Reconstructing $f(R)$ gravity from the spectral index

Chiba, Takeshi

doi:10.1093/ptep/pty111

Cited by 5 publications

(7 citation statements)

References 27 publications

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“…The limitation of this formulation is that it's success is crucially dependent on the invertibility of the relation (27) to find R = R(y/z). This renders the present formulation useless in many situations.…”

Section: The Usual Dynamical System Formulationmentioning

confidence: 99%

“…where C 1 , C 2 , n are free parameters and m 2 is a characteristic mass scale which can be taken, for example, to be m 2 = κρ m0 /3 = Ω m0 H 2 0 . For this model the relation (27) becomes…”

Section: The Usual Dynamical System Formulationmentioning

confidence: 99%

“…In the bottom-up approach of doing cosmology one first specifies a cosmology (a(t)) and, given a matter content, tries to find out what functional form of f (R) gravity can produces the specified dynamics. This can be achieved via various reconstruction methods [21,22,23,24,25,26,27]. Then one can carry out a dynamical systems analysis of the reconstructed f (R) model.…”

Section: The Form-independent Dynamical System Approachmentioning

confidence: 99%

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A note on the dynamical system formulations in $f(R)$ gravity

Chakraborty,

Dunsby,

Macdevette

2021

Preprint

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A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in f (R) gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting them in a chronological order as they appeared in the history of the relevant scientific literature. In this way we illuminate how the shortcoming(s) of an existing formulation encouraged the development of an alternative formulation. Whenever possible, a 2-dimensional phase portrait is given for a better visual representation of the dynamics of phase space. We also touch upon how cosmological perturbations can be analyzed using the phase space language.

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Section: The Usual Dynamical System Formulationmentioning

confidence: 99%

Section: The Usual Dynamical System Formulationmentioning

confidence: 99%

Section: The Form-independent Dynamical System Approachmentioning

confidence: 99%

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A note on the dynamical system formulations in $f(R)$ gravity

Chakraborty,

Dunsby,

Macdevette

2021

Preprint

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“…In Ref. [51] this relationship was used to reconstruct the functional form of f (R) gravity, with the result that f (R) → R 2 in the large R limit. This result also supports an inflation-era action that is near scaleinvariant.…”

Section: Is the Model Viable?mentioning

confidence: 99%

“…The analysis of Ref. [50] and [51] was performed within the metric formalism of f (R) gravity, not the Palatini formalism, and so it only strictly supports a globally scale invariant action at high energies. However, since global scale invariance is a special type of local scale invariance these findings are at least consistent with our model.…”

Section: Is the Model Viable?mentioning

confidence: 99%

Asymptotically Weyl-invariant gravity

Coumbe¹

2019

Int. J. Mod. Phys. A

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We propose a novel theory of gravity that by construction is renormalizable, evades Ostragadsky's no-go theorem, is locally scale-invariant in the high-energy limit, and equivalent to general relativity in the low-energy limit. The theory is defined by a pure f (R) = R n action in the Palatini formalism, where the dimensionless exponent n runs from a value of two in the high-energy limit to one in the low-energy limit. We show that the proposed model contains no obvious cosmological curvature singularities. The viability of the proposed model is qualitatively assessed using several key criteria. PACS numbers: 04.60.-m, 04.60.Bc IntroductionGeneral relativity is theoretically beautiful, experimentally successful, and defines our best current description of gravity. Its key equations follow almost inevitably from a single symmetry principle and yield predictions that agree with experiment over a vast range of distance scales [1].Yet, general relativity is almost certainly incomplete. One major problem is that it appears to be incompatible with quantum field theory at high energies. Although general relativity has been successfully formulated as an effective quantum field theory at low energies, new divergences appear at each order in the perturbative expansion, leading to a complete loss of predictivity at high energies. Gravity is said to be perturbatively non-renormalizable, a fact demonstrated by explicit calculation at the one-loop level including matter content [2], and at the two-loop level without matter [3]. This behaviour stems from the fact that the gravitational coupling introduces a length scale into the theory so that higher-order corrections in a perturbative expansion come with ever-increasing powers of the cut-off scale.Higher-order actions have been explored as a possible solution to this problem [4]. Explicit calculations show that Lagrangians quadratic in the curvature tensor are renormalizable [5]. However, quadratic theories of gravity are not hailed as the theory of quantum gravity because they are not typically unitary, often containing unphysical ghost modes [5]. Higher-order theories are also generally unstable, violating a powerful no-go theorem first proposed by Ostragadsky [6]. Ostrogradsky's theorem proves that there is a fatal linear instability in any Hamiltonian associated with Lagrangians which depend on two or more time derivatives. This result helps explain the otherwise mysterious fact that the fundamental laws of physics seem to include at most two time derivatives [7]. The only higher-order theories that are both stable and unitary are f (R) theories, in which the Lagrangian is a general function f of the Ricci scalar R [8].Since f (R) gravity is not a single theory but a potentially infinite set of theories, one for each particular function f (R), we must identify a principle capable of selecting a specific function f (R). We contend that this principle should be local scale invariance. One reason for this is that scale-invariant theories of gravity are gauge theories [9,10]. ...

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