Applications of scalar attractor solutions to cosmology

Ng, S. C. Cindy; Nunes, Nelson J.; Rosati, Francesca

doi:10.1103/physrevd.64.083510

Cited by 145 publications

(173 citation statements)

References 42 publications

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“…In this context, many potentials have been introduced that yield late-time acceleration and tracking behaviour (see [15][16][17][18][19][20][21][22][23][24]). …”

Section: Introductionmentioning

confidence: 99%

Ghosts, instabilities, and superluminal propagation in modified gravity models

Felice

Hindmarsh

Trodden

2006

J. Cosmol. Astropart. Phys.

165

167

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We consider Modified Gravity models involving inverse powers of fourth-order curvature invariants.Using these models' equivalence to the theory of a scalar field coupled to a linear combination of the invariants, we investigate the properties of the propagating modes. Even in the case for which the fourth derivative terms in the field equations vanish, we find that the second derivative terms can give rise to ghosts, instabilities, and superluminal propagation speeds. We establish the conditions which the theories must satisfy in order to avoid these problems in Friedmann backgrounds, and show that the late-time attractor solutions generically exhibit superluminally propagating tensor or scalar modes. * a. de-felice@sussex.ac.uk

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“…In this context, many potentials have been introduced that yield late-time acceleration and tracking behaviour (see [15][16][17][18][19][20][21][22][23][24]). …”

Section: Introductionmentioning

confidence: 99%

Ghosts, instabilities, and superluminal propagation in modified gravity models

Felice

Hindmarsh

Trodden

2006

J. Cosmol. Astropart. Phys.

165

167

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“…In this paper, quintessence potentials V (φ) are generated using the phase-space approach introduced in [28] and subsequently used by a number of authors [29,30] to study the dynamics of specific quintessence potentials. To keep the discussion simple, we ignore any coupling of the quintessence field to matter, and we assume that the universe is spatially flat.…”

Section: A Energy Variablesmentioning

confidence: 99%

Can we ever distinguish between quintessence and a cosmological constant?

Chongchitnan

Efstathiou

2007

Phys. Rev. D

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Many ambitious experiments have been proposed to constrain dark energy and detect its evolution. At present, observational constraints are consistent with a cosmological constant and there is no firm evidence for any evolution in the dark energy equation of state w. In this paper, we pose the following question: suppose that future dark energy surveys constrain w at low redshift to be consistent with −1 to a percent level accuracy, what are the implications for models of dynamical dark energy? We investigate this problem in a model-independent way by following quintessence field trajectories in 'energy' phase-space. Attractor dynamics in this phase-space leads to two classes of acceptable models: 1) models with flat potentials, i.e. an effective cosmological constant, and 2) models with potentials that suddenly flatten with a characteristic kink. The prospect of further constraining the second class of models from distance measurements and fluctuation growth rates at low redshift (z 3) seems poor. However, in some models of this second class, the dark energy makes a significant contribution to the total energy density at high redshift. Such models can be further constrained from observation of the cosmic microwave background anisotropies and from primordial nucleosynthesis. It is possible, therefore, to construct models in which the dark energy at high redshift causes observable effects, even if future dark energy surveys constrain w at low redshift to be consistent with −1 to high precision.

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“…6 and 8 also show that it is not only the tracker solution that attracts Finally, it is worth noting that the underlying reason for why the early behavior of the tracker solution exhibits a "tracking property" is because the present case can be viewed as a bifurcation where EM 0 merges with FL 0 in the limit λ → ∞. The property that γ φ = γ m = 1 for EM, irrespective of λ (as long as EM exists until it merges with PL), can subsequently be exploited by comparing the reduced twodimensional dynamics of a sequence of reduced exponential scalar field state spaces, as done in [13,22,23], to yield an approximate heuristic description of the behavior of the tracking solution. Nevertheless, it should be clear that the dynamics of an inverse power-law potential model is globally very different from that of a given exponential potential, which is what can be expected from a model that does not exhibit scaling symmetries.…”

Section: Dynamical λCdm Dynamics 41 Inverse Power-law Potentialsmentioning

confidence: 99%

“…The associated solution of the exact FLRW equations has subsequently been referred to as an attractor or tracker solution [5], and has resulted in numerous papers. In [13] a thorough local dynamical systems analysis of the present models was performed, based on previous work, e.g., [22,23,24] (for additional references see, e.g., [6,13]). Here we will use a slight variation of this approach and use the following bounded scalar field variable:…”

Section: Dynamical λCdm Dynamics 41 Inverse Power-law Potentialsmentioning

confidence: 99%

Scalar field deformations ofΛCDMcosmology

Alho

Uggla

2015

Phys. Rev. D

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This paper treats nonrelativistic matter and a scalar field φ with a monotonically decreasing potential minimally coupled to gravity in flat FriedmannLemaître-Robertson-Walker cosmology. The field equations are reformulated as a three-dimensional dynamical system on an extended compact state space, complemented with cosmographic diagrams. A dynamical systems analysis provides global dynamical results describing possible asymptotic behavior. It is shown that one should impose global and asymptotic bounds on λ = −V −1 dV /dφ to obtain viable cosmological models that continuously deform ΛCDM cosmology. In particular we introduce a regularized inverse power-law potential as a simple specific example.

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Applications of scalar attractor solutions to cosmology

Cited by 145 publications

References 42 publications

Ghosts, instabilities, and superluminal propagation in modified gravity models

Ghosts, instabilities, and superluminal propagation in modified gravity models

Can we ever distinguish between quintessence and a cosmological constant?

Scalar field deformations ofΛCDMcosmology

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