Narrow Results

We propose a dynamical (quintessence) model of dark energy in the current Universe with a renormalizable (Higgs-like) scalar potential. We prove the viability of our model (after fine-tuning) for the certain range of the average scalar curvature values, and study the cosmological signatures distinguishing our model from the standard description of dark energy in terms of a cosmological constant.

In string theory with ten dimensions, all Dp-branes are constructed from D0-branes whose action has two-dimensional brackets of Lie 2-algebra. Also, in M-theory, with 11 dimensions, all Mp-branes are built from M0-branes whose action contains three-dimensional brackets of Lie 3-algebra. In these theories, the reason for difference between bosons and fermions is unclear and especially in M-theory there is not any stable object like stable M3-branes on which our universe would be formed on it and for this reason it cannot help us to explain cosmological events. For this reason, we construct G-theory with M dimensions whose branes are formed from G0-branes with N-dimensional brackets. In this theory, we assume that at the beginning there is nothing. Then, two energies, which differ in their signs only, emerge and produce 2M degrees of freedom. Each two degrees of freedom create a new dimension and then M dimensions emerge. M-N of these degrees of freedom are removed by symmetrically compacting half of M-N dimensions to produce Lie-N-algebra. In fact, each dimension produces a degree of freedom. Consequently, by compacting M-N dimensions from M dimensions, N dimensions and N degrees of freedom is emerged. These N degrees of freedoms produce Lie-N-algebra. During this compactification, some dimensions take extra i and are different from other dimensions, which are known as time coordinates. By this compactification, two types of branes, Gp and anti-Gp-branes, are produced and rank of tensor fields which live on them changes from zero to dimension of brane. The number of time coordinates, which are produced by negative energy in anti-Gp-branes, is more sensible to number of times in Gp-branes. These branes are compactified anti-symmetrically and then fermionic superpartners of bosonic fields emerge and supersymmetry is born. Some of gauge fields play the role of graviton and gravitino and produce the supergravity. The question may arise that what is the physical reason which shows that this theory is true. We shown that G-theory can be reduced to other theories like nonlinear gravity theories in four dimensions. Also, this theory, can explain the physical properties of fermions and bosons. On the other hand, this theory explains the origin of supersymmetry. For this reason, we can prove that this theory is true. By reducing the dimension of algebra to three and dimension of world to 11 and dimension of brane to four, G-theory is reduced to F(R)-gravity.

We deal with the duality symmetry of the dilaton field in cosmology and specifically with the so-called Gasperini–Veneziano duality transformation. In particular, we determine two conformal equivalent theories to the dilaton field, and we show that under conformal transformations Gasperini–Veneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the dilaton field. Finally, we show that the Lagrangian of the dilaton field is equivalent with the two-dimensional “hyperbolic oscillator” in a Lorentzian space whose O(d, d) invariance is transformed into the Gasperini–Veneziano duality invariance in the original coordinates.

The source theory provides a straightforward way to obtain the Newton’s potential upon establishing the vacuum-to-vacuum transition amplitude in quantized Einstein theory of gravity. Here, we use the same method to derive the gravitational potential of two static point masses in f(R) = R + aR² gravity.

Mazharimousavi and Halilsoy [S. H. Mazharimousavi and M. Halilsoy, Mod. Phys. Lett. A31, 1650192 (2016)] recently proposed wormhole solutions in f(R)-gravity that satisfy energy conditions but are unstable. We show here that stability could still be achieved for thin-shell wormholes obtained by gluing the wormholes in f(R)-gravity with the exterior Schwarzschild vacuum. Using the new geometrical constraints from thin-shell “mass” and from external “force” developed by Garcia, Lobo and Visser, we demarcate and analyze the stability regions.

We discuss the existence and properties of a nontrivial fixed point in f(R)-gravity, where f is a polynomial of order up to six. Within this seven-parameter class of theories, the fixed point has three ultraviolet-attractive and four ultraviolet-repulsive directions; this brings further support to the hypothesis that gravity is nonperturbatively renormalizable.

We consider super-inflating solutions in modified gravity for several popular families of f(R) functions. Using scalar field reformulation of f(R)-gravity we describe how the form of effective scalar field potential can be used for explaining existence of stable super-inflation solutions in the theory under consideration. Several new solutions of this type have been found analytically and checked numerically.

In this work, we obtain the black hole solutions in the dilaton $f(R)$-gravity (R is not considered as a constant here) and investigate their thermodynamics especially phase transition and critical behavior in the anti-de Sitter (AdS) extended phase-space. We obtain the exact Banados, Teitelboim and Zanelli (BTZ) counterpart solutions in dilaton $f(R)$-gravity which is the basis of our work. We also obtain the exact form of $f(R)$ model for some solutions. In the thermodynamical analysis, we calculate the thermodynamical quantities like the temperature and entropy for these solutions and we compare them with the BTZ corresponding quantities. After that, we investigate the stability (local and global) for these obtained solutions. In the critical behavior analysis, we find that there is no evidence to show the existence of P–V criticality (like the ordinary BTZ case) in this modified gravity model except some unusual P–V behavior in the corresponding diagrams.

The new model of modified F(R)-gravity theory with the function F(R) = R + (a/γ) arcsin(γR) is suggested and investigated. Constant curvature solutions corresponding to the extremum of the effective potential are obtained. We consider both the Jordan and Einstein frames, and the potential and the mass of the scalar degree of freedom are found. It was shown that the de Sitter space-time is unstable but the flat space-time is stable. We calculate the slow-roll parameters ϵ, η, and the e-fold number of the model. Critical points of autonomous equations for the de Sitter phase and the matter dominated epoch are obtained and learned.

Sobouti proposes an action-based $f(R)$ modification of Einstein’s gravity, which admits a similar Schwarzschild metric. A test star moving in such a space–time acquires a constant asymptotic speed at large distances. As we are concerned with two classical tests of Einstein’s theory which are gravitational red shift of spectral lines and time delay of radar echo passing the sun, we shall calculate them in the $f(R)$-gravity and show that the results are consistent with the experimental observation data.

A new theory, named G(General)-theory in 14 dimensions, has been proposed that is reduced to $F(R)$-gravity and produces the metric of FRW universe in four dimensions. In this theory, the Universe is born in six stages. First, there is nothing in the world. Then, two strings, one with positive energy and one with negative energy in 14th, dimension are created such that the sum over their energies is zero. These strings are excited and for flowing their energies, other dimensions are produced. Second, these strings decay to G0-branes. Third, these branes join each other and construct Gp-branes which tensor fields live on. The rank of these fields can change from zero to p for $p\le 6$ and from zero to six for $p>6$. Four, by compacting Gp-branes on three circles, supersymmetry is born which contains the equal number of degrees of freedom for fermions and bosons. Six, by reducing G-theory to four dimensions, FRW universe is emerges and initial tensor fields produce the predicted shape of $F(R)$-gravity.

In general, a perfect fluid spacetime is not a generalized Robertson–Walker spacetime and the converse is also not true. In this paper, it is shown that if a perfect fluid spacetime satisfies the critical point equation, then either the spacetime becomes a generalized Robertson–Walker spacetime and represents dark era or the vorticity of the fluid vanishes as well as the spacetime is expansion free. Besides, we prove that if a generalized Robertson–Walker spacetime with constant scalar curvature satisfies the critical point equation, then the spacetime becomes a perfect fluid spacetime. Next, the existence of critical point equation is established by a non-trivial example. Finally, we discuss the critical point equation in $f(r)$-gravity. For the model $f(r)=r-\alpha (1-e^{-\frac{r}{\alpha }})$ ($\alpha$ = constant and $r$ is the scalar curvature of the spacetime), various energy conditions in terms of the scalar curvature are examined and state that the Universe is in an accelerating phase and satisfies the weak, null, dominant, and strong energy conditions.

In this paper, we give some classification of conformally harmonic $Z$-recurrent spacetime in the context of $F(R)$-gravity theory based on its scalar curvature and obtained the expression for energy density and isotopic pressure. Their behaviors along with EoS parameter are analyzed by considering two $F(R)$-gravity models. Moreover, the energy conditions for the considered models are studied and found to support the accelerated expansion of the universe.

We develop the parameterized post-Keplerian approach for class of analytic $f(R)$-gravity models. Using the double binary pulsar system PSR J0737-3039 data we obtain restrictions on the parameters of this class of $f(R)$-models and show that $f(R)$-gravity is not ruled out by the observations in strong field regime. The additional and more strong corresponding restriction is extracted from solar system data.

We develop the parameterized post-Keplerian approach for class of analytic f(R)-gravity models. Using the double binary pulsar system PSR J0737-3039 data we obtain restrictions on the parameters of this class of f(R)-models and show that f(R)-gravity is not ruled out by the observations in strong field regime.