Cosmological dynamics with modified induced gravity on the normal DGP branch

In this Letter we investigate cosmological dynamics on the normal branch of a DGP-inspired scenario within a phase space approach where induced gravity is modified in the spirit of f(R)$f(R)$-theories. We apply the dynamical system analysis to achieve the stable solutions of the scenario in the normal DGP branch. Firstly, we consider a general form of the modified induced gravity and we show that there is a standard de Sitter point in phase space of the model. Then we prove that this point is stable attractor only for those f(R)$f(R)$ functions that account for late-time cosmic speed-up.     

Graviton and scalar propagations on AdS<Subscript>4</Subscript> space in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravities

We investigate propagations of graviton and additional scalar on four-dimensional anti-de Sitter (AdS₄) space using f(R) gravity models with external sources. It is shown that there is the van Dam–Veltman–Zakharov (vDVZ) discontinuity in f(R) gravity models because f(R) gravity implies GR with additional scalar. This clearly indicates a difference between general relativity and f(R) gravity.     

A no-hair theorem for spherically symmetric black holes in $$R^2$$ gravity

In a recent paper Cañate (Class Quantum Grav 35:025018, 2018) proved a no hair theorem to static and spherically symmetric or stationary axisymmetric black holes in general f(R) gravity. The theorem applies for isolated asymptotically flat or asymptotically de Sitter black holes and also in the case when vacuum is replaced by a minimally coupled source having a traceless energy momentum tensor. This theorem excludes the case of pure quadratic gravity, \(f(R) = R^2\). In this paper we use the scalar tensor representation of general f(R) theory to show that there are no hairy black hole in pure \(R^2\) gravity. The result is limited to spherically symmetric black holes but does not assume asymptotic flatness or de-Sitter asymptotics as in most of the no-hair theorems encountered in the literature. We include an example of a static and spherically symmetric black hole in \(R^2\) gravity with a conformally coupled scalar field having a Higgs-type quartic potential.     

Gravitational theories with de Sitter constant vacuum solution

We consider a large class of geometric Lagrangian forms defined in the manifold of the reference frames. The theories described by those Lagrangians are such that, in an empty region, the manifold can be identified with one of the de Sitter groups. The Lagrangian forms are classified according to their symmetry properties with respect to transformation groups acting on the linear space of the infinitesimal transformations of the frames. Requiring invariance with respect to aSO(3) group and a reasonable physical behavior under space reflections, we obtain only three different theories. Then we show that every Lagrangian form of the kind we are considering, is equivalent to anSO(3)-invariant one.     

Letter: On the Newtonian Limit in Gravity Models with Inverse Powers of R

I reconsider the problem of the Newtonian limit in nonlinear gravity models in the light of recently proposed models with inverse powers of R. Expansion around a maximally symmetric local background with curvature scalar R ₀ > 0 gives the correct Newtonian limit on length scales R ₀ ^–1/2 if the gravitational Lagrangian satisfies f(R ₀)f(R₀) 1, and I propose two models with f(R ₀) = 0.     

Gravitational lensing and <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) theories in the Palatini approach

We investigate gravitational lensing in the Palatini approach to the f (R) extended theories of gravity. Starting from an exact solution of the f (R) field equations, which corresponds to the Schwarzschild–de Sitter metric and, on the basis of recent studies on this metric, we focus on some lensing observables, in order to evaluate the effects of the nonlinearity of the gravity Lagrangian. We give estimates for some astrophysical events, and show that these effects are tiny for galactic lenses, but become interesting for extragalactic ones.     

Conservation of Energy,Entropy Identity,and Local Stability for the Spatially Homogeneous Boltzmann Equation

For nonsoft potential collision kernels with angular cutoff, we prove that under the initial condition f ₀(v)(1+|v|²+|logf ₀(v)|)L ¹(R ³), the classical formal entropy identity holds for all nonnegative solutions of the spatially homogeneous Boltzmann equation in the class L ([0, ); L ¹ ₂(R ³))C ¹([0, ); L ¹(R ³)) [where L ¹ _s (R ³)={ff(v)(1+|v|²) ^s/2L ¹(R ³)}], and in this class, the nonincrease of energy always implies the conservation of energy and therefore the solutions obtained all conserve energy. Moreover, for hard potentials and the hard-sphere model, a local stability result for conservative solutions (i.e., satisfying the conservation of mass, momentum, and energy) is obtained. As an application of the local stability, a sufficient and necessary condition on the initial data f ₀ such that the conservative solutions f belong to L ¹ _loc([0, ); L ¹ ₂₊ (R ³)) is also given.     

Does entropic force always imply the Newtonian force law?

We investigate propagations of graviton and additional scalar on four-dimensional anti-de Sitter (AdS₄) space using f(R) gravity models with external sources. It is shown that there is the van Dam–Veltman–Zakharov (vDVZ) discontinuity in f(R) gravity models because f(R) gravity implies GR with additional scalar. This clearly indicates a difference between general relativity and f(R) gravity.     

On the cosmological viability of the Hu-Sawicki type modified induced gravity

It has been shown recently that the normal branch of a DGP braneworld scenario self-accelerates if the induced gravity on the brane is modified in the spirit of f(R) modified gravity. Within this viewpoint, we investigate cosmological viability of the Hu-Sawicki type modified induced gravity. Firstly, we present a dynamical system analysis of a general f(R)-DGP model. We show that in the phase space of the model, there exist three standard critical points; one of which is a de Sitter point corresponding to accelerating phase of the universe expansion. The stability of this point depends on the effective equation of state parameter of the curvature fluid. If we consider the curvature fluid to be a canonical scalar field in the equivalent scalar-tensor theory, the mentioned de Sitter phase is unstable, otherwise it is an attractor, stable phase. We show that the effective equation of state parameter of the model realizes an effective phantom-like behavior. A cosmographic analysis shows that this model, which admits a stable de Sitter phase in its expansion history, is a cosmologically viable scenario.     

Gradient conformal killing vectors and exact solutions

We establish a connection between conformally related Einstein spaces and conformai killing vectors (CKV). We begin with the conformal map and prove that (a) under the conformal mapping¯g _ik=^–2g_ik, the necessary and sufficient condition for the tracefree part of the Ricci tensor (S _ik=R_ik–(R/4)g _ik) to remain invariant is that _i is a CKV ofg _ik, and (b) the most general form for for conformally flat Einstein space, which is the de Sitter space, is composed of three terms each of which alone represents a flat space. The existence of gradient CKV (GCKV) is examined in relation to vacuum and perfect fluid spacetimes.     

Spherical Symmetric Solution in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Model Around Charged Black Hole

A static, asymptotically flat, spherically symmetric solutions is investigated in f(R) theories of gravity for a charged black hole. We have studied the weak field limit of f(R) gravity for the some f(R) model such as f(R)=R+ε h(R). In particular, we consider the case lim  _R→0 h(R)/h′(R)→0 and find the space time metric for f(R)=R+[(m⁴)/(R)]f(R)=R+{\mu^{4}\over R} and f(R)=R ^1+ε theories of gravity far away a charged mass point.     

Screening of cosmological constant in non-local gravity

We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of non-local gravity with the Lagrangian of the form, R+f(^□−1R)−2Λ$R+f({\square }^{-1}R)-2\Lambda$ where f(X)$f(X)$ is a quadratic function of X, there is a flat spacetime solution despite the presence of the cosmological constant Λ. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of ‘time’. Nevertheless our result suggests the possibility of solving the cosmological constant problem in the context of non-local gravity.     

f(R) Cosmology in the First Order Formalism

In the present work we consider those theories that are obtained from a Lagrangian density _T (R) = f(R){-g} + _M , that depends on the curvature scalar and a matter Lagrangian that does not depend on the connection, and apply Palatini's method to obtain the field equations. We start with a brief discussion of the field equations of the theory and apply them to a cosmological model described by the FRW metric. Then, we introduce an auxiliary metric to put the resultant equations into the form of GR with cosmological constant and coupling constant that are curvature depending. We show that we reproduce known results for the quadratic case. We find relations among the present values of the cosmological parameters q ₀, H ₀, and . Next we use a simple perturbation scheme to find the departure in angular diameter distance with respect to General Relativity. Finally, we use the observational data to estimate the order of magnitude of what is essentially the departure of f(R) from linearity. The bound that we find for f (0) is so huge that permit almost any f(R). This is in the nature of things: the effect of higher order terms in f(R) are strongly suppressed by power of Planck's time 8G ₀. In order to improve these bounds more research on mathematical aspects of these theories and experimental consequences is necessary.     

Spherically symmetric vacuum solutions of modified gravity theory in higher dimensions

In this paper we investigate spherically symmetric vacuum solutions of f(R) gravity in a higher-dimensional spacetime. With this objective we construct a system of non-linear differential equations whose solutions depend on the explicit form assumed for the function F(R)=\fracdf(R)dRF(R)=\frac{df(R)}{dR} . We explicit show that for specific classes of this function exact solutions from the field equations are obtained; also we find approximated results for the metric tensor for more general cases admitting F(R) close to the unity.     

Disappearing cosmological constant in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

For higher-derivative f(R) gravity, where R is the Ricci scalar, a class of models is proposed, which produce viable cosmology different from the ACDM at recent times and satisfy cosmological, Solar System, and laboratory tests. These models have both flat and de Sitter spacetimes as particular solutions in the absence of matter. Thus, a cosmological constant is zero in a flat spacetime, but appears effectively in a curved one for sufficiently large R. A “smoking gun” for these models would be a small discrepancy in the values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed out, which is connected with the possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe. The text was submitted by the author in English.     

On Diffusive Equilibria in Generalized Kinetic Theory

We investigate the solvability of equations Q(f,f)+ ² f=0 in term of nonnegative integrable densities fL ¹ ₊(R ³). Here, Q(f, f) is a generalized collision operator. If Q is the Boltzmann operator, the only solution is 0. In contrast, we show that if Q is the pseudo-Maxwellian collision operator for granular flow, then there are non -trivial weak solutions of ().     

De Sitter superalgebras and supergravity

A general analysis of all possible super-extensions of anti-de Sitter and de Sitter algebrasO(3, 2) andO(4, 1) is presented. It is shown that actions with de Sitter local supersymmetry exist, but contain vector-ghosts.Supported in part by the NSF under grant PHY 81-09110 A-01On leave from the Institute of Theoretical Physics, University of Wrocaw, Wrocaw, Poland     

Nonminimal Derivative Couplings and Inflation in Generalized Theories of Gravity

We study extended theories of gravity where nonminimal derivative couplings of the form R^klϕ,_kϕ,_l are present in the Lagrangian. We show how and why the other couplings of similar structure may be ruled out and then deduce the field equations and the related cosmological models. Finally, we get inflationary solutions which do follow neither from any effective scalar field potential nor from a cosmological constant introduced “by hand”, and we show the de Sitter space‐time to be an attractor solution.