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Register a new userLocal gravity test of unified models of inflation and dark energy in $f(R)$ gravity
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We consider $f(R)$ gravity theories which unify $R^n$ inflation and dark energy models. First, from the final Planck data of the cosmic microwave background, we obtain a condition, $1.977 < n < 2.003$. Next, under this constraint, we investigate local-gravity tests for three models. We find that the $R^n$ term can dominate over the dark energy term even at the Earths curvature scale, contrary to intuition; however, the $R^n$ term does not relax or tighten the constraints on the three models.
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Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newtons potential given by $f(R)$ gravity. We compute the corrected $N$-particle partition function analytically. The corrected partition function leads to more exact equations of states of the system. By assuming that system follows quasi-equilibrium, we derive the exact distribution function which exhibits the $f(R)$ correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of $f(R)$ gravity on the power law behavior of particle-particle correlation function also. In order to check feasibility of an $f(R)$ gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalog.
We study generalized Misner-Sharp energy in $f(R)$ gravity in a spherically symmetric spacetime. We find that unlike the cases of Einstein gravity and Gauss-Bonnet gravity, the existence of the generalized Misner-Sharp energy depends on a constraint condition in the $f(R)$ gravity. When the constraint condition is satisfied, one can define a generalized Misner-Sharp energy, but it cannot always be written in an explicit quasi-local form. However, such a form can be obtained in a FRW universe and for static spherically symmetric solutions with constant scalar curvature. In the FRW universe, the generalized Misner-Sharp energy is nothing but the total matter energy inside a sphere with radius $r$, which acts as the boundary of a finite region under consideration. The case of scalar-tensor gravity is also briefly discussed.
It is nowadays accepted that the universe is undergoing a phase of accelerated expansion as tested by the Hubble diagram of Type Ia Supernovae (SNeIa) and several LSS observations. Future SNeIa surveys and other probes will make it possible to better characterize the dynamical state of the universe renewing the interest in cosmography which allows a model independent analysis of the distance - redshift relation. On the other hand, fourth order theories of gravity, also referred to as $f(R)$ gravity, have attracted a lot of interest since they could be able to explain the accelerated expansion without any dark energy. We show here how it is possible to relate the cosmographic parameters (namely the deceleration $q_0$, the jerk $j_0$, the snap $s_0$ and the lerk $l_0$ parameters) to the present day values of $f(R)$ and its derivatives $f^{(n)}(R) = d^nf/dR^n$ (with $n = 1, 2, 3$) thus offering a new tool to constrain such higher order models. Our analysis thus offers the possibility to relate the model independent results coming from cosmography to the theoretically motivated assumptions of $f(R)$ cosmology.
In gravity theories derived from a f(R) Lagrangian, matter is usually supposed to be minimally coupled to the metric, which hence defines a ``Jordan frame. However, since the field equations are fourth order, gravity possesses an extra degree of freedom on top of the standard graviton, as is manifest from its equivalent description in the conformally related, Einstein, frame. We introduce explicitly this extra scalar degree of freedom in the action and couple it to matter, so that the original metric no longer defines a Jordan frame. This ``detuning puts f(R) gravity into a wider class of scalar--tensor theories. We argue that a ``chameleon-like detuning tracing the background matter density may provide purely gravitational models which account for the present acceleration of the universe and evade local gravity constraints.
The article presents modeling of inflationary scenarios for the first time in the $f(R,T)$ theory of gravity. We assume the $f(R,T)$ functional from to be $R + eta T$, where $R$ denotes the Ricci scalar, $T$ the trace of the energy-momentum tensor and $eta$ the model parameter (constant). We first investigated an inflationary scenario where the inflation is driven purely due to geometric effects outside of GR. We found the inflation observables to be independent of the number of e-foldings in this setup. The computed value of the spectral index is consistent with latest Planck 2018 dataset while the scalar to tensor ratio is a bit higher. We then proceeded to analyze the behavior of an inflation driven by $f(R,T)$ gravity coupled with a real scalar field. By taking the slow-roll approximation, we generated interesting scenarios where a Klein Gordon potential leads to observationally consistent inflation observables. Our results makes it clear-cut that in addition to the Ricci scalar and scalar fields, the trace of energy momentum tensor also play a major role in driving inflationary scenarios.
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