Gravity In Palatini Formalism Research Articles

Cosmology with a new f(R) gravity model in Palatini formalism

One of the most favorable extensions of General Relativity is the [Formula: see text] gravity. [Formula: see text] gravity in Palatini formalism can be a realistic alternative to the dark energy problem. In this work, we study a recently introduced dark energy [Formula: see text] gravity model along with two other models in cosmological perspectives under the Palatini formalism. First, we study the cosmic expansion history of these models with the help of the important cosmographic parameters, such as the Hubble parameter, luminosity distance, effective equation of state, etc. This study shows that the new model behaves similarly with the other two models as well as with the [Formula: see text]CDM model in some respects in the early or very early phases of the universe. It could predict the present accelerated expansion of the universe somewhat differently from the other models with a peculiar future history of the universe. Within a constrained range of parameters all models show a good agreement with the Union2.1 luminosity distance data. However, the new model shows a quite satisfactory agreement in the whole range of its allowed parameters than that of the other two models. We also obtain cosmological constraints on these models from the observed Hubble data. Further, models have been tested by using [Formula: see text] test and statefinder diagnostics. These diagnostics especially the statefinder diagnostic shows that the evolutionary differences between these models are distinct. The evolutionary trajectories of the new model are completely different from the other two models we have considered.

Some aspects of modified theory of gravity in Palatini formalism unveiled

Under conformal transformation, [Formula: see text] theory of gravity in Palatini formalism leads to a Brans–Dicke type of scalar-tensor equivalent theory with a wrong sign in the effective kinetic energy term. This means that the effective scalar acts as the dark energy and so late-time cosmic acceleration in the matter-dominated era is accountable. However, we unveil some aspects of Palatini formalism, which reveals the fact that the formalism is not suitable to explain the cosmological evolution of the early universe with [Formula: see text] gravity alone. Additionally, it is noticed that some authors, in an attempt to explore Noether symmetry of the theory changed the sign of the kinetic term and hence obtained the wrong answer. Here, we make the correction and unmask a very interesting aspect of symmetry analysis. Mathematical inequivalence between Jordan’s and Einstein’s frame in Palatini [Formula: see text] theory has also been revealed.

Energy Conditions in Palatini Approach to Modified <i>f(R)</i> Gravity

In this paper, we review modified $f(R)$ 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. Energy conditions derived in Palatini version of $f(R)$ 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.

Bianchi I and V cosmologies with Hu-Sawicki f(R) gravity in Palatini formalism

The main objective of this work is the pursuit of a detailed analysis of the cosmological solutions corresponding to each fixed point belonging to an exclusive form of f(R) initially introduced by Hu and Sawicki in the background of Palatini f(R) gravity. Fixed points and their associated solutions for the anisotropic Bianchi type I and V models are derived by utilizing an approach used to solve autonomous ordinary differential equations. Building on this background, an exhaustive study on the phase space is accomplished and the existence of a sequence of evolution that starts from unstable anisotropic universe to a stable phase of late times de Sitter expansion through the standard radiation and matter dominated era has been established.

Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation

We consider, in Palatini formalism, a modified gravity of which the scalar field derivative couples to Einstein tensor. In this scenario, Ricci scalar, Ricci tensor and Einstein tensor are functions of connection field. As a result, the connection field gives rise to relation, $h_{\mu\nu} = f g_{\mu\nu}$ between effective metric, $h_{\mu\nu}$ and the usual metric $g_{\mu\nu}$ where $f \,=\,1 - \kappa{\phi}^{,\alpha}{\phi}_{,\alpha}/2 $. In FLRW universe, NMDC coupling constant is limited in a range of $ -2/ \dot{\phi}^{2} < \kappa \leq \infty $ preserving Lorentz signature of the effective metric. Slowly-rolling regime provides $\kappa < 0$ forbidding graviton from travelling at superluminal speed. Effective gravitational coupling and entropy of blackhole's apparent horizon are derived. In case of negative coupling, acceleration could happen even with $w_{\rm eff} > -1/3$. Power-law potentials of chaotic inflation are considered. For $V \propto \phi^2$ and $V \propto \phi^4$, it is possible to obtain tensor-to-scalar ratio lower than that of GR so that it satisfies $r < 0.12$ as constrained by Planck 2015 \cite{Ade:2015lrj}. The $V \propto \phi^2$ case yields acceptable range of spectrum index and $r$ values. The quartic potential's spectrum index is disfavored by the Planck results. Viable range of $\k$ for $V \propto \phi^2$ case lies in positive region, resulting in less blackhole's entropy, superluminal metric, more amount of inflation, avoidance of super-Planckian field initial value and stronger gravitational constant.

Measurement of the space–time interval in modified gravity theories in Palatini formalism

There are strong motivations that lead cosmologists to consider alternatives to Einstein’s theory of gravity in Palatini formalism. In addition, there are two distinguishable local frames in this formalism in which one of them is local inertial frame and the equivalence principle is satisfied. Different features of speed of light such as the causal structure constant, electromagnetic and gravitational wave velocities and Einstein velocity will not coincide in this local inertial frame for extended gravity theories in Palatini formalism. On the other hand, both the measurement of time and exchange of a signal between the distant points are required to determine spatial distances. In a particular situation where these aspects of the speed of light do not coincide, the distance determination will become more demanding because light will follow a time-like geodesic of the metric. In modified gravity theories in Palatini approach, theories involve a varying speed of photon. Therefore these kinds of theories must be based on some other technique of measuring spatial distances than radar or some terms should be corrected in the line element in the proposed model. We found out we should consider a coefficient which is proportional to energy density in each era, in the line element in order to be able to use radar for measuring distance in modified gravity theories in Palatini formalism. Analysis of some observational data will be affected by considering this coefficient in the line element.

Noether gauge symmetry for f(R) gravity in Palatini formalism

In this study, we consider a flat Friedmann-Robertson-Walker (FRW) universe in the context of Palatini $f(R)$ theory of gravity. Using the dynamical equivalence between $f(R)$ gravity and scalar-tensor theories, we construct a point Lagrangian in the flat FRW spacetime. Applying {\em Noether gauge symmetry approach} for this $f(R)$ Lagrangian we find out the form of $f(R)$ and the exact solution for cosmic scale factor. It is shown that the resulting form of $f(R)$ yield a power-law expansion for the scale factor of the universe.

Constraints of f(R) gravity in Palatini approach with observational Hubble data

We use the newly released observational H(z) data (OHD), the Cosmic Microwave Background (CMB) shift parameter, and the Baryon Acoustic Oscillation (BAO) measurements data to constrain cosmological parameters of f(R) gravity in Palatini formalism in which the f(R) form is defined as f(R) = R − β/Rn. Under the assumption of a spatially flat FRW universe, we get the best fitting results of the free parameters (Ωm0, n). In the calculation, we marginalize the likelihood function over H0 by integrating the probability density \(P \propto e^{{{ - \chi ^2 } \mathord{\left/ {\vphantom {{ - \chi ^2 } 2}} \right. \kern-\nulldelimiterspace} 2}} \) to obtain the best fitting results and the confidence regions in the Ωm0-n plane. The constraints results of (Ωm0, n) = (0.33, 0.41) by OHD only and (Ωm0, n) = (0.23, 0.08) by the combination of OHD+CMB+BAO both indicate that the universe goes through three last phases, i.e., radiation dominated, matter-dominated, and late time accelerated expansion without introduction of dark energy.

Cosmological consequences of exponential gravity in Palatini formalism

We investigate cosmological consequences of a class of exponential f(R) gravity in the Palatini formalism. By using the current largest type Ia Supernova sample along with determinations of the cosmic expansion at intermediary and high-z we impose tight constraints on the model parameters. Differently from other f(R) models, we find solutions of transient acceleration, in which the large-scale modification of gravity will drive the Universe to a new decelerated era in the future. We also show that a viable cosmological history with the usual matter-dominated era followed by an accelerating phase is predicted for some intervals of model parameters.

Scale Transformation, Modified Gravity, and Brans-Dicke Theory

A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless matter with non-vanishing modified terms together with dynamical cosmological and gravitational coupling terms. The obtained modified Einstein equations are neither those in $f(R)$ metric formalism nor the ones in $f({\cal R})$ Palatini formalism, whereas the modified source terms are {\it formally} equivalent to those of $f({\cal R})=\frac{1}{2}{\cal R}^2$ gravity in Palatini formalism. The correspondence between the present model, the modified gravity theory, and Brans-Dicke theory with $\omega=-\frac{3}{2}$ is explicitly shown, provided the dilaton field is condensated to its vacuum state.

Hydrogen atom in Palatini theories of gravity

We study the effects that the gravitational interaction of $f(R)$ theories of gravity in Palatini formalism has on the stationary states of the hydrogen atom. We show that the role of gravity in this system is very important for Lagrangians $f(R)$ with terms that grow at low curvatures, which have been proposed to explain the accelerated expansion rate of the universe. In fact, new gravitationally induced terms in the atomic Hamiltonian generate a strong backreaction that is incompatible with the very existence of bound states. In fact, in the $1/R$ model, hydrogen disintegrates in less than two hours. The universe that we observe is, therefore, incompatible with that kind of gravitational interaction. Lagrangians with high curvature corrections do not lead to such instabilities.

Violation of the Equivalence Principle in Modified Theories of Gravity

We show that the metric in f(R) theories of gravity in Palatini formalism can be solved as the product of a rank-two tensor times a scalar function which is very sensitive to the local energy-momentum densities. This local dependence of the metric generates new gravitationally-induced microscopic interactions, which eventually would lead to self-accelerated test body trajectories. These facts make very unlikely the viability of Palatini f(R) models designed to change the late-time cosmic evolution.