Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity

E. Elizalde; F. Briscese; S. D. Odintsov; S. Nojiri

REVIEW

Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity

F. Briscese, E. Elizalde, S. Nojiri, S. D. Odintsov

High Energy Physics - Theory · Submitted 20 Dec 2006 · 13 references

Pith's verdict: A clean, checkable extension of the scalar-to-F(R) mapping to the phantom case, with a Big Rip claim that is stated more sharply than the equations support.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 4 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-th/0612220 (version 2)

Pith ID4QOHZUQU, Pith's permanent record of this paper and its review

CitationE. Elizalde, F. Briscese, S. D. Odintsov, S. Nojiri. "Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity." arXiv:hep-th/0612220 (2006). https://pith.science/paper/4QOHZUQU

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The useful thing here is the complex conformal factor. Everyone knew a canonical scalar maps to F(R) via g' = e^{±κφ√(2/3)}g; the authors point out that for a phantom you just make the exponent imaginary and the same algebra goes through. That is a clean, checkable extension of their earlier published construction, and it immediately explains why the phantom case is awkward: the resulting F(R) is complex for generic potentials. The even-potential observation — take φ = iψ and the action becomes real, at the cost of turning the phantom into a canonical scalar with a flipped-sign potential — is a nice structural remark, and the worked examples (exponential, massive, cosh) are explicit enough to check by hand. The physical point, that the two descriptions are mathematically equivalent but physically distinct because the metrics differ by a conformal factor, is correct and worth saying clearly. Where I would push back is the Big Rip claim. The abstract says F(R) becomes complex at the region where the phantom theory develops a Big Rip. That is not quite what the equations say. For any real φ, R = e^{iκφ√(2/3)}(4κ²V − i√6κV') is complex unless the potential satisfies the special alignment condition (11). So the phantom trajectory sits at complex R the whole time; the rip is where |R| diverges, not where complexity starts. What the paper actually shows is that the real branch of F(R) (the φ = iψ branch) does not reach the rip — the rip lies off it. That is defensible, but it is not the sentence in the abstract, and the branch structure is never spelled out. Related: the line in §III that generically the Big Rip region cannot be mapped to real F(R) rests on one cosh example. It is probably true, but it is asserted, not shown. Two smaller things. 'Only for even potentials is the F(R) real' is a sufficiency claim dressed as a biconditional; the necessity argument is not given, though I think it is actually right, since odd V picks up an extra i on the imaginary branch. And the instanton section ends with 'seems difficult to continue analytically' (Eq. 67), which is a shrug rather than a result. None of this breaks the main point. Who should read it: anyone working on phantom dark energy or F(R) reconstruction who needs the mapping spelled out. It is a letter, not a landmark. Send it out; the referee should ask for the branch-structure clarification and either a proof or a downgrade of the genericity claim.

Referee report

Significance

If correct, the paper supplies a structural explanation for the Big Rip: it is the point at which the phantom branch of the solution cannot be continued into the real F(R) sector. The closed-form F(R) obtained for three potentials, and the observation that a real F(R) forces the phantom to reduce to a canonical scalar (Eq. 13), are useful and directly checkable. The frame-dependence of the singularity type (Eqs. 41–44) is a concrete statement about which frame's singularity structure is physical, and it is the kind of claim that can be tested against explicit cosmological solutions. The paper ships no code or machine-checked proofs; its support is the standard conformal technique of Ref. [5] together with worked examples, which is appropriate for a letter of this kind.

Major objections (4)

[Abstract (s1) and §II] The abstract states that 'Only for even scalar potentials is the ensuing modified gravity real', which is a necessity claim. §II establishes only sufficiency: for V = U(ϕ²), demanding real R forces ϕ to be pure imaginary and hence F(R) real. The body itself records a counterexample, Eq. (11), V(ϕ) = V₀/cos(κϕ√(2/3)), which is not even yet yields real R for real ϕ, and it explicitly concedes that 'There still could be, however, the possibility that ... the resulting action might be real' for non-even potentials. As written, the abstract's 'only' is contradicted by the paper's own Eq. (11). Either the abstract should be weakened to a sufficiency statement, or a necessity argument excluding non-even potentials with real F(R) should be supplied.
[Abstract (s2) and §III, Eqs. (30)–(34)] The abstract says modified gravity 'becomes complex at the region where the original phantom dark energy theory develops a Big Rip singularity', but complexity is not rip-specific. Eq. (4) shows that for real ϕ the curvature R = e^{±iκϕ√(2/3)}(4κ²V ∓ i√6κV′) is complex for every ϕ unless the alignment condition (11) holds; for the cosh model, Eq. (32) is complex along the entire real-ϕ trajectory. The Big Rip is distinguished only by |R| → ∞, as Eqs. (33)–(34) show. The correct statement is that the phantom branch never maps onto the real F(R) branch, and the rip is where that branch diverges. The genericity claim in §III ('a quite general situation in the examples we have discussed') also rests on a single cosh model; a one-line argument that the phase e^{iκϕ√(2/3)} is nontrivial for any real ϕ unless Eq. (11) holds would establish it, and would also make clear that a rip occurring at finite field value is covered.
[§II, Eq. (4) and Eq. (9)] The step from Eq. (4) to F(R) assumes that ϕ = ϕ(R) can be inverted globally, but Eq. (4) is transcendental in ϕ for general V and the inversion is at best local. The exponential-potential example makes this explicit: Eq. (9) carries an undetermined integer n through the factor (1 + 2nπi) in the exponent, arising from the branch of the logarithm, and the paper does not say how the branch is fixed or whether F(R) is single-valued. Since the abstract claims that 'any' phantom scalar model can be mapped to F(R), the range of validity of the inversion, and the branch dependence of the resulting F(R), should be stated.
[§III, Eqs. (42)–(44)] As printed, the chain of substitutions does not close. Eq. (42) gives σ ~ −2(n+1)ln(t₀−t), hence e^σ ~ (t₀−t)^{−2(n+1)}, whereas the text uses dt̃ = ±e^σ dt ~ ±(t₀−t)^{n+1}dt. Likewise, the exponent (n+1)(2n+5)/(n+2)² in Eq. (44) does not follow from combining the a(t) of Eq. (41) with the stated σ. Because the conclusions of this paragraph — that for n < −2 the rip is pushed to infinite time and for −1 < n < −1/2 it becomes a Big Crunch — rest on these scalings, the intermediate steps should be shown explicitly, or the convention relating σ to the conformal factor should be stated so that the reader can verify them.

Minor objections (8)

[§IV, Eqs. (55) and (57)] Eq. (55) gives g(t) = ln[(1/2)(1 + t²/a₀²)], so a(t) = a₀e^g = (a₀/2)(1 + t²/a₀²), but Eq. (57) writes a(t) = (a₀/2)(1 + t²/a₀²)². Eq. (59) inherits the squared form, so the reader cannot tell which is intended; please correct one of the two.
[§II, Eq. (17)] The first term of Eq. (17) contains iκϕ while the second contains iκφ(R); since φ = −iϕ was introduced precisely to make the expression real, the notation should be φ throughout.
[§II, Eq. (16)] The exponent in Eq. (16) is written e^{∓κφ}, whereas Eq. (4) with ϕ = iφ gives e^{∓κφ√(2/3)}. Please check the exponent and the overall normalization of the right-hand side.
[§IV, Eqs. (47)–(48) and (53)] The cancellation that yields ω(φ) = 0 in Eq. (53) for the closed de Sitter solution (51)–(52) depends on the sign convention for k (k = 2 for the sphere). The convention should be stated explicitly so that the reader can verify Eq. (53) against Eqs. (47)–(48).
[Abstract] Typographical: 'deccelerating' should read 'decelerating'.
[References] Reference [4] lists the second entry as 'arXiv:hep-th 0611071', which is not a well-formed identifier; please correct it.
[§V] The closing paragraph notes that any scalar-tensor theory can be presented as a fluid and that the correspondence extends to modified gravity, but this is not developed. A sentence on how the complex F(R) maps onto a fluid equation of state would strengthen the conclusion.
[§II, discussion after Eq. (13)] The paper notes that the inverse-transformed theory (18) contains a tachyon, but does not comment on the analogous F″(R) < 0 for the real branch of Eq. (25). Since the motivation is to replace the phantom by a healthier modified gravity, a remark on whether the real branches obtained here are physically viable would be useful.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Phantom dark energy can be rewritten as a modified gravity theory, but the rewrite turns complex exactly where the universe hits the Big Rip.

The reading

The paper asks a concrete question: if a phantom scalar field (a field with negative kinetic energy) is driving the current acceleration, can that same cosmology be described by modified gravity, a theory where gravity itself is changed rather than a field added? The authors show the answer is yes mathematically, but only at a price: the standard conformal trick that converts a scalar-tensor theory into an $F(R)$ gravity has to be performed with an imaginary conformal factor, so the resulting $F(R)$ is complex in general. It becomes real only when the scalar potential is even in the field, and even then the reality holds only up to the point where the scale factor blows up in finite time. That is the paper's central payoff: the Big Rip is not an accident of phantom fields but the precise boundary of the region where the equivalent modified gravity is a real, usable theory. The authors also stress that mathematical equivalence is not physical equivalence, because the two theories use different metrics, so an accelerating universe in one can look decelerating in the other.

What carries the argument

The complex conformal transformation. The usual conformal rescaling of the metric is what lets a scalar-tensor theory be rewritten as $F(R)$ gravity, but its real form cancels the kinetic term only when that term has the canonical sign. Making the exponent imaginary, $e^{±iκφ√{2/3}}$, cancels the phantom's negative kinetic term instead, at the cost of letting the curvature and the action acquire imaginary parts. The reality of $F(R)$ then becomes a diagnostic: it holds where the phantom description is benign and fails where the phantom description degenerates.

Extended reading notes

Core claim

Starting from a phantom scalar-tensor action, the authors replace the usual real conformal rescaling $g'_{μν}=e^{±κφ√{2/3}}g_{μν}$ — which removes the kinetic term only for a canonical scalar — with the complex version $g'_{μν}=e^{±iκφ√{2/3}}g_{μν}$. The kinetic term still cancels, the scalar becomes an auxiliary field fixed by the algebraic equation $R=e^{±iκφ√{2/3}}(4κ^2V(φ)∓i√6κV'(φ))$, and the action takes the $F(R)$ form $F(R)=e^{±iκφ√{2/3}}R/(2κ^2)-e^{±2iκφ√{2/3}}V(φ)$. The authors show that this $F(R)$ is complex for generic potentials, is real when the potential depends only on $φ^2$ (in which case the auxiliary field is purely imaginary and the phantom is secretly a canonical scalar with an inverted potential), and is real for the special cosine potential $V∝1/κ^2$. Turning to the Big Rip, they take the model $V=V_0��cosh(2φ/φ_0)$, whose asymptotic solution has $H∼1/(t_0-t)$ and $|φ|→∞$ at the rip; the curvature then diverges as a complex power, $F(R)∝R^{(2-2/φ_0)/(±iκ√{2/3}+2/φ_0)}$, so no real $F(R)$ sector corresponds to the rip. Running the map backwards, they show that an $F(R)$ model with its own Big Rip, $F∝R^{-n}$, becomes a scalar-tensor theory where the singularity is pushed to infinite time (for $n<-2$) or turns into a Big Crunch (for $-1<n<-1/2$).

Load-bearing premise

The claim that the Big Rip always sits where the equivalent modified gravity turns complex is extrapolated from a handful of worked potentials, chiefly the cosh model, rather than proved for an arbitrary phantom potential.

Editorial extensions

If this is right

Any phantom cosmology has a mathematically equivalent $F(R)$ description, but that description is complex unless the scalar potential is even in the field.
For even potentials the equivalence is real only away from the Big Rip; at the rip the modified gravity side has no real solution, so the two descriptions cannot both be trusted there.
Because the two theories are related by a conformal factor, an accelerating FRW solution in the phantom theory can appear as a decelerating one in the equivalent modified gravity, and an FRW instanton can fail to be an instanton.
Conversely, an $F(R)$ model that produces an effective phantom phase with a future rip maps onto a scalar-tensor theory where the singularity either moves to infinite time or becomes a Big Crunch.
The complex character of the equivalent $F(R)$ is offered as a structural symptom of the known instabilities of phantom fields, rather than as a new pathology.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the Big Rip is exactly where the equivalent $F(R)$ becomes complex, one could use the imaginary part of $F(R)$ as a bookkeeping device for the rip: the phase of $F$ would encode how far a given phantom model sits from a real modified-gravity description.
The argument suggests a selection criterion among phantom potentials: those with an even potential survive longest as real modified gravity, so observational constraints on $F(R)$ might indirectly disfavour odd phantom potentials.
The conformal-factor mismatch means cosmological observables (luminosity distance, growth rate) should be computed in the metric that is actually physical in each frame; the paper's examples imply that frame choice can flip the sign of the deceleration parameter, which is a testable ambiguity in fitting data.
The reverse direction — $F(R)$ rip becoming an infinite-time singularity or a Big Crunch — hints that the same geometry can be either a finite-time disaster or a harmless future asymptote depending on frame, which is worth checking against the standard classification of future singularities.

Original abstract

It is shown that phantom scalar models can be mapped into a mathematically equivalent, modified $F(R)$ gravity, which turns out to be complex, in general. Only for even scalar potentials is the ensuing modified gravity real. It is also demonstrated that, even in this case, modified gravity becomes complex at the region where the original phantom dark energy theory develops a Big Rip singularity. A number of explicit examples are presented which show that these two theories are not completely equivalent, from the physical viewpoint. This basically owes to the fact that the physical metric in both theories differ in a time-dependent conformal factor. As a result, an FRW accelerating solution, or FRW instanton, in the scalar-tensor theory may look as a deccelerating FRW solution, or a non-instantonic one, in the corresponding modified gravity theory.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,916 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.84 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.21 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

It is shown that phantom scalar models can be mapped into a mathematically equivalent, modified $F(R)$ gravity, which turns out to be complex, in general. Only for even scalar potentials is the ensuing modified gravity real. It is also demonstrated that, even in this case, modified gravity becomes complex at the region where the original phantom dark energy theory develops a Big Rip singularity. A number of explicit examples are presented which show that these two theories are not completely equivalent, from the physical viewpoint. This basically owes to the fact that the physical metric in both theories differ in a time-dependent conformal factor. As a result, an FRW accelerating solution, or FRW instanton, in the scalar-tensor theory may look as a deccelerating FRW solution, or a non-instantonic one, in the corresponding modified gravity theory.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	It is shown that phantom scalar models can be mapped into a mathematically equivalent, modified $F(R)$ gravity, which turns out to be complex, in general.	result 0.74	0.85	0.28	asserted 1.00
s1	Only for even scalar potentials is the ensuing modified gravity real.	result 0.98	0.79	0.08	asserted 1.00
s2	It is also demonstrated that, even in this case, modified gravity becomes complex at the region where the original phantom dark energy theory develops a Big Rip singularity.	result 1.00	0.91	0.30	asserted 1.00
s3	A number of explicit examples are presented which show that these two theories are not completely equivalent, from the physical viewpoint.	result 0.97	0.91	0.34	asserted 1.00
s4	This basically owes to the fact that the physical metric in both theories differ in a time-dependent conformal factor.	interpretation 0.96	0.78	0.14	asserted 1.00
s5	As a result, an FRW accelerating solution, or FRW instanton, in the scalar-tensor theory may look as a deccelerating FRW solution, or a non-instantonic one, in the corresponding modified gravity theory.	interpretation 0.81	0.78	0.18	hedged possibility 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (13)

[5]

S. Capozziello, S. Nojiri and S. D. Odintsov, Phys. Lett. B 634 (2006) 93 [arXiv:hep-th/0512118]; S. Nojiri and S. D. Odintsov, Phys. Rev. D 68 (2003) 123512 [arXiv:hep-th/0307288]

View on Pith Pith review arXiv 2006
[1]

S. Nesseris and L. Perivolaropoulos, arXiv:astro-ph/0 610092; H. Jassal, J. Bagla and T. Padmanabhan, arXiv:astro-ph/0601389; P. Wu and H. Yu, arXiv:astro-ph/0611507; Z. Huang, Q. Sun, W. Fang and H. Lu, hep-th/0612176

View on Pith Pith review arXiv
[2]

V. Faraoni, Phys. Rev. D 68 (2003) 063508; Class. Quant. Grav. 22 (2005) 3235; E. Elizalde, S. Nojiri and S. D. Odintsov, Phys. Rev. D 70 (2004) 043539 [arXiv:hep-th/0405034]; S. Nojiri and S. D. O dintsov, Phys. Lett. B 595 (2004) 1 [arXiv:hep-th/0405078]; Phys. Lett. B 571 (2003) 1 [arXiv:hep-th/0306212]; B. Gumjudpai, T. Naskar, M. Sami and S. Tsujikaw...

View on Pith Pith review arXiv 2003
[3]

B. McInnes, JHEP 0208 (2002) 029

View on Pith 2002
[4]

S. D. Odintsov, S. Nojiri, arXiv:hep-th/0601213; arXiv :hep-th 0611071

View on Pith Pith review arXiv
[6]

T. Sotiriou, Class. Quant. Grav. 23 (2006) 5117

View on Pith 2006
[7]

S. Capozziello, S. Nojiri, S.D. Odintsov and A. Troisi, P hys. Lett. B 639 (2006) 135 [arXiv:astro-ph/0604431]

View on Pith Pith review arXiv 2006
[8]

T. Chiba, T. Smith, and A. Erickcek, arXiv:astro-ph/061 1867; G. Olmo, arXiv:gr-qc/0612047; X. Jin, D. Liu and X. Li, arXiv:astro-ph/0610854

View on Pith Pith review arXiv
[9]

S. Nojiri and S. D. Odintsov, Phys. Lett. B 562 (2003) 147 [arXiv:hep-th/0303117]

View on Pith Pith review arXiv 2003
[10]

V. K. Onemli and R. Woodard, Phys. Rev. D 70 (2004) 107301; E. Kahya and V. Onemli, gr-qc/0612026

View on Pith Pith review arXiv 2004
[11]

S. Nojiri, S. D. Odintsov and S. Tsujikawa, Phys. Rev.D 71 (2005) 063004 [arXiv:hep-th/0501025]

View on Pith Pith review arXiv 2005
[12]

V. Faraoni and S. Nadeau, arXiv:gr-qc/0612075

View on Pith Pith review arXiv
[13]

S. Nojiri, S. D. Odintsov, Gen. Rel. Grav. 38 (2006) 1285 [arXiv:hep-th/0506212]; S. Capozziello, S. No jiri, S. D. Odintsov, Phys. Lett. B 632 (2006) 597 [arXiv:hep-th/0507182]; S. Nojiri, S. D. Odints ov, H. Stefancic, Phys. Rev. D 74 (2006) 086009 [arXiv:hep-th/0608168]

View on Pith Pith review arXiv 2006

Forward citations

Cited by 23 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Constraints on the sum of the neutrino masses in dynamical dark energy models with $w(z) \geq -1$ are tighter than those obtained in $\Lambda$CDM
astro-ph.CO 2018-01 accept novelty 6.0 of 10

Forbidding phantom dark energy tightens the cosmological upper bound on the sum of neutrino masses to 0.13 eV, versus 0.16 eV in LambdaCDM and 0.41 eV when the dark energy equation of state is left free.
The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
hep-th 2008-04 conditional novelty 6.0 of 10

Any of the four known finite-time cosmic singularities can be realized in F(R) gravity, but in the equivalent Einstein frame only the mildest (Type IV) survives, and a hand-tuned F(R) model is proposed that avoids sin...
Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
gr-qc 2020-05 accept novelty 5.0 of 10

Metric and Palatini formulations of scalar-tensor inflation yield identical observables when their conformally invariant potentials are proportional, and the paper gives explicit conditions and a reconstruction recipe...
Precision Predictions for the Primordial Power Spectra from f(R) Models of Inflation
gr-qc 2016-06 conditional novelty 5.0 of 10

Evolving the norm-squared of mode functions yields analytic power spectra for f(R) inflation accurate to 0.3 percent, and reveals that the same spectrum takes different functional forms in the Jordan and Einstein frames.
Correspondence of $F(R)$ Gravity Singularities in Jordan and Einstein Frames
gr-qc 2016-03 conditional novelty 5.0 of 10

Conformal transformations between Jordan and Einstein frames in F(R) gravity can change the type of finite-time cosmological singularity, and in some cases remove it entirely.

Show 18 more citing papers

Big-Bounce with Finite-time Singularity: The $F(R)$ Gravity Description
gr-qc 2015-12 conditional novelty 5.0 of 10

A bounce with a Type IV singularity at the bounce point, realized in F(R) gravity, fails to produce a scale-invariant primordial power spectrum and is dynamically unstable at the singularity.
Cosmological disformal invariance
gr-qc 2015-05 conditional novelty 5.0 of 10

A pure cosmological disformal transformation is equivalent to a rescaling of time, so it leaves all observables invariant.
Dynamical behavior in $f(T,T_G)$ cosmology
gr-qc 2014-04 conditional novelty 5.0 of 10

A phase-space analysis of f(T,T_G) gravity shows the model admits stable dark-energy attractors with quintessence, cosmological-constant, or phantom behavior, plus a scaling solution, for suitable choices of two free ...
Further stable neutron star models from f(R) gravity
gr-qc 2013-09 conditional novelty 5.0 of 10

Perturbative f(R) gravity with a cubic curvature correction produces a second stable branch of neutron stars at high central density, with radii near 9 km and masses near 1.9 solar masses for the SLy equation of state.
Cyclic, ekpyrotic and little rip universe in modified gravity
hep-th 2011-08 conditional novelty 5.0 of 10

F(R) gravity can be constructed to reproduce cyclic, ekpyrotic, and little rip expansion histories, with a little rip dissolving the Sun-Earth system in roughly 30/alpha billion years for a model parameter alpha.
Constraints on Perturbative f(R) Gravity via Neutron Stars
gr-qc 2010-03 conditional novelty 5.0 of 10

Perturbative f(R) gravity with |alpha| near 10^9 cm^2 shifts neutron star mass-radius relations as much as swapping equations of state, bounding |alpha| below about 10^10 cm^2.
A simple $F({\cal R},\phi)$ deformation of Starobinsky inflationary model
hep-th 2019-01 conditional novelty 4.0 of 10

A scalar field non-minimally coupled to an R² gravity term yields viable two-field inflation for vanishing, mass, and Higgs potentials, with observables matching Starobinsky's predictions.
Autonomous Dynamical System Approach for $f(R)$ Gravity
gr-qc 2017-11 conditional novelty 4.0 of 10

For f(R) gravity with m = -Ḧ/H³ ≈ 0, the cosmological phase space has a stable de Sitter attractor at (x1, x2, x3) = (-1, 0, 2), and R² gravity instead flows to the unstable de Sitter point (0, -1, 2).
Solving higher curvature gravity theories
gr-qc 2016-04 conditional novelty 4.0 of 10

The field equations of f(R) gravity and its scalar-tensor reformulation are shown to be equivalent, and this equivalence is used to generate explicit solutions in five-dimensional warped and brane cosmological settings.
The bounce universe history from unimodular $F(R)$ gravity
gr-qc 2016-01 conditional novelty 4.0 of 10

Four bouncing cosmologies (matter, superbounce, singular, symmetric) are reconstructed as vacuum solutions of unimodular F(R) gravity, with the resulting F(R) forms tabulated and the theory's Newtonian limit and ghost...
Accelerating Cosmology and Phase Structure of F(R) Gravity with Lagrange Multiplier Constraint: Mimetic Approach
gr-qc 2015-11 conditional novelty 4.0 of 10

Given any Hubble rate and any F(R) function, two algebraic equations fix the mimetic potential and Lagrange multiplier that reproduce that expansion history, making the reconstruction true by construction rather than ...
Extreme neutron stars from Extended Theories of Gravity
gr-qc 2014-08 conditional novelty 4.0 of 10

Cubic f(R) gravity corrections can raise the maximum neutron star mass above four solar masses, and quadratic f(G) corrections allow stable stars with central densities of 1.5 to 2.0 GeV per cubic femtometer.
Maximal neutron star mass and the resolution of hyperon puzzle in modified gravity
gr-qc 2014-01 conditional novelty 4.0 of 10

A negative cubic curvature term in f(R) gravity raises the maximum neutron star mass for soft hyperon equations of state to about two solar masses, matching the PSR J1614-2230 observation.
Cosmological behavior in extended nonlinear massive gravity
astro-ph.CO 2013-01 conditional novelty 4.0 of 10

Extended nonlinear massive gravity admits stable late-time attractors that behave like quintessence, phantom, or a cosmological constant, according to a dynamical systems analysis of flat and open FRW cosmologies.
Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
hep-th 2008-07 conditional novelty 4.0 of 10

By reverse-engineering the gravitational action from a chosen expansion history, the authors exhibit F(R), Gauss-Bonnet, and non-minimal Maxwell-Einstein models that end in each of the four known finite-time future si...
Equivalence of the Einstein and Jordan frames
astro-ph.CO 2014-07 conditional novelty 3.0 of 10

The Einstein and Jordan frames describe identical physics, and the paper makes this explicit by rewriting the action in dimensionless variables that a conformal transformation leaves unchanged.
Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
gr-qc 2017-05 accept novelty 2.0 of 10

Modified gravity theories supply viable mathematical frameworks for inflation, bounces, and dark energy eras that match observational data.
Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
gr-qc 2010-11 conditional novelty 2.0 of 10

The paper reviews how arbitrary cosmic expansion histories can be reverse-engineered into modified-gravity actions, especially F(R) and related theories.

How later papers used it

51 later papers cite it

Evidence: thin. 30 of the citing papers share no author with it, and 1 of those carries a confident label from Pith's citation classifier.

Pith read 16 of the 88 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 paper by the same authors is listed below: 1 used its method or tool.

Uses its method or tool 1 paper · 1 by the same authors

By the same authors

Used this paper's complex conformal transformation in the phantom phase to vanish the kinetic term of χ.

Crossing of the phantom divide in modified gravity (2008) (same authors) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

44 arXiv papers cite this in 80 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 68 sentences without a confident label

Uses its method or tool 1 paper

Similarly, in the phantom phase we use the complex conformal transformation [ref] in order to vanish the kinetic term of $χ$ [equation] As a result, the action in the Jordan frame for the phantom phase is given by [equation] The equation of motion of $χ$ is given by [equation] This equation can be solved with respect to $χ$ as $χ= χ(R)$.

Crossing of the phantom divide in modified gravity · Relations between scalar field theories and the corresponding theories of $F(R)$ gravity · 0.95

Cites it as support 4 papers

However, this equivalence is clearly broken when singularities are present as it has been explicitly demonstrated in Ref. [ref] .

Thermodynamical correspondence of $f(R)$ gravity in Jordan and Einstein frames · Conclusions · 0.98
Also, the type of a singularity changes from one frame to other frame [ref] .

Finite-time Cosmological Singularities and the Possible Fate of the Universe · Occurrence of Singularities in Different Frames: $F(R)$ Gravity · 0.96
Further in the cosmological context for $f(R)$ gravity model it was explicitly demonstrated [ref] that neither the Hubble parameter nor the deceleration parameter matches in Jordan and Einstein frame, showing the physical non-equivalence.

Solving higher curvature gravity theories · Introduction · 0.97

Cites it as background 6 papers

In Refs. [ref] , [ref] , [ref] , [ref] - [ref] , it was pointed out that $F(R)$ gravity can be written in terms of a scalar field—quintessence or phantom like—by redefining the function $F(R)$ with the use of a convenient scalar field and then performing a conformal transformation.

F(R) cosmology in presence of a phantom fluid and its scalar-tensor counterpart:towards a unified precision model of the universe evolution · Scalar-tensor theories and $F(R)$ gravity with a fluid · 0.92
In Refs. [ref] , it was pointed out that $F(R)$ gravity can be written in terms of a scalar field—quintessence or phantom like—by redefining the function $F(R)$ with the use of a convenient scalar field and then performing a conformal transformation.

On Friedmann-Lema\^{\i}tre-Robertson-Walker cosmologies in non-standard gravity · Scalar-tensor theories and $F(R)$ gravity with a fluid · 0.83
It is well known that $F(R)$ gravity can also be formulated in Einstein frame, for detailed discussion, see for example [ref] and also [ref] and for the discussion of equivalence of these two frames, see also [ref] .

Einstein and Jordan-Frame Covariant Hamiltonians for F(R) Gravity and Their Canonical Relationships · Introduction and Summary · 0.98

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [5]

S. Capozziello, S. Nojiri and S. D. Odintsov, Phys. Lett. B 634 (2006) 93 [arXiv:hep-th/0512118]; S. Nojiri and S. D. Odintsov, Phys. Rev. D 68 (2003) 123512 [arXiv:hep-th/0307288]

View on Pith Pith review arXiv 2006

[2] [1]

S. Nesseris and L. Perivolaropoulos, arXiv:astro-ph/0 610092; H. Jassal, J. Bagla and T. Padmanabhan, arXiv:astro-ph/0601389; P. Wu and H. Yu, arXiv:astro-ph/0611507; Z. Huang, Q. Sun, W. Fang and H. Lu, hep-th/0612176

View on Pith Pith review arXiv

[3] [2]

V. Faraoni, Phys. Rev. D 68 (2003) 063508; Class. Quant. Grav. 22 (2005) 3235; E. Elizalde, S. Nojiri and S. D. Odintsov, Phys. Rev. D 70 (2004) 043539 [arXiv:hep-th/0405034]; S. Nojiri and S. D. O dintsov, Phys. Lett. B 595 (2004) 1 [arXiv:hep-th/0405078]; Phys. Lett. B 571 (2003) 1 [arXiv:hep-th/0306212]; B. Gumjudpai, T. Naskar, M. Sami and S. Tsujikaw...

View on Pith Pith review arXiv 2003

[4] [3]

B. McInnes, JHEP 0208 (2002) 029

View on Pith 2002

[5] [4]

S. D. Odintsov, S. Nojiri, arXiv:hep-th/0601213; arXiv :hep-th 0611071

View on Pith Pith review arXiv

[6] [6]

T. Sotiriou, Class. Quant. Grav. 23 (2006) 5117

View on Pith 2006

[7] [7]

S. Capozziello, S. Nojiri, S.D. Odintsov and A. Troisi, P hys. Lett. B 639 (2006) 135 [arXiv:astro-ph/0604431]

View on Pith Pith review arXiv 2006

[8] [8]

T. Chiba, T. Smith, and A. Erickcek, arXiv:astro-ph/061 1867; G. Olmo, arXiv:gr-qc/0612047; X. Jin, D. Liu and X. Li, arXiv:astro-ph/0610854

View on Pith Pith review arXiv

[9] [9]

S. Nojiri and S. D. Odintsov, Phys. Lett. B 562 (2003) 147 [arXiv:hep-th/0303117]

View on Pith Pith review arXiv 2003

[10] [10]

V. K. Onemli and R. Woodard, Phys. Rev. D 70 (2004) 107301; E. Kahya and V. Onemli, gr-qc/0612026

View on Pith Pith review arXiv 2004

[11] [11]

S. Nojiri, S. D. Odintsov and S. Tsujikawa, Phys. Rev.D 71 (2005) 063004 [arXiv:hep-th/0501025]

View on Pith Pith review arXiv 2005

[12] [12]

V. Faraoni and S. Nadeau, arXiv:gr-qc/0612075

View on Pith Pith review arXiv

[13] [13]

S. Nojiri, S. D. Odintsov, Gen. Rel. Grav. 38 (2006) 1285 [arXiv:hep-th/0506212]; S. Capozziello, S. No jiri, S. D. Odintsov, Phys. Lett. B 632 (2006) 597 [arXiv:hep-th/0507182]; S. Nojiri, S. D. Odints ov, H. Stefancic, Phys. Rev. D 74 (2006) 086009 [arXiv:hep-th/0608168]

View on Pith Pith review arXiv 2006