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We study scalar field FLRW cosmology in the content of f( R) gravity. Our consideration is restricted to the spatially flat Friedmann universe. We derived the general evolution equations of the model, and showed that the scalar field equation is automatically satisfied for any form of the f( R) function. We also derived representations for kinetic and potential energies, as well as for the acceleration in terms of the Hubble parameter and the form of the f( R) function. Next we found the exact cosmological solutions in modified gravity without specifying the f( R) function. With negligible acceleration of the scalar curvature, we found that the de Sitter inflationary solution is always attained. Also we obtained new solutions with special restrictions on the integration constants. These solutions contain oscillating, accelerating, decelerating and even contracting universes. For further investigation, we selected special cases which can be applied with early or late inflation. We also found exact solutions for the general case for the model with negligible acceleration of the scalar curvature in terms of special Airy functions. Using initial conditions which represent the universe at the present epoch, we determined the constants of integration. This allows for the comparison of the scale factor in the new solutions with that for current stage of the universe evolution in the CDM model. [ABSTRACT FROM AUTHOR]

We study gravity models in the language of scalar-tensor (ST) theories. The correspondence between gravity and ST theories is revisited since gravity is a subclass of Brans-Dicke models, with a vanishing coupling constant (). In this treatment, four toy models are used to analyze the early-universe cosmology, when the scalar field dominates over standard matter. We have obtained solutions to the Klein-Gordon equation for those models. It is found that for the first model , as time increases the scalar field decreases and decays asymptotically. For the second model , it was found that the function crosses the -axis at different values for different values of . For the third model , when the value of is small, the potential behaves like the standard inflationary potential. For the fourth model , we show that there is a transition between . The behavior of the potentials with is totally different from those with . The slow-roll approximation is applied to each of the four models and we obtain the respective expressions for the spectral index and the tensor-to-scalar ratio . [ABSTRACT FROM AUTHOR]

In this paper we study the dynamics of the universe in Friedmann-Robertson-Walker models including perfect fluid and coupled scalar field with nonzero scalar potential in higher derivative theory of gravitation. We study the evolution of the universe by assuming the scalar potential and scale factor as functions of the scalar field. Exact cosmological solutions are obtained for flat, closed and open models, which are physically interesting for the description of the present-day universe. The properties of scalar field and other physical parameters are discussed in detail. Some special cases have been studied by imposing certain constraints on constants to discuss the decelerated and accelerated phases of the universe. [ABSTRACT FROM AUTHOR]

This paper studies the cosmological equations for a scalar field φ in the framework of a quantum gravity modified Einstein–Hilbert Lagrangian where G and Λ are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Λ = Λ(G) and the potential V = V(φ) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, the additional variable being the running Newton coupling. [ABSTRACT FROM AUTHOR]

In the brane-world framework, we consider static, spherically symmetric configurations of a scalar field with the Lagrangian (∂ϕ)2/2-V(ϕ), confined on the brane. We use the 4D Einstein equations on the brane obtained by Shiromizu et al., containing the conventional stress tensor $T_\mu^\nu$, the tensor $\Pi_\mu^\nu$ which is quadratic in $T_\mu^\nu$, and $E_\mu^\nu$ describing interaction with the bulk. For models under study, the tensor $\Pi_\mu^\nu$ has zero divergence, allowing one to consider $E_\mu^\nu =0$. Such a brane, whose 4D gravity is decoupled from the bulk geometry, may be called minimally coupled. Assuming $E_\mu^\nu=0$, we try to extend to brane worlds some theorems valid for scalar fields in general relativity (GR). Thus, the list of possible global causal structures in all models under consideration is shown to be the same as is known for vacuum with a cosmological constant in GR: Minkowski, Schwarzschild, (anti-) de Sitter and Schwarzschild–(anti-)de Sitter. A no-hair theorem, saying that, given a potential V≥0, asymptotically flat black holes cannot have nontrivial external scalar fields, is proved under certain restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g, traversable wormholes supported by a scalar field, but only at the expense of enormous matter densities in the strong field region. [ABSTRACT FROM AUTHOR]