological models.
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