scholarly journals Dynamical equivalence of f(R) gravity in Jordan and Einstein frames

2019 ◽  
Vol 99 (2) ◽  
Author(s):  
Saikat Chakraborty ◽  
Sanchari Pal ◽  
Alberto Saa
Keyword(s):  
Dynamical Equivalence ◽  
Jordan And Einstein Frames

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

scholarly journals Local dynamical equivalence of certain food webs

2008 ◽  
Vol 59 (2) ◽  
pp. 417-427 ◽  
Author(s):  
Thilo Gross ◽  
Ulrike Feudel
Keyword(s):  
Food Webs ◽  
Dynamical Equivalence

scholarly journals Mesoscale symmetries explain dynamical equivalence of food webs

2012 ◽  
Vol 14 (10) ◽  
pp. 105014 ◽  
Author(s):  
Helge Aufderheide ◽  
Lars Rudolf ◽  
Thilo Gross
Keyword(s):  
Food Webs ◽  
Dynamical Equivalence

A NOTE ON THE UNIFIED FIRST LAW IN f(R) GRAVITY THEORY

2012 ◽  
Vol 21 (04) ◽  
pp. 1250034 ◽  
Author(s):  
YI ZHANG ◽  
YUNGUI GONG ◽  
ZONG-HONG ZHU
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Conformal Transformation ◽  
Dynamical Equation ◽  
Einstein Frame ◽  
Jordan Frame ◽  
View Point ◽  
Minimal Coupling ◽  
Friedmann Equations ◽  
Dynamical Equivalence

Because of the dynamical equivalence between the f(R) gravity and the Brans-Dicke theory, the dynamical equation in the f(R) gravity is suggested to be derived from a view point of thermodynamics here. By a conformal transformation, the Brans–Dicke theory in the Jordan frame could be expressed as a minimal coupling scalar field theory in Einstein frame. Using the entropy-area relation [Formula: see text], the correct Friedmann equations could be gotten in both frames. Furthermore, we also discuss the corresponding generalized Misner–Sharp energies for theoretical consistence.

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