Dynamical systems approach and cosmological attractors in newer general relativity | Paper Citation Record

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This paper cites In this case we find the constraint √ 3Hcosα+Ksinα= 0,(34) which possesses the general solution H=Xsinα , K=− √ 3Xcosα ,(35) whereX=X(t)is the only dynamical variable in this case.

Dynamical systems approach and cosmological attractors in newer general relativity In this case we find the constraint √ 3Hcosα+Ksinα= 0,(34) which possesses the general solution H=Xsinα , K=− √ 3Xcosα ,(35) whereX=X(t)is the only dynamical variable in this case

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This paper cites Hence, the solution consists of two planes spanned bySandT, which intersect atS= 0.

Dynamical systems approach and cosmological attractors in newer general relativity Hence, the solution consists of two planes spanned bySandT, which intersect atS= 0

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This paper cites Forϵ=−1/12, it is a non-hyperbolic projective fixed point.

Dynamical systems approach and cosmological attractors in newer general relativity Forϵ=−1/12, it is a non-hyperbolic projective fixed point

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This paper cites For the lower sign, we find a repeller forH >0and an attractor forH <0.

Dynamical systems approach and cosmological attractors in newer general relativity For the lower sign, we find a repeller forH >0and an attractor forH <0

Reference 11

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This paper cites Following the same procedure as for the first branch, one finds that the Jacobi matrix vanishes identically, and so this is a non-hyperbolic projective fixed point.

Dynamical systems approach and cosmological attractors in newer general relativity Following the same procedure as for the first branch, one finds that the Jacobi matrix vanishes identically, and so this is a non-hyperbolic projective fixed point

Reference 13

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This paper cites Forϵ >0orϵ <−3 20, we find that this fixed point is an attractor forH >0and a repeller forH <0.

Dynamical systems approach and cosmological attractors in newer general relativity Forϵ >0orϵ <−3 20, we find that this fixed point is an attractor forH >0and a repeller forH <0

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This paper cites First, note that the projective fixed point denoted by the lower sign is always a saddle point, since in this case the two eigenvalues always have opposite signs, independently ofϵ.

Dynamical systems approach and cosmological attractors in newer general relativity First, note that the projective fixed point denoted by the lower sign is always a saddle point, since in this case the two eigenvalues always have opposite signs, independently ofϵ

Reference 15

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This paper cites The radial dynamics is governed by the relation ˙z=−4Kz ,(126) which shows that it is a past finite time singularity forK >0and a future finite time singularity forK <0.

Dynamical systems approach and cosmological attractors in newer general relativity The radial dynamics is governed by the relation ˙z=−4Kz ,(126) which shows that it is a past finite time singularity forK >0and a future finite time singularity forK <0

Reference 17

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This paper cites In this case the barotropic index (99) takes the value wλ =−1− 1 6ϵ .(131).

Dynamical systems approach and cosmological attractors in newer general relativity In this case the barotropic index (99) takes the value wλ =−1− 1 6ϵ .(131)

Reference 19

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This paper cites Forϵ >0orϵ <−1 12, this point is an attractor forH >0and a repeller forH <0.

Dynamical systems approach and cosmological attractors in newer general relativity Forϵ >0orϵ <−1 12, this point is an attractor forH >0and a repeller forH <0

Reference 20

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This paper cites The same applies to the lower sign forϵ <−1 12, but the opposite is the case for−1 12 < ϵ <0, while atϵ=− 1 12 one finds a non-hyperbolic projective fixed point.

Dynamical systems approach and cosmological attractors in newer general relativity The same applies to the lower sign forϵ <−1 12, but the opposite is the case for−1 12 < ϵ <0, while atϵ=− 1 12 one finds a non-hyperbolic projective fixed point

Reference 21

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This paper cites Also in this case the barotropic index (99) takes the stiff fluid valuewλ = 1.

Dynamical systems approach and cosmological attractors in newer general relativity Also in this case the barotropic index (99) takes the stiff fluid valuewλ = 1

Reference 23

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This paper cites In this case there is only one projective fixed point (101), as discussed in section VE1.

Dynamical systems approach and cosmological attractors in newer general relativity In this case there is only one projective fixed point (101), as discussed in section VE1

Reference 25

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This paper cites Here two projective fixed points coincide, and merge into a singular non-hyperbolic projective fixed point.

Dynamical systems approach and cosmological attractors in newer general relativity Here two projective fixed points coincide, and merge into a singular non-hyperbolic projective fixed point

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This paper cites In this case we must distinguish eight different cases, each of which exhibits a different qualitative behavior.

Dynamical systems approach and cosmological attractors in newer general relativity In this case we must distinguish eight different cases, each of which exhibits a different qualitative behavior

Reference 31

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This paper cites The projective fixed point (111) is unchanged compared to the previous case, and will remain unchanged for all further parameter values we consider here.

Dynamical systems approach and cosmological attractors in newer general relativity The projective fixed point (111) is unchanged compared to the previous case, and will remain unchanged for all further parameter values we consider here

Reference 33

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This paper cites Now the projective fixed point (113) has turned into a saddle point, which is located in the middle of the lower halfL <0of the central vertical lineK= 0.

Dynamical systems approach and cosmological attractors in newer general relativity Now the projective fixed point (113) has turned into a saddle point, which is located in the middle of the lower halfL <0of the central vertical lineK= 0

Reference 35

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This paper cites We now find that the fixed point (113) becomes non-hyperbolic, now displayed by the symbol•in the lower halfL <0of the central 29 FIG.

Dynamical systems approach and cosmological attractors in newer general relativity We now find that the fixed point (113) becomes non-hyperbolic, now displayed by the symbol•in the lower halfL <0of the central 29 FIG

Reference 36

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This paper cites Now the projective fixed point given by the upper sign of the solution (113) becomes non-hyperbolic.

Dynamical systems approach and cosmological attractors in newer general relativity Now the projective fixed point given by the upper sign of the solution (113) becomes non-hyperbolic

Reference 39

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This paper cites This case is essentially the opposite of the case− 1 12 < ϵ <0we discussed before.

Dynamical systems approach and cosmological attractors in newer general relativity This case is essentially the opposite of the case− 1 12 < ϵ <0we discussed before

Reference 40

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Dynamical systems approach and cosmological attractors in newer general relativity Here we have four types of qualitatively different phase diagrams which we must distinguish

Reference 41

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Dynamical systems approach and cosmological attractors in newer general relativity We first take a look at the projective fixed points appearing in this case

Reference 42

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Dynamical systems approach and cosmological attractors in newer general relativity Note that the location and properties of the projective fixed point (123) are unchanged, and will remain so for all values ofϵ

Reference 43

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Dynamical systems approach and cosmological attractors in newer general relativity Here we find that several projective fixed points coincide and their stability changes

Reference 44

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Dynamical systems approach and cosmological attractors in newer general relativity Fundamental Universe

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Dynamical systems approach and cosmological attractors in newer general relativity Linking Tests of Gravity On All Scales: from the Strong-Field Regime to Cosmology

Reference 46

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Dynamical systems approach and cosmological attractors in newer general relativity Planck 2018 results. VI. Cosmological parameters

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Dynamical systems approach and cosmological attractors in newer general relativity In the Realm of the Hubble tension $-$ a Review of Solutions

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Dynamical systems approach and cosmological attractors in newer general relativity DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations

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Dynamical systems approach and cosmological attractors in newer general relativity DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

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Dynamical systems approach and cosmological attractors in newer general relativity Introduction to Modified Gravity and Gravitational Alternative for Dark Energy

Reference 51

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Dynamical systems approach and cosmological attractors in newer general relativity Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

Reference 52

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Dynamical systems approach and cosmological attractors in newer general relativity Faraoni and S

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Dynamical systems approach and cosmological attractors in newer general relativity Modified Gravity and Cosmology

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Dynamical systems approach and cosmological attractors in newer general relativity Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests

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Dynamical systems approach and cosmological attractors in newer general relativity Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

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Dynamical systems approach and cosmological attractors in newer general relativity Beyond $\Lambda$CDM: Problems, solutions, and the road ahead

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Dynamical systems approach and cosmological attractors in newer general relativity A systematic approach to generalisations of General Relativity and their cosmological implications

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Dynamical systems approach and cosmological attractors in newer general relativity Modified Gravity and Cosmology: An Update by the CANTATA Network

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Dynamical systems approach and cosmological attractors in newer general relativity Recent Advances on Inflation

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Dynamical systems approach and cosmological attractors in newer general relativity Pfeifer and C

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Dynamical systems approach and cosmological attractors in newer general relativity The Geometrical Trinity of Gravity

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Dynamical systems approach and cosmological attractors in newer general relativity Teleparallel gravity

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Dynamical systems approach and cosmological attractors in newer general relativity Symmetric teleparallel general relativity

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Dynamical systems approach and cosmological attractors in newer general relativity Lagrange formulation of the symmetric teleparallel gravity

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Dynamical systems approach and cosmological attractors in newer general relativity The Non-Metricity Formulation of General Relativity

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Dynamical systems approach and cosmological attractors in newer general relativity Gauge Approach to The Symmetric Teleparallel Gravity

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Dynamical systems approach and cosmological attractors in newer general relativity Nonmetricity formulation of general relativity and its scalar-tensor extension

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Dynamical systems approach and cosmological attractors in newer general relativity Family of scalar-nonmetricity theories of gravity

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Dynamical systems approach and cosmological attractors in newer general relativity Coincident General Relativity

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Dynamical systems approach and cosmological attractors in newer general relativity Propagation of gravitational waves in symmetric teleparallel gravity theories

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Dynamical systems approach and cosmological attractors in newer general relativity Post-Newtonian limit of generalized symmetric teleparallel gravity

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Dynamical systems approach and cosmological attractors in newer general relativity ADM formulation and Hamiltonian analysis of Coincident General Relativity

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Dynamical systems approach and cosmological attractors in newer general relativity An axiomatic purification of gravity

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Dynamical systems approach and cosmological attractors in newer general relativity Symmetric Teleparallel Connection and Spherical Solutions in Newer GR

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Dynamical systems approach and cosmological attractors in newer general relativity Weak Gravity Limit in Newer General Relativity

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Dynamical systems approach and cosmological attractors in newer general relativity General covariant symmetric teleparallel cosmology

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Dynamical systems approach and cosmological attractors in newer general relativity Lost in translation: the Abelian affine connection (in the coincident gauge)

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Dynamical systems approach and cosmological attractors in newer general relativity Geometry and covariance of symmetric teleparallel theories of gravity

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Dynamical systems approach and cosmological attractors in newer general relativity Dynamical systems approach and generic properties of $f(T)$ cosmology

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Dynamical systems approach and cosmological attractors in newer general relativity A class of ghost-free theories in symmetric teleparallel geometry

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Dynamical systems approach and cosmological attractors in newer general relativity Cosmological teleparallel perturbations

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Dynamical systems approach and cosmological attractors in newer general relativity Gauge-invariant cosmological perturbations in general teleparallel gravity

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Dynamical systems approach and cosmological attractors in newer general relativity Cosmology in $f(Q)$ geometry

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Dynamical systems approach and cosmological attractors in newer general relativity Accidental gauge symmetries of Minkowski spacetime in Teleparallel theories

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Dynamical systems approach and cosmological attractors in newer general relativity Pathological Character of Modifications to Coincident General Relativity: Cosmological Strong Coupling and Ghosts in $f(\Q)$ Theories

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