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The nonlinear power spectrum in clustering quintessence cosmologies
Cosmology and Nongalactic Astrophysics · Submitted 1 Jun 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Although such differences vanish in the w \rightarrow -1, {\Lambda}CDM limit, we argue that the relation between linear and nonlinear growth of structures should be properly taken into account in constraining models with inhomogeneous dark energy.
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We study the nonlinear evolution of density perturbations in cosmologies where the late-time accelerated expansion is driven by a quintessence field with vanishing speed of sound. For these models matter and quintessence perturbations are comoving and it is possible to write a single continuity equation for the total density fluctuations given by a weighted sum of the two components. Including the Euler equation for the common velocity field we solve the evolution equations for the nonlinear, total density power spectrum in the Time-Renormalization Group approach. In fact any cosmological observable is directly related by gravity only to the total density perturbations, with the two components being individually unobservable. We show that the clustering of quintessence perturbations induces small corrections with respect to the nonlinear evolution of power spectrum in smooth quintessence models described by the same equation of state. Such small corrections, however, contrast with the large effect of a vanishing speed of sound on the linear growth function at low redshift. For this reason, models with the same normalization of the linear density power spectrum can present significantly different nonlinear corrections depending on the value of the sound speed. Although such differences vanish in the w \rightarrow -1, {\Lambda}CDM limit, we argue that the relation between linear and nonlinear growth of structures should be properly taken into account in constraining models with inhomogeneous dark energy.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the nonlinear evolution of density perturbations in cosmologies where the late-time accelerated expansion is driven by a quintessence field with vanishing speed of sound. | contribution 0.97 | 0.88 | 0.05 | asserted 0.94 |
| s1 | For these models matter and quintessence perturbations are comoving and it is possible to write a single continuity equation for the total density fluctuations given by a weighted sum of the two components. | method 0.65 | 0.41 | 0.05 | asserted 0.68 |
| s2 | Including the Euler equation for the common velocity field we solve the evolution equations for the nonlinear, total density power spectrum in the Time-Renormalization Group approach. | method 0.94 | 0.95 | 0.07 | asserted 1.00 |
| s3 | In fact any cosmological observable is directly related by gravity only to the total density perturbations, with the two components being individually unobservable. | interpretation 0.64 | 0.13 | 0.09 | asserted 1.00 |
| s4 | We show that the clustering of quintessence perturbations induces small corrections with respect to the nonlinear evolution of power spectrum in smooth quintessence models described by the same equation of state. | result 1.00 | 0.91 | 0.45 | asserted 1.00 |
| s5 | Such small corrections, however, contrast with the large effect of a vanishing speed of sound on the linear growth function at low redshift. | interpretation 0.51 | 0.69 | 0.18 | asserted 1.00 |
| s6 | For this reason, models with the same normalization of the linear density power spectrum can present significantly different nonlinear corrections depending on the value of the sound speed. | interpretation 0.75 | 0.64 | 0.26 | asserted 0.82 |
| s7 | Although such differences vanish in the w \rightarrow -1, {\Lambda}CDM limit, we argue that the relation between linear and nonlinear growth of structures should be properly taken into account in constraining models with inhomogeneous dark energy. | interpretation 0.93 | 0.42 | 0.65 | hedged possibility 0.43 |
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Original abstract
We study the nonlinear evolution of density perturbations in cosmologies where the late-time accelerated expansion is driven by a quintessence field with vanishing speed of sound. For these models matter and quintessence perturbations are comoving and it is possible to write a single continuity equation for the total density fluctuations given by a weighted sum of the two components. Including the Euler equation for the common velocity field we solve the evolution equations for the nonlinear, total density power spectrum in the Time-Renormalization Group approach. In fact any cosmological observable is directly related by gravity only to the total density perturbations, with the two components being individually unobservable. We show that the clustering of quintessence perturbations induces small corrections with respect to the nonlinear evolution of power spectrum in smooth quintessence models described by the same equation of state. Such small corrections, however, contrast with the large effect of a vanishing speed of sound on the linear growth function at low redshift. For this reason, models with the same normalization of the linear density power spectrum can present significantly different nonlinear corrections depending on the value of the sound speed. Although such differences vanish in the w \rightarrow -1, {\Lambda}CDM limit, we argue that the relation between linear and nonlinear growth of structures should be properly taken into account in constraining models with inhomogeneous dark energy.
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References
How the literature uses it
10 arXiv papers cite this in 21 sentences
Papers citing it · 14 sentences without a confident label
Contests it 1 paper
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One can see also [ref] for other approaches to non-linear clustering quintessence, which differ from our approach in the treatment of UV modes.[ In particular, references [ref] claim to apply some resummation schemes for the infrared modes below the non-linear scale, but ignore contaminations from non-linear modes.
An effective description of dark matter and dark energy in the mildly non-linear regime · EFTofLSS with DE: clustering quintessence example · contest 0.72
Builds on it 1 paper
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More generally, the limit of zero sound speed for models with $p_D ≠-ρ_D$ can be obtained as a small deformation of the ghost condensate theory [ref] (see however [ref] for another way of reproducing this limit).
The Effective Field Theory of Dark Energy · Ghost condensate and khronon · 0.83
Uses its data or values 1 paper
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This is shown in Fig. [ref] (reproducing Fig. 1 of [ref] ), where $C(τ)$ is plotted as a function of redshift for $Ω_m,0=0.25$ and different values of $w$.
Nonlinear effects of dark energy clustering beyond the acoustic scales · Equations of motion and linear solutions · 0.84
Cites it as support 1 paper
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This is the likely consequence of the fact, already suggested in earlier works [ref] , that nonlinear growth is driven predominantly by the matter component.
Nonlinear effects of dark energy clustering beyond the acoustic scales · Conclusions · 0.98
Cites it as background 3 papers
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The equations of motion of matter and dark energy perturbations for a quintessence field characterized by a vanishing speed of sound, along with their linear solutions, have been studied in several works [ref] .
Nonlinear effects of dark energy clustering beyond the acoustic scales · Equations of motion and linear solutions · 0.97
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Clustering quintessence has been considered within the context of structure formation in [ref] and in the EFTofLSS in [ref] (see also [ref] for embeddings of other dark energy theories in the EFTofLSS).
Limits on Clustering and Smooth Quintessence from the EFTofLSS · Introduction and Summary · 0.91
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For an incomplete list of references where dark energy perturbations are studied see [ref] .
Nonlinear cosmological consistency relations and effective matter stresses · Dark energy pressure perturbation · 1.00
What it cites · 30 sentences without a confident label
Uses the method or tool of 3 papers
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We compute the nonlinear power spectrum of total matter and quintessence density in the Time-RG approach introduced by [ref] .
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations · Conclusions · 0.98
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The equations of motions are solved at second order in standard Eulerian Perturbation Theory [ref] .
Large-Scale Structure of the Universe and Cosmological Perturbation Theory · Introduction · 0.98
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It is convenient to rewrite the fluid equations in terms of the doublet [ref] [ ϕ_1, (η); ϕ_2, (η) ] ≡e^-η [ _̣(η); _(η) ] , so that eqs.
Transients from Initial Conditions: A Perturbative Analysis · Non-linear evolution and the Time-RG approach · 0.81
Compares with 3 papers
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In this appendix we simply compare the predictions at redshift $z=0$ and $z=1$ for the $Λ$CDM cosmology assumed in our results, with N-body simulations [ref] as well as with predictions in RPT [ref] [We thank Vincent Desjacques and Martin Crocce for providing us, respectively, with the power spectrum measurements and the RPT predictions.].
Scale-dependent bias induced by local non-Gaussianity: A comparison to N-body simulations · On the accuracy and validity of the Time-RG approach · 0.88
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In this appendix we simply compare the predictions at redshift $z=0$ and $z=1$ for the $Λ$CDM cosmology assumed in our results, with N-body simulations [ref] as well as with predictions in RPT [ref] [We thank Vincent Desjacques and Martin Crocce for providing us, respectively, with the power spectrum measurements and the RPT predictions.].
Renormalized Cosmological Perturbation Theory · On the accuracy and validity of the Time-RG approach · 0.88
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In addition, as shown in the figure, we find that the RPT approach, in this case evaluated at the two-loop approximation, provides a prediction better than 1% up to $0.24$ at redshift zero and up to $0.32$ at $z=1$, in agreement with [ref] .
Nonlinear Evolution of Baryon Acoustic Oscillations · On the accuracy and validity of the Time-RG approach · 0.86
Cites as background 24 papers
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Most of recent investigations on the observational effects of a clustering quintessence focused so far on the linear regime [ref] .
Constraints on the sound speed of dark energy · Introduction · 0.87
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Most of recent investigations on the observational effects of a clustering quintessence focused so far on the linear regime [ref] .
Constraining dark energy with cross-correlated CMB and Large Scale Structure data · Introduction · 0.87
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Most of recent investigations on the observational effects of a clustering quintessence focused so far on the linear regime [ref] .
Can a galaxy redshift survey measure dark energy clustering? · Introduction · 0.87
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