f(R) dual theories of quintessence: expansion-collapse duality

Mukherjee, Dipayan; Jassal, H. K.; Lochan, Kinjalk

doi:10.1088/1475-7516/2021/12/016

Cited by 4 publications

(8 citation statements)

References 103 publications

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“…Here we would like to mention that in a previous study [16], we obtained a similar expansion-collapse duality condition between Einstein and Jordan frames, where the Jordan frame was governed by an f (R) theory. The expansion-collapse condition in the case of f (R) theories is solely determined by the Einstein frame quantities (w ϕ , ρ ϕ , H), the Jordan frame function f (R) does not appear explicitly in the condition.…”

Section: Expansion-collapse Duality Between Einstein and Jordan Framessupporting

confidence: 57%

“…The scalar-tensor theories belong to a class of modified theories of gravity, which can be mapped to Einstein's gravity using the Jordan frame-Einstein frame duality. The Einstein and Jordan frame descriptions are mathematically equivalent, it is, however, possible that the Jordan frame universe goes through a quite distinct cosmological evolution, in comparison with its Einstein frame counterpart [9][10][11][12][13][14][15][16]. In this paper we study a class of dual universes with contrasting nature of evolutions.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…However, the equations of motion in these frames may lead to drastically different evolutions of the corresponding universes. Recent studies exploring conformally connected universes with contrasting cosmological evolutions can be found in [9][10][11][12][13][14][15][16]. In [13] it is demonstrated that a decelerating Einstein frame universe can be conformally equivalent to accelerating Jordan frame universes, governed by f (R) and scalar-tensor theories.…”

Section: Introductionmentioning

confidence: 99%

“…The conformal correspondence between different types cosmological singularities is explored in [12], there it is shown that the type of cosmological singularity may vary depending on the choice of the conformal frame. The duality between an expanding Einstein frame and a collapsing Jordan frame is studied in [16]. It is shown that for some viable quintessence models in the Einstein frame, the corresponding Jordan frame, governed by an f (R) gravity theory, may have collapsing description.…”

Section: Introductionmentioning

confidence: 99%

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Bouncing universe dual to the concordance model: Scalar-tensor theories in the Jordan frame

Mukherjee¹,

Jassal²,

Lochan³

2022

Preprint

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Scalar-tensor theories of gravity provide mathematically equivalent descriptions of Einstein's gravity with a scalar field, in a conformally connected spacetime, described in terms of the Jordan frame and the Einstein frame. In this paper, we use the Jordan frame-Einstein frame correspondence to explore dual universes with contrasting cosmological evolutions. We study the mapping between Einstein and Jordan frames where the Einstein frame universe effectively describes the late-time evolution of the physical universe, driven by dark energy and non-relativistic matter. The Brans-Dicke theory of gravity is taken to be the dual scalar-tensor theory in the Jordan frame. We show that the standard Einstein frame universe, with dark energy and non-relativistic matter, always corresponds to a bouncing Jordan frame universe, if it is governed by a Brans-Dicke theory. This essentially leads to an alternative description of the late-time evolution of the physical universe, in terms of a bouncing Brans-Dicke universe in the Jordan frame. Previous studies have shown that for a bouncing Jordan frame, particularly for an early-time accelerating phase of the universe, the map between the Einstein and Jordan frames may become singular in the perturbative regime, causing the conformal correspondence to break down. In order to check whether the present bouncing model for late-time acceleration is free of such instabilities, we study the evolution of scalar metric perturbations. The Jordan frame metric perturbations are numerically solved, first via pulling the perturbations in the Einstein frame using the conformal correspondence, and then directly in the Jordan frame. The evolutions of perturbations obtained in these two cases are in a good agreement. Thus, the duality between the Einstein frame, mimicking the physical universe, and the bouncing Brans-Dicke Jordan frame, is shown to be stable against linear perturbations. An effective bouncing description of the current accelerating universe has interesting implications, for example, one may study the late-time cosmological perturbations as fluctuations in a bouncing scenario.

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Section: Expansion-collapse Duality Between Einstein and Jordan Framessupporting

confidence: 57%

Section: Summary and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bouncing universe dual to the concordance model: Scalar-tensor theories in the Jordan frame

Mukherjee¹,

Jassal²,

Lochan³

2022

Preprint

Self Cite

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“…Regardless of Dicke's argument, the Einstein and Jordan frame descriptions generally differ in their cosmological evolutions [16][17][18][19][20][21][22]. Although different conformal frames are mathematically equivalent, the equations of motion in these frames may lead to quite different properties of the scale factors, Hubble parameters, accelerations, and any higher-order derivatives of the scale factors in the two frames.…”

Section: Introductionmentioning

confidence: 99%

Condition for expansion-collapse duality between Einstein and Jordan frames

Mukherjee

Jassal

Lochan

2023

The Sixteenth Marcel Grossmann Meeting

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The conformal correspondence between FLRW universes in the Einstein and Jordan frames allows for an expansion-collapse duality -an always expanding Einstein frame universe can have a dual Jordan frame description that is contracting forever. The scenario eventually runs into an apparent paradox. When a collapsing universe approaches singularity, the classical description of the spacetime becomes inadequate. The contracting Jordan frame universe is expected to develop quantum characteristics when its scale factor becomes sufficiently small. However, at the same time, the corresponding Einstein frame universe is expected to behave classically, due to the arbitrarily large size it has grown to. In this case, the conformal map appears to be providing a duality between a quantum effect-dominated universe and a universe behaving classically. We investigate the status of the conformal map at the quantum level in such a scenario, focusing on addressing this paradox. The Einstein and Jordan frame universes are quantized individually using the Wheeler-DeWitt prescription. We show that the classical conformal map holds true at the quantum level when compared through the expectation values of the scale factor operators in the two frames. The relative quantum fluctuation in the scale factor is found to be conformally invariant, and it increases in both the past and future directions according to the internal clock. Expectedly, the quantum fluctuations in the collapsing Jordan frame keep on increasing as it shrinks towards singularity. More surprisingly, the quantum fluctuations in the expanding Einstein frame keep on increasing as well, even as its classical scale factor becomes larger. Despite having drastically different cosmological evolutions, the rise in quantum characteristics in a collapsing frame implies the same in its expanding counterpart, thereby resolving the apparent paradox.

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Einstein and Jordan frame correspondence in quantum cosmology: expansion-collapse duality

Mukherjee,

Sahota

2023

Eur. Phys. J. C

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The conformal correspondence between FLRW universes in the Einstein and Jordan frames allows for an expansion-collapse duality – an always expanding Einstein frame universe can have a dual Jordan frame description that is contracting forever. The scenario eventually runs into an apparent paradox. When the contracting Jordan frame universe becomes sufficiently small, the classical description becomes inadequate and the universe is expected to develop quantum characteristics. However, at this time, the corresponding Einstein frame universe is expected to behave classically, due to the arbitrarily large size it has grown to. The conformal map here appears to be providing a duality between a quantum effect-dominated universe and a classical universe. We investigate the status of the conformal map at the quantum level in such a scenario, focusing on addressing this paradox. The Einstein and Jordan frame universes are quantized using the Wheeler-DeWitt prescription. We show that the classical conformal map holds at the quantum level when compared through expectation values of scale factors. The relative quantum fluctuation in the scale factor becomes conformally invariant, it increases in both the past and future directions according to the internal clock. Expectedly, the quantum fluctuations in the collapsing Jordan frame increase as it shrinks towards singularity. More surprisingly, the quantum fluctuations in the expanding Einstein frame increase as well, even as its classical scale factor becomes larger. Despite having drastically different cosmological evolutions, the rise in quantum characteristics in a collapsing frame implies the same in its expanding counterpart, thereby resolving the apparent paradox.

show abstract

f(R) dual theories of quintessence: expansion-collapse duality

Cited by 4 publications

References 103 publications

Bouncing universe dual to the concordance model: Scalar-tensor theories in the Jordan frame

Bouncing universe dual to the concordance model: Scalar-tensor theories in the Jordan frame

Condition for expansion-collapse duality between Einstein and Jordan frames

Einstein and Jordan frame correspondence in quantum cosmology: expansion-collapse duality

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