Geometrical diagnostic methods were often applied to distinguish the gravitational models. But it is scarce to investigate the differences between the different formalisms of modified gravitational theories (e.g. the ...Geometrical diagnostic methods were often applied to distinguish the gravitational models. But it is scarce to investigate the differences between the different formalisms of modified gravitational theories (e.g. the metric formalism and the Palatini formalism). In this paper, we discriminate the gravitational theory with the different formalisms by using the geometrical diagnostic methods. For a considered modified theory of gravity (e.g. the f(R) theory or GBD theory), we can see that the difference between the two formalisms is remarkable according to the diagnostic results. And relative to the ΛCDM model, there are more deviations in metric formalism than those in Palatini formalism, according to the {r, s} diagnostic. Given that the GBD (generalized Brans-Dicke theory) is a time-variable Newton gravitational constant (VG) theory, the differences between the VG theory and the constant-G theory are studied. It indicates that the variation of Newton’s gravitational constant could induce notable effects on geometrical quantities (e.g. r, s and q) in both metric formalism and Palatini formalism.展开更多
In this paper, we review modified <i>f(R)</i> theories of gravity in Palatini formalism. In this framework, we use the Raychaudhuri’s equation along with the requirement that the gravity is attractive, wh...In this paper, we review modified <i>f(R)</i> theories of gravity in Palatini formalism. In this framework, we use the Raychaudhuri’s equation along with the requirement that the gravity is attractive, which holds for any geometrical theory of gravity to discuss the energy conditions. Then, to derive these conditions, we obtain an expression for effective pressure and energy density by considering FLRW metric. To simply express the energy conditions, we write the Ricci scalar and its derivatives in terms of the deceleration (<i>q</i>), jerk (<i>j</i>) and snap (<i>s</i>) parameters. Energy conditions derived in Palatini version of <i>f(R)</i> Gravity differ from those derived in GR. We will see that the WEC (weak energy condition) derived in Palatini formalism has exactly the same expression in its metric approach.展开更多
文摘Geometrical diagnostic methods were often applied to distinguish the gravitational models. But it is scarce to investigate the differences between the different formalisms of modified gravitational theories (e.g. the metric formalism and the Palatini formalism). In this paper, we discriminate the gravitational theory with the different formalisms by using the geometrical diagnostic methods. For a considered modified theory of gravity (e.g. the f(R) theory or GBD theory), we can see that the difference between the two formalisms is remarkable according to the diagnostic results. And relative to the ΛCDM model, there are more deviations in metric formalism than those in Palatini formalism, according to the {r, s} diagnostic. Given that the GBD (generalized Brans-Dicke theory) is a time-variable Newton gravitational constant (VG) theory, the differences between the VG theory and the constant-G theory are studied. It indicates that the variation of Newton’s gravitational constant could induce notable effects on geometrical quantities (e.g. r, s and q) in both metric formalism and Palatini formalism.
文摘In this paper, we review modified <i>f(R)</i> theories of gravity in Palatini formalism. In this framework, we use the Raychaudhuri’s equation along with the requirement that the gravity is attractive, which holds for any geometrical theory of gravity to discuss the energy conditions. Then, to derive these conditions, we obtain an expression for effective pressure and energy density by considering FLRW metric. To simply express the energy conditions, we write the Ricci scalar and its derivatives in terms of the deceleration (<i>q</i>), jerk (<i>j</i>) and snap (<i>s</i>) parameters. Energy conditions derived in Palatini version of <i>f(R)</i> Gravity differ from those derived in GR. We will see that the WEC (weak energy condition) derived in Palatini formalism has exactly the same expression in its metric approach.
