Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBianchi cosmologies with $p$-form gauge fields
119
0
0.0
(
0
)
Added by
Ben David Normann Mr.
Publication date
2017
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
We find that the recently-proposed ghost-free interaction of a 2-form gauge field in four dimensions, which contains derivative couplings in a nonperturbative manner, can be regarded as a resummation of ghostly interaction terms. We investigate the higher derivative structure of this model in a minisuperspace description and demonstrate that the higher derivative terms can be removed by taking appropriate combinations of the Euler-Lagrange equations, while a truncation at a finite order spoils this structure. We also show that this nature is peculiar to four dimensions.
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.
Why is the Universe so homogeneous and isotropic? We summarize a general study of a $gamma$-law perfect fluid alongside an inhomogeneous, massless scalar gauge field (with homogeneous gradient) in anisotropic spaces with General Relativity. The anisotropic matter sector is implemented as a $j$-form (field-strength level), where $j,in,{1,3}$, and the spaces studied are Bianchi space-times of solvable type. Walds no-hair theorem is extended to include the $j$-form case. We highlight three new self-similar space-times: the Edge, the Rope and Wonderland. The latter solution is so far found to exist in the physical state space of types I,II, IV, VI$_0$, VI$_h$, VII$_0$ and VII$_h$, and is a global attractor in I and V. The stability analysis of the other types has not yet been performed. This paper is a summary of ~[1], with some remarks towards new results which will be further laid out in upcoming work.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
