اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMetric-Affine Myrzakulov Gravity Theories
142
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper we review the Myrzakulov Gravity models (MG-N, with $mathrm{N = I, II, ldots, VIII}$) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the case in which the function characterizing the aforementioned metric-affine models is linear and consider a Friedmann-Lema^{i}tre-Robertson-Walker background to study cosmological aspects and applications.
قيم البحث
اقرأ أيضاً
We derive the full set of field equations for the Metric-Affine version of the Myrzakulov gravity model and also extend this family of theories to a broader one. More specifically, we consider theories whose gravitational Lagrangian is given by $F(R,
T,Q, {cal T},{cal D})$ where $T$, $Q$ are the torsion and non-metricity scalars, ${cal T}$ is the trace of the energy-momentum tensor and ${cal D}$ the divergence of the dilation current. We then consider the linear case of the aforementioned theory and assuming a cosmological setup we obtain the modified Friedmann equations. In addition, focusing on the vanishing non-metricity sector and considering matter coupled to torsion we obtain the complete set of equations describing the cosmological behaviour of this model along with solutions.
The intriguing choice to treat alternative theories of gravity by means of the Palatini approach, namely elevating the affine connection to the role of independent variable, contains the seed of some interesting (usually under-explored) generalizatio
ns of General Relativity, the metric-affine theories of gravity. The peculiar aspect of these theories is to provide a natural way for matter fields to be coupled to the independent connection through the covariant derivative built from the connection itself. Adopting a procedure borrowed from the effective field theory prescriptions, we study the dynamics of metric-affine theories of increasing order, that in the complete version include invariants built from curvature, nonmetricity and torsion. We show that even including terms obtained from nonmetricity and torsion to the second order density Lagrangian, the connection lacks dynamics and acts as an auxiliary field that can be algebraically eliminated, resulting in some extra interactions between metric and matter fields.
This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian geometry.
In the second Chapter we explore the MAG model building. In Chapter 3 we use a well known procedure to excite torsional degrees of freedom by coupling surface terms to scalars. Then, in Chapter 4 which seems to be the most important Chapter of the thesis, at least with regards to its use in applications, we present a step by step way to solve for the affine connection in non-Riemannian geometries, for the first time in the literature. A peculiar f(R) case is studied in Chapter 5. This is the conformally (as well as projective invariant) invariant theory f(R)=a R^{2} which contains an undetermined scalar degree of freedom. We then turn our attention to Cosmology with torsion and non-metricity (Chapter 6). In Chapter 7, we formulate the necessary setup for the $1+3$ splitting of the generalized spacetime. Having clarified the subtle points (that generally stem from non-metricity) in the aforementioned formulation we carefully derive the generalized Raychaudhuri equation in the presence of both torsion and non-metricity (along with curvature). This, as it stands, is the most general form of the Raychaudhuri equation that exists in the literature. We close this Thesis by considering three possible scale transformations that one can consider in Metric-Affine Geometry.
This article presents a systematic way to solve for the Affine Connection in Metric-Affine Geometry. We start by adding to the Einstein-Hilbert action, a general action that is linear in the connection and its partial derivatives and respects project
ive invariance. We then generalize the result for Metric-Affine f(R) Theories. Finally, we generalize even further and add an action (to the Einstein-Hilbert) that has an arbitrary dependence on the connection and its partial derivatives. We wrap up our results as three consecutive Theorems. We then apply our Theorems to some simple examples in order to illustrate how the procedure works and also discuss the cases of dynamical/non-dynamical connections.
We present a framework in which the projective symmetry of the Einstein-Hilbert action in metric-affine gravity is used to induce an effective coupling between the Dirac lagrangian and the Maxwell field. The effective $U(1)$ gauge potential arises as
the trace of the non-metricity tensor $Q_{mu a}{}^a$ and couples in the appropriate way to the Dirac fields to in order to allow for local phase shifts. On shell, the obtained theory is equivalent to Einstein-Cartan-Maxwell theory in presence of Dirac spinors.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
