Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userIntegrable scalar cosmologies with matter and curvature
95
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We show that several integrable (i.e., exactly solvable) scalar cosmologies considered by Fre, Sagnotti and Sorin (Nuclear Physics textbf{B 877}(3) (2013), 1028--1106) can be generalized to include cases where the spatial curvature is not zero and, besides a scalar field, matter or radiation are present with an equation of state $p^{(m)} = w, rho^{(m)}$; depending on the specific form of the self-interaction potential for the field, the constant $w$ can be arbitrary or must be fixed suitably.
rate research
Read More
The main purpose of this paper is to advance a unified theory of dark matter, dark energy, and inflation first formulated in 2008. Our minimal affine extension of the GR has geodesics coinciding with the pseudo Riemannian ones, up to parameterizations. It predicts a `sterile massive vecton and depends on two new dimensional constants, which can be measured in the limit of small vecton velocity. In a special gauge, this velocity has an upper limit near which it grows to infinity. The linearized vecton theory is similar to the scalar models of inflation except the fact of internal anisotropy of the vecton. For this reason we study general solutions of scalar analogs of the vecton theory without restricting the curvature parameter and anisotropy by using previously derived exact solutions as functions of the metric. It is shown that the effects of curvature and anisotropy fast decrease in expanding universes. Our approach can be applied to anisotropic universes, which is demonstrated on an exactly solvable strongly anisotropic cosmology. To characterize different cosmological scenarios in detail we introduce three characteristic functions, two of which are small and almost equal during inflation and grow near the exit. Instead of the potential it is possible to use one of the two characteristic functions. This allows to approximately derive flat isotropic universes with `prescribed scenarios, which is the essence of our constructive cosmology of early universes. The most natural application of our approach is in analytically constructing characteristic functions of inflationary models with natural exits. However, the general construction can be applied to other problems, e.g., to evolution of contracting universes.
In the 2-spinor formalism, the gravity can be dealt with curvature spinors with four spinor indices. Here we show a new effective method to express the components of curvature spinors in the rank-2 $4 times 4$ tensor representation for the gravity in a locally inertial frame. In the process we have developed a few manipulating techniques, through which the roles of each component of Riemann curvature tensor are revealed. We define a new algebra `sedon, whose structure is almost the same as sedenion except the basis multiplication rule. Finally we also show that curvature spinors can be represented in the sedon form and observe the chiral structure in curvature spinors. A few applications of the sedon representation, which includes the quaternion form of differential Binanchi indentity, are also presented.
We examine homogeneous but anisotropic cosmologies in scalar-tensor gravity theories, including Brans-Dicke gravity. We present a method for deriving solutions for any isotropic perfect fluid with a barotropic equation of state ($pproptorho$) in a spatially flat (Bianchi type~I) cosmology. These models approach an isotropic, general relativistic solution as the expansion becomes dominated by the barotropic fluid. All models that approach general relativity isotropize except for the case of a maximally stiff fluid. For stiff fluid or radiation or in vacuum we are able to give solutions for arbitrary scalar-tensor theories in a number of anisotropic Bianchi and Kantowski-Sachs metrics. We show how this approach can also be used to derive solutions from the low-energy string effective action. We discuss the nature, and possibly avoidance of, the initial singularity where both shear and non-Einstein behavior is important.
Some exact solutions for the Einstein field equations corresponding to inhomogeneous $G_2$ cosmologies with an exponential-potential scalar field which generalize solutions obtained previously are considered. Several particular cases are studied and the properties related to generalized inflation and asymptotic behaviour of the models are discussed.
Recently a cubic Galileon cosmological model was derived by the assumption that the field equations are invariant under the action of point transformations. The cubic Galileon model admits a second conservation law which means that the field equations form an integrable system. The analysis of the critical points for this integrable model is the main subject of this work. To perform the analysis, we work on dimensionless variables different from that of the Hubble normalization. New critical points are derived while the gravitational effects which follow from the cubic term are studied.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
