Superstring theoryをめぐって(放談室)

https://pure.mpg.de/pubman/item/item_2533988_4/component/file_2533987/1712.03107.pdf

Dynamical systems applied to cosmology: dark energy and modified gravity

An analysis of the first set of low-redshift (z < 0.08) Type Ia supernovae (SNe Ia) monitored by the Carnegie Supernova Project between 2004 and 2006 is presented. The data consist of well-sampled, high-precision optical (ugriBV) and near-infrared (NIR; YJHKs ) light curves in a well-understood photometric system. Methods are described for deriving light-curve parameters, and for building template light curves which are used to fit SN Ia data in the ugriBVYJH bands. The intrinsic colors at maximum light are calibrated using a subsample of supernovae (SNe) assumed to have suffered little or no reddening, enabling color excesses to be estimated for the full sample. The optical-NIR color excesses allow the properties of the reddening law in the host galaxies to be studied. A low average value of the total-to-selective absorption coefficient, RV 1.7, is derived when using the entire sample of SNe. However, when the two highly reddened SNe (SN 2005A and SN 2006X) in the sample are excluded, a value RV 3.2 is obtained, similar to the standard value for the Galaxy. The red colors of these two events are well matched by a model where multiple scattering of photons by circumstellar dust steepens the effective extinction law. The absolute peak magnitudes of the SNe are studied in all bands using a two-parameter linear fit to the decline rates and the colors at maximum light, or alternatively, the color excesses. In both cases, similar results are obtained with dispersions in absolute magnitudes of 0.12-0.16?mag, depending on the specific filter-color combination. In contrast to the results obtained from the comparison of the color excesses, these fits of absolute magnitude give RV 1-2 when the dispersion is minimized, even when the two highly reddened SNe are excluded. This discrepancy suggests that, beyond the normal interstellar reddening produced in the host galaxies, there is an intrinsic dispersion in the colors of SNe Ia which is correlated with luminosity but independent of the decline rate. Finally, a Hubble diagram for the best-observed subsample of SNe is produced by combining the results of the fits of absolute magnitude versus decline rate and color excess for each filter. The resulting scatter of 0.12 mag appears to be limited by the peculiar velocities of the host galaxies as evidenced by the strong correlation between the distance-modulus residuals observed in the individual filters. The implication is that the actual precision of SNe Ia distances is 3%-4%.

The Carnegie Supernova Project: Analysis of the First Sample of Low-Redshift Type-Ia Supernovae

The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late-time cosmology.

We investigate the instability of the ghost dark energy model against perturbations in different cases. To this goal we use the squared sound speed whose sign determines the stability of the model. When the model is unstable against perturbation. At first we discuss the noninteracting ghost dark energy model in a flat FRW universe and find out that such a model is unstable due to the negativity of the in all epoches. The interacting ghost dark energy model in both flat and nonflat universe are studied in the next parts and in both cases we find that the squared sound speed of ghost dark energy is always negative. This implies that the perfect fluid for ghost dark energy is classically unstable against perturbations. In both flat and non flat cases we find that the instability of the model increases with increasing the value of the interacting coupling parameter.

Instability of qcd ghost dark energy model

We investigate the instability of the ghost dark energy model against perturbations in different cases. To this goal we use the squared sound speed $v_s^2$ whose sign determines the stability of the model. When $v_s^2<0$ the model is unstable against perturbation. At first we discuss the noninteracting ghost dark energy model in a flat FRW universe and find out that such a model is unstable due to the negativity of the $v_s^2$ in all epoches. The interacting ghost dark energy model in both flat and non-flat universe are studied in the next parts and in both cases we find that the squared sound speed of ghost dark energy is always negative. This implies that the perfect fluid for ghost dark energy is classically unstable against perturbations. In both flat and non flat cases we find that the instability of the model increases with increasing the value of the interacting coupling parameter.

Instability of QCD ghost dark energy model

Interacting ghost dark energy in Brans–Dicke theory

Recently it has been argued that a possible source for the dark energy may arise due to the contribution to the vacuum energy of the QCD ghost in a time-dependent background. In this paper we establish a connection between interacting ghost dark energy and tachyon field. It is demonstrated that the evolution of the ghost dark energy dominated universe can be described completely by a single tachyon scalar field. The potential and the dynamics of the tachyon field are reconstructed according to the evolutionary behavior of ghost energy density.

https://www.tpbin.com/Uploads/Subjects/4ce42bb4-8ae2-4a05-81f1-bc52ce947c03.pdf

Tachyon reconstruction of ghost dark energy

/pdf/tachyon-reconstruction-of-ghost-dark-energy-5f1hdw1xd3.pdf

Esmaeil Ebrahimi

Papers

Instability of qcd ghost dark energy model

Instability of QCD ghost dark energy model

Interacting ghost dark energy in Brans–Dicke theory

Tachyon reconstruction of ghost dark energy

Tachyon Reconstruction of Ghost Dark Energy