ترغب بنشر مسار تعليمي؟ اضغط هنا

On solving dynamical equations in general homogeneous isotropic cosmologies with scalaron

140   0   0.0 ( 0 )
 نشر من قبل Alexandre Filippov
 تاريخ النشر 2015
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We study general dynamical equations describing homogeneous isotropic cosmologies coupled to a scalaron $psi$. For flat cosmologies ($k=0$), we analyze in detail the gauge-independent equation describing the differential, $chi(alpha)equivpsi^prime(alpha)$, of the map of the metric $alpha$ to the scalaron field $psi$, which is the main mathematical characteristic locally defining a `portrait of a cosmology in `$alpha$-version. In the `$psi$-version, a similar equation for the differential of the inverse map, $bar{chi}(psi)equiv chi^{-1}(alpha)$, can be solved asymptotically or for some `integrable scalaron potentials $v(psi)$. In the flat case, $bar{chi}(psi)$ and $chi(alpha)$ satisfy the first-order differential equations depending only on the logarithmic derivative of the potential. Once we know a general analytic solution for one of these $chi$-functions, we can explicitly derive all characteristics of the cosmological model. In the $alpha$-version, the whole dynamical system is integrable for $k eq 0$ and with any `$alpha$-potential, $bar{v}(alpha)equiv v[psi(alpha)]$, replacing $v(psi)$. There is no a priori relation between the two potentials before deriving $chi$ or $bar{chi}$, which implicitly depend on the potential itself, but relations between the two pictures can be found by asymptotic expansions or by inflationary perturbation theory. Explicit applications of the results to a more rigorous treatment of the chaotic inflation models and to their comparison with the ekpyrotic-bouncing ones are outlined in the frame of our `$alpha$-formulation of isotropic scalaron cosmologies. In particular, we establish an inflationary perturbation expansion for $chi$. When all the conditions for inflation are satisfied and $chi$ obeys a certain boundary (initial) condition, we get the standard inflationary parameters, with higher-order corrections.



قيم البحث

اقرأ أيضاً

205 - M. K. Mak , T. Harko 2013
We present a general solution of the Einstein gravitational field equations for the static spherically symmetric gravitational interior spacetime of an isotropic fluid sphere. The solution is obtained by transforming the pressure isotropy condition, a second order ordinary differential equation, into a Riccati type first order differential equation, and using a general integrability condition for the Riccati equation. This allows us to obtain an exact non-singular solution of the interior field equations for a fluid sphere, expressed in the form of infinite power series. The physical features of the solution are studied in detail numerically by cutting the infinite series expansions, and restricting our numerical analysis by taking into account only $n=21$ terms in the power series representations of the relevant astrophysical parameters. In the present model all physical quantities (density, pressure, speed of sound etc.) are finite at the center of the sphere. The physical behavior of the solution essentially depends on the equation of state of the dense matter at the center of the star. The stability properties of the model are also analyzed in detail for a number of central equations of state, and it is shown that it is stable with respect to the radial adiabatic perturbations. The astrophysical analysis indicates that this solution can be used as a realistic model for static general relativistic high density objects, like neutron stars.
We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational dust mode ls (Paper I) and irrotational perfect fluids (Paper II) in flow-orthogonal foliations of spacetime. It complements them by considering arbitrary foliations, arbitrary lapse and shift, and by allowing for a tilted fluid flow with vorticity. As for the first studies, the propagation of the spatial averaging domain is chosen to follow the congruence of the fluid, which avoids unphysical dependencies in the averaged system that is obtained. We present two different averaging schemes and corresponding systems of averaged evolution equations providing generalizations of Papers I and II. The first one retains the averaging operator used in several other generalizations found in the literature. We extensively discuss relations to these formalisms and pinpoint limitations, in particular regarding rest mass conservation on the averaging domain. The alternative averaging scheme that we subsequently introduce follows the spirit of Papers I and II and focuses on the fluid flow and the associated 1+3 threading congruence, used jointly with the 3+1 foliation that builds the surfaces of averaging. This results in compact averaged equations with a minimal number of cosmological backreaction terms. We highlight that this system becomes especially transparent when applied to a natural class of foliations which have constant fluid proper time slices.
We discuss the most general field equations for cosmological spacetimes for theories of gravity based on non-linear extensions of the non-metricity scalar and the torsion scalar. Our approach is based on a systematic symmetry-reduction of the metric- affine geometry which underlies these theories. While for the simplest conceivable case the connection disappears from the field equations and one obtains the Friedmann equations of General Relativity, we show that in $f(mathbb{Q})$ cosmology the connection generically modifies the metric field equations and that some of the connection components become dynamical. We show that $f(mathbb{Q})$ cosmology contains the exact General Relativity solutions and also exact solutions which go beyond. In $f(mathbb{T})$~cosmology, however, the connection is completely fixed and not dynamical.
A powerful result in theoretical cosmology states that a subset of anisotropic Bianchi models can be seen as the homogeneous limit of (standard) linear cosmological perturbations. Such models are precisely those leading to Friedmann spacetimes in the limit of zero anisotropy. Building on previous works, we give a comprehensive exposition of this result, and perform the detailed identification between anisotropic degrees of freedom and their corresponding scalar, vector, and tensor perturbations of standard perturbation theory. In particular, we find that anisotropic models very close to open (i.e., negatively curved) Friedmann spaces correspond to some type of super-curvature perturbations. As a consequence, provided anisotropy is mild, its effects on all types of cosmological observables can always be computed as simple extensions of the standard techniques used in relativistic perturbation theory around Friedmann models. This fact opens the possibility to consistently constrain, for all cosmological observables, the presence of large scale anisotropies on the top of the stochastic fluctuations.
In this paper the dynamics of free gauge fields in Bianchi type I-VII$_{h}$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p,in,{1,3}$), a cosmological constant ($4$-form) and perfect fluid in Bianchi type I-VII$_{h}$ space-times are computed using the orthonormal frame method. The number of independent components of a $p$-form in all Bianchi types I-IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are performed and strong global results regarding the general behaviour are obtained. New self-similar cosmological solutions appear both in Bianchi type I and Bianchi type V, in particular, a one-parameter family of self-similar solutions,Wonderland ($lambda$) appears generally in type V and in type I for $lambda=0$. Depending on the value of the equation of state parameter other new stable solutions are also found (The Rope and The Edge) containing a purely spatial field strength that rotates relative to the co-moving inertial tetrad. Using monotone functions, global results are given and the conditions under which exact solutions are (global) attractors are found.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا