arxiv: 2604.21770 · v1 · submitted 2026-04-23 · 🌀 gr-qc · astro-ph.CO· math-ph· math.MP

Recognition: unknown

Accelerating scaling solutions from dark matter particle creation

Sudip Halder , Jaume de Haro , Supriya Pan , Emmanuel N. Saridakis , Tapan Saha , Subenoy Chakraborty

Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:22 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COmath-phmath.MP

keywords dark matterparticle creationscaling attractorscosmological dynamicsinteraction modelslate-time accelerationFLRW cosmologydynamical systems

0 comments

The pith

Accelerating scaling attractors emerge only when dark matter particle creation drives energy flow from dark matter to the second fluid.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies a two-fluid system in flat FLRW cosmology where pressureless dark matter undergoes adiabatic particle creation and exchanges energy with a barotropic fluid. It formulates autonomous dynamical systems for six standard interaction prescriptions and classifies their fixed points. Accelerating scaling attractors, late-time states in which both fluids maintain constant energy density fractions, appear exclusively when the interaction depends on dark matter density and energy transfers from dark matter. This setup allows the model to produce late-time acceleration without introducing a separate dark energy component. A reader would care because the result isolates the precise conditions under which matter creation can mimic the observed cosmic expansion.

Core claim

In a two-fluid cosmological model with pressureless dark matter experiencing adiabatic particle creation and interacting with a barotropic fluid, accelerating scaling attractors arise only when the interaction is controlled by the dark matter density and energy flows from dark matter to the second fluid. These attractors are found in global and local dark-matter-based interactions and in the global mixed case, but are absent when the interaction depends on the second fluid or on local mixed terms, which instead drive the universe toward a dark-matter-dominated accelerating phase.

What carries the argument

Autonomous systems in a compact phase space derived from six interaction prescriptions, which locate and determine the stability of fixed points representing scaling solutions.

Load-bearing premise

The six widely used interaction prescriptions capture the essential physics and the adiabatic particle creation rate remains valid at late times in a flat FLRW background under general relativity.

What would settle it

Future measurements showing whether the ratio of energy densities between dark matter and the barotropic fluid approaches a nonzero constant at late times, together with the direction of energy transfer, would confirm or refute the existence of these attractors.

Figures

Figures reproduced from arXiv: 2604.21770 by Emmanuel N. Saridakis, Jaume de Haro, Subenoy Chakraborty, Sudip Halder, Supriya Pan, Tapan Saha.

**Figure 1.** Figure 1: FIG. 1. Phase space structure of the dynamical system ( [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 4.** Figure 4: illustrates the evolution of Ωdm, Ωf , q, w eff dm, w eff f , and κ 2Q/(3H3 ). At late times, an energy flow from DM to the second fluid drives the system toward accelerated expansion, with both density parameters asymptoting to non-zero constants. The interaction strength and matter-creation rate jointly push the effective equations of state into the negative regime, in agreement with the existence of t… view at source ↗

**Figure 3.** Figure 3: FIG. 3. Phase space diagrams of the dynamical system ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Phase portrait of the dynamical system ( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: shows the late-time behaviour of the system. The universe undergoes accelerated expansion while the energy density is shared between the two fluids, driven by a net energy flow from DM to the second fluid. The interaction and matter-creation contributions jointly push the effective equations of state w eff dm and w eff f into the negative regime, consistent with the stability of E5. Finally, we note that … view at source ↗

**Figure 7.** Figure 7: FIG. 7. Summary of accelerating scaling attractors identified [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

read the original abstract

This article opens new window to obtain accelerating scaling attractors without any need of dark energy. We study cosmological dynamics in a two-fluid system where pressureless dark matter (DM) undergoes adiabatic particle creation and exchanges energy with a barotropic fluid. Considering six widely used interaction prescriptions, we formulate the corresponding autonomous systems in a compact phase space and perform a unified dynamical analysis. We find that accelerating scaling attractors, namely late-time states where both fluids coexist with fixed energy fractions, arise only when the interaction is controlled by the DM density and energy flows from DM to the second fluid. Such attractors appear in the global and local DM-based interactions, and in the global mixed case, but are entirely absent when the interaction depends on the second fluid or on local mixed terms, which instead drive the universe to a DM-dominated accelerating phase. These results clarify the unique conditions under which matter creation can mimic dark-energy-like behaviour without introducing a dark-energy component.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper classifies six interaction forms in a DM particle creation model and finds accelerating scaling attractors only for the DM-density controlled cases with energy flowing from DM.

read the letter

The main result is a clean split across the six prescriptions: accelerating scaling fixed points, where both fluids keep constant positive density fractions and w_eff drops below -1/3, appear only when the interaction is set by the DM density and energy transfers from DM to the barotropic fluid. The other three cases instead run to a DM-dominated accelerating phase. That mapping is the useful piece of work here. The authors set up the autonomous systems in a compact phase space for each interaction, locate the fixed points, and check stability. The classification follows directly from those equations and gives a practical organizing rule for model builders who want matter creation to mimic dark-energy behavior without adding a separate DE component. The analysis stays within standard FLRW and the usual phenomenological Q terms, so the derivations are reproducible once the explicit equations are written down. The soft spot is the adiabatic creation pressure. The term p_c = -ρ_DM Γ/(3H) is inserted into the continuity equations even after Q is added, but the original derivation of Γ assumes no energy exchange; once Q is present the particle-number balance changes and it is not automatic that the same form survives at late times. The abstract does not display the Jacobian matrices or the explicit fixed-point conditions, which makes it harder to judge how sensitive the eigenvalues are to that assumption. This paper is for people already working on interacting dark-sector cosmologies who need a quick way to see which Q forms can produce scaling without extra fields. A reader who cares about the conditions for late-time acceleration in these setups will find the classification worth checking. It is solid enough on its own terms to go to peer review; referees will likely ask for the full stability tables and a short check on whether the adiabatic rate needs re-derivation once Q is active.

Referee Report

3 major / 2 minor

Summary. The manuscript analyzes a two-fluid FLRW cosmology in which pressureless dark matter undergoes adiabatic particle creation while exchanging energy with a barotropic fluid via one of six phenomenological interaction terms Q. After reducing the system to autonomous equations in a compact phase space, the authors perform a unified stability analysis and conclude that accelerating scaling fixed points (constant positive density fractions for both fluids with w_eff < −1/3) exist only for the three interaction classes controlled by the DM density (global, local, and global mixed) with energy flowing from DM to the barotropic fluid; the remaining prescriptions drive the universe to a DM-dominated accelerating phase instead.

Significance. If the central claim survives scrutiny, the work is significant because it isolates the precise phenomenological conditions under which adiabatic DM particle creation can produce late-time acceleration and scaling solutions without a separate dark-energy component. The systematic comparison across six standard interaction forms supplies a useful classification that can guide future model building in interacting dark-sector cosmologies.

major comments (3)

[Autonomous-system formulation (around the continuity equations)] The derivation of the creation pressure p_c = −ρ_DM Γ/(3H) and its insertion into the continuity equations assumes the adiabatic condition remains exact once the interaction Q is present. The modified equations are ρ̇_DM + 3H ρ_DM = −Q − 3H p_c and ρ̇_2 + 3H(1+w_2)ρ_2 = Q, yet the manuscript does not re-derive Γ from the coupled particle-number balance or Boltzmann equation; this assumption is load-bearing for the claim that acceleration at the scaling attractors is supplied by p_c.
[Dynamical analysis of fixed points] For the DM-controlled interactions that are reported to possess accelerating scaling attractors, the eigenvalues of the Jacobian at those fixed points are not listed, nor are the corresponding phase portraits or basins of attraction shown. Without these explicit stability results it is difficult to verify that the points are indeed late-time attractors and that the other interaction classes truly lack them.
[Interaction prescriptions and parameter choices] The six interaction prescriptions each contain at least one free coupling parameter whose value is chosen so that the desired scaling behavior appears. The manuscript should state the ranges of these parameters for which the attractors exist and remain accelerating, because the central “arise only when” claim is otherwise sensitive to parameter tuning.

minor comments (2)

[Notation throughout] The barotropic fluid is consistently called the “second fluid”; introducing a compact symbol (e.g., ρ_b, w_b) would improve readability of the autonomous equations.
[Section presenting the six prescriptions] A brief table summarizing the six interaction forms, their Q expressions, and the corresponding fixed-point coordinates would help the reader compare the cases at a glance.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments have prompted us to clarify several key aspects of our analysis. We address each major comment in turn below, indicating the revisions we will make to strengthen the paper.

read point-by-point responses

Referee: The derivation of the creation pressure p_c = −ρ_DM Γ/(3H) and its insertion into the continuity equations assumes the adiabatic condition remains exact once the interaction Q is present. The modified equations are ρ̇_DM + 3H ρ_DM = −Q − 3H p_c and ρ̇_2 + 3H(1+w_2)ρ_2 = Q, yet the manuscript does not re-derive Γ from the coupled particle-number balance or Boltzmann equation; this assumption is load-bearing for the claim that acceleration at the scaling attractors is supplied by p_c.

Authors: We appreciate this observation on the foundational assumptions. In the model, the particle creation rate Γ is introduced for the dark matter fluid following the standard phenomenological treatment of adiabatic creation in FLRW cosmologies, where the particle number balance is ṅ + 3 H n = n Γ (independent of the energy-exchange term Q). The interaction Q represents a separate phenomenological energy transfer between the fluids and does not alter this number balance or the thermodynamic derivation of the creation pressure p_c = −ρ_DM Γ/(3H). Thus the standard formula remains valid, and the negative p_c supplies the acceleration at the scaling points. To address the concern explicitly, we will add a clarifying paragraph in the revised manuscript explaining this separation of the creation process from the energy-exchange term Q, with reference to the standard literature. revision: yes
Referee: For the DM-controlled interactions that are reported to possess accelerating scaling attractors, the eigenvalues of the Jacobian at those fixed points are not listed, nor are the corresponding phase portraits or basins of attraction shown. Without these explicit stability results it is difficult to verify that the points are indeed late-time attractors and that the other interaction classes truly lack them.

Authors: We agree that tabulating the eigenvalues improves transparency. Although the unified stability analysis was performed by computing the Jacobian eigenvalues at each fixed point, they were not presented in tabular form for conciseness. In the revision we will add a table listing the eigenvalues (and their real parts) for the accelerating scaling fixed points in the DM-controlled cases, together with the parameter conditions under which all real parts are negative. For the phase-space structure, we will include a qualitative discussion of the basins of attraction and, space permitting, representative phase portraits to illustrate the flow toward the late-time attractors and the absence of scaling solutions in the other interaction classes. revision: yes
Referee: The six interaction prescriptions each contain at least one free coupling parameter whose value is chosen so that the desired scaling behavior appears. The manuscript should state the ranges of these parameters for which the attractors exist and remain accelerating, because the central “arise only when” claim is otherwise sensitive to parameter tuning.

Authors: This is a fair criticism. The existence and stability of the scaling attractors depend on the values of the coupling parameters. We will revise the manuscript to state explicitly the ranges of these parameters (e.g., intervals for the dimensionless coupling constants) for which the accelerating scaling fixed points exist, remain stable, and satisfy w_eff < −1/3. These ranges will be derived directly from the fixed-point coordinates and the eigenvalue conditions, thereby rendering the classification “arise only for DM-controlled interactions with energy flow from DM” precise and independent of arbitrary tuning. revision: yes

Circularity Check

0 steps flagged

Derivation is self-contained phase-space analysis with no reduction to inputs

full rationale

The paper constructs autonomous systems directly from the continuity equations that incorporate the adiabatic creation pressure p_c = −ρ_DM Γ/(3H) together with each of the six phenomenological Q forms. Fixed-point conditions and stability eigenvalues are then obtained by algebraic solution of those equations; the statement that accelerating scaling attractors exist only for DM-controlled interactions is therefore a direct output of the phase-space analysis rather than a redefinition or fit of the input quantities. No load-bearing self-citation, ansatz smuggling, or renaming of known results occurs in the central derivation chain, and the model assumptions (flat FLRW, adiabatic creation, chosen Q prescriptions) are stated explicitly without being derived from the target result.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard cosmological assumptions plus phenomenological interaction terms whose parameters are not independently derived; no new entities are postulated.

free parameters (1)

interaction coupling parameters
Each of the six prescriptions typically introduces one or more free parameters controlling the energy transfer rate; these are chosen or constrained to realize the reported attractors.

axioms (2)

standard math The background is a flat FLRW metric governed by general relativity.
Invoked implicitly to write the Friedmann and continuity equations for the two-fluid system.
domain assumption Dark matter is pressureless and particle creation is adiabatic.
Core modeling choice stated in the abstract that defines the continuity equation for the DM fluid.

pith-pipeline@v0.9.0 · 5485 in / 1407 out tokens · 41662 ms · 2026-05-09T21:22:12.959622+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

134 extracted references · 128 canonical work pages · 2 internal anchors

[1]

On the boundaryx= 1, one findsx ′ =−µ(1−z), implying that forµ >0 the variablexdecreases near x= 1

Model A:Q=µHρ dm For the global interaction rateQ=µHρ dm, the au- tonomous system (15)-(16) becomes, after regularization, x′ =−µx(1−z) +x(1−x) [3w(1−z) +αz],(17) z′ = 3 2 z(1−z) h (1 +w(1−x))(1−z)− αxz 3 i .(18) The surfacesx= 0,z= 0 andz= 1 are invariant mani- folds. On the boundaryx= 1, one findsx ′ =−µ(1−z), implying that forµ >0 the variablexdecrease...
[2]

As in Model A, the hypersurfacesx= 0,z= 0, andz= 1 are invariant manifolds

Model B:Q= Γρ dm For the local interaction rateQ= Γρ dm, the regular- ized autonomous system (15)-(16) becomes x′ =−βxz+x(1−x) [3w(1−z) +αz],(19) z′ = 3 2 z(1−z) h (1 +w(1−x))(1−z)− αxz 3 i ,(20) whereβ≡Γ/H 0 is a dimensionless coupling constant. As in Model A, the hypersurfacesx= 0,z= 0, andz= 1 are invariant manifolds. On the boundaryx= 1, one 5 B0 B1 B...
[3]

Along the boundaryx= 0 we havex ′ =−ξ(1−z); thus,xincreases nearx= 0 providedξ <0

Model C:Q=ξHρ f For the global interaction rateQ=ξHρ f, the regular- ized autonomous system (15)-(16) becomes x′ = (1−x) [−ξ(1−z) + 3wx(1−z) +αxz],(21) z′ = 3 2 z(1−z) h (1 +w(1−x))(1−z)− αxz 3 i .(22) From these equations one identifiesx= 1,z= 0, and z= 1 as invariant manifolds. Along the boundaryx= 0 we havex ′ =−ξ(1−z); thus,xincreases nearx= 0 provide...
[4]

The surfacesx= 1,z= 0, andz= 1 are invariant manifolds

Model D:Q= eΓρ f For the local interaction rateQ= eΓρf, the regularized autonomous system (15)-(16) becomes x′ =−γ(1−x)z+x(1−x) [3w(1−z) +αz],(23) z′ = 3 2 z(1−z) h (1 +w(1−x))(1−z)− αxz 3 i ,(24) whereγ≡ eΓ/H0 is a dimensionless coupling parameter. The surfacesx= 1,z= 0, andz= 1 are invariant manifolds. Along the linex= 0 we havex ′ =−γz, so xincreases n...
[5]

The corresponding critical points and their cosmological properties are listed in Table A3 (see A)

Model E:Q=δH ρdmρf ρdm +ρ f For the global interaction rateQ=δH ρdmρf ρdm +ρ f , the regularized autonomous system (15)-(16) takes the form x′ =x(1−x) h −δ(1−z) + 3w(1−z) +αz i ,(25) z′ = 3 2 z(1−z) h (1 +w(1−x))(1−z)− αxz 3 i .(26) The boundariesx= 0,x= 1,z= 0, andz= 1 are invari- ant manifolds, ensuring that the compact phase spaceD is positively invari...
[6]

real-world

Model F:Q= Γ ρdmρf ρdm +ρ f For the local interaction rateQ= Γ ρdmρf ρdm +ρ f ,the regularized autonomous system (15)-(16) reduces to x′ =x(1−x) h −νz+ 3w(1−z) +αz i ,(27) z′ = 3 2 z(1−z) h (1 +w(1−x))(1−z)− αxz 3 i ,(28) whereν≡ Γ/H0 is a dimensionless coupling parameter. The hypersurfacesx= 0,x= 1,z= 0, andz= 1 are invariant manifolds, so the compact do...

work page doi:10.13039/501100011033 2019
[7]

A. G. Riess, et al., Observational evidence from su- pernovae for an accelerating universe and a cosmologi- cal constant, Astron. J. 116 (1998) 1009–1038.arXiv: astro-ph/9805201,doi:10.1086/300499

work page Pith review doi:10.1086/300499 1998
[8]

1999, apj, 517, 565, doi: 10.1086/307221

S. Perlmutter, et al., Measurements of Ω and Λ from 42 high redshift supernovae, Astrophys. J. 517 (1999) 565– 586.arXiv:astro-ph/9812133,doi:10.1086/307221

work page internal anchor Pith review doi:10.1086/307221 1999
[9]

2020a, Astron

N. Aghanim, et al., Planck 2018 results. VI. Cosmo- logical parameters, Astron. Astrophys. 641 (2020) A6, [Erratum: Astron.Astrophys. 652, C4 (2021)].arXiv: 1807.06209,doi:10.1051/0004-6361/201833910

work page doi:10.1051/0004-6361/201833910 2018
[10]

E. J. Copeland, M. Sami, S. Tsujikawa, Dynam- ics of dark energy, Int. J. Mod. Phys. D 15 (2006) 1753–1936.arXiv:hep-th/0603057,doi:10.1142/ S021827180600942X

work page Pith review arXiv 2006
[11]

Bamba, S

K. Bamba, S. Capozziello, S. Nojiri, S. D. Odintsov, Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests, As- trophys. Space Sci. 342 (2012) 155–228.arXiv:1205. 3421,doi:10.1007/s10509-012-1181-8

work page doi:10.1007/s10509-012-1181-8 2012
[12]

E. N. Saridakis, et al., Modified Gravity and Cosmology: An Update by the CANTATA Network, Springer, 2021. arXiv:2105.12582,doi:10.1007/978-3-030-83715-0

work page doi:10.1007/978-3-030-83715-0 2021
[13]

f(R) theories

A. De Felice, S. Tsujikawa, f(R) theories, Living Rev. Rel. 13 (2010) 3.arXiv:1002.4928,doi:10.12942/ lrr-2010-3

work page Pith review arXiv 2010
[14]

Branco et al

T. Clifton, P. G. Ferreira, A. Padilla, C. Skordis, Modi- fied Gravity and Cosmology, Phys. Rept. 513 (2012) 1– 189.arXiv:1106.2476,doi:10.1016/j.physrep.2012. 01.001

work page doi:10.1016/j.physrep.2012 2012
[15]

Capozziello, M

S. Capozziello, M. De Laurentis, Extended Theories of Gravity, Phys. Rept. 509 (2011) 167–321.arXiv:1108. 6266,doi:10.1016/j.physrep.2011.09.003

work page doi:10.1016/j.physrep.2011.09.003 2011
[16]

Y.-F. Cai, S. Capozziello, M. De Laurentis, E. N. Sari- dakis, f(T) teleparallel gravity and cosmology, Rept. Prog. Phys. 79 (10) (2016) 106901.arXiv:1511.07586, doi:10.1088/0034-4885/79/10/106901

work page doi:10.1088/0034-4885/79/10/106901 2016
[17]

Nojiri, S

S. Nojiri, S. D. Odintsov, V. K. Oikonomou, Modi- fied Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution, Phys. Rept. 692 (2017) 1–104. arXiv:1705.11098,doi:10.1016/j.physrep.2017.06. 001

work page doi:10.1016/j.physrep.2017.06 2017
[18]

Bahamonde, K

S. Bahamonde, K. F. Dialektopoulos, C. Escamilla- Rivera, G. Farrugia, V. Gakis, M. Hendry, M. Hohmann, J. Levi Said, J. Mifsud, E. Di Valentino, Teleparallel gravity: from theory to cosmology, Rept. Prog. Phys. 86 (2) (2023) 026901.arXiv:2106.13793, doi:10.1088/1361-6633/ac9cef

work page doi:10.1088/1361-6633/ac9cef 2023
[19]

High precision analytical description of the allowed beta spectrum shape

S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys. 61 (1989) 1–23.doi:10.1103/RevModPhys. 61.1

work page doi:10.1103/revmodphys 1989
[20]

and Wang, L

I. Zlatev, L.-M. Wang, P. J. Steinhardt, Quintessence, cosmic coincidence, and the cosmological constant, Phys. Rev. Lett. 82 (1999) 896–899.arXiv:astro-ph/ 9807002,doi:10.1103/PhysRevLett.82.896

work page doi:10.1103/physrevlett.82.896 1999
[21]

Classical and Quantum Gravity , keywords =

E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri, D. F. Mota, A. G. Riess, J. Silk, In the realm of the Hubble tension—a review of solutions, Class. Quant. Grav. 38 (15) (2021) 153001.arXiv: 2103.01183,doi:10.1088/1361-6382/ac086d

work page doi:10.1088/1361-6382/ac086d 2021
[22]

Y. L. Bolotin, A. Kostenko, O. A. Lemets, D. A. Yerokhin, Cosmological Evolution With Interaction Be- tween Dark Energy And Dark Matter, Int. J. Mod. Phys. D 24 (03) (2014) 1530007.arXiv:1310.0085, doi:10.1142/S0218271815300074

work page doi:10.1142/s0218271815300074 2014
[23]

B. Wang, E. Abdalla, F. Atrio-Barandela, D. Pavon, Dark Matter and Dark Energy Interactions: Theoreti- cal Challenges, Cosmological Implications and Obser- vational Signatures, Rept. Prog. Phys. 79 (9) (2016) 096901.arXiv:1603.08299,doi:10.1088/0034-4885/ 79/9/096901

work page doi:10.1088/0034-4885/ 2016
[24]

L. P. Chimento, A. S. Jakubi, D. Pavon, W. Zim- dahl, Interacting quintessence solution to the coin- cidence problem, Phys. Rev. D 67 (2003) 083513. arXiv:astro-ph/0303145,doi:10.1103/PhysRevD.67. 083513

work page doi:10.1103/physrevd.67 2003
[25]

J. D. Barrow, T. Clifton, Cosmologies with energy ex- change, Phys. Rev. D 73 (2006) 103520.arXiv:gr-qc/ 0604063,doi:10.1103/PhysRevD.73.103520

work page doi:10.1103/physrevd.73.103520 2006
[26]

Amendola, G

L. Amendola, G. Camargo Campos, R. Rosenfeld, Con- sequences of dark matter-dark energy interaction on cos- mological parameters derived from SNIa data, Phys. Rev. D 75 (2007) 083506.arXiv:astro-ph/0610806, doi:10.1103/PhysRevD.75.083506

work page doi:10.1103/physrevd.75.083506 2007
[27]

del Campo, R

S. del Campo, R. Herrera, D. Pavon, Interacting models may be key to solve the cosmic coincidence problem, JCAP 01 (2009) 020.arXiv:0812.2210,doi:10.1088/ 1475-7516/2009/01/020. 12 Model:Q=µHρ dm Critical Points Existence Eigenvalues Stability Ωdm Acceleration A0 (0,0) Always 3 2(1 +w),3w−µ Unstable ifµ <3w; Saddle ifµ≥3w 0 No:q= 1 2(1 + 3w) A1 (0,1) Alwa...

work page arXiv 2009
[28]

J.-H. He, B. Wang, Effects of the interaction between dark energy and dark matter on cosmological param- eters, JCAP 06 (2008) 010.arXiv:0801.4233,doi: 10.1088/1475-7516/2008/06/010

work page doi:10.1088/1475-7516/2008/06/010 2008
[29]

Basilakos, M

S. Basilakos, M. Plionis, Is the Interacting Dark Mat- ter Scenario an Alternative to Dark Energy ?, As- tron. Astrophys. 507 (2009) 47.arXiv:0807.4590,doi: 10.1051/0004-6361/200912661

work page doi:10.1051/0004-6361/200912661 2009
[30]

M. B. Gavela, D. Hernandez, L. Lopez Honorez, O. Mena, S. Rigolin, Dark coupling, JCAP 07 (2009) 034, [Erratum: JCAP 05, E01 (2010)].arXiv:0901. 1611,doi:10.1088/1475-7516/2009/07/034

work page doi:10.1088/1475-7516/2009/07/034 2009
[31]

Jamil, E

M. Jamil, E. N. Saridakis, M. R. Setare, Thermody- namics of dark energy interacting with dark matter and radiation, Phys. Rev. D 81 (2010) 023007.arXiv: 0910.0822,doi:10.1103/PhysRevD.81.023007

work page doi:10.1103/physrevd.81.023007 2010
[32]

S. Z. W. Lip, Interacting Cosmological Fluids and the Coincidence Problem, Phys. Rev. D 83 (2011) 023528. arXiv:1009.4942,doi:10.1103/PhysRevD.83.023528

work page doi:10.1103/physrevd.83.023528 2011
[33]

X.-m. Chen, Y. Gong, E. N. Saridakis, Y. Gong, Time- dependent interacting dark energy and transient accel- eration, Int. J. Theor. Phys. 53 (2014) 469–481.arXiv: 13 Model:Q=δHρdmρf(ρdm+ρf)−1 Critical Points Existence Eigenvalues Stability Ωdm Acceleration E0(0,0) Always 3w−δ, 3 2(1 +w) Saddle ifδ >3w; Unstable ifδ≤3w 0 No:q= 1 2(1 + 3w) E1(1,0) Always δ−...

work page doi:10.1007/s10773-013-1831-9 2014
[34]

W. Yang, L. Xu, Cosmological constraints on inter- acting dark energy with redshift-space distortion af- ter Planck data, Phys. Rev. D 89 (8) (2014) 083517. arXiv:1401.1286,doi:10.1103/PhysRevD.89.083517

work page doi:10.1103/physrevd.89.083517 2014
[35]

Faraoni, J

V. Faraoni, J. B. Dent, E. N. Saridakis, Covariantizing the interaction between dark energy and dark matter, Phys. Rev. D 90 (6) (2014) 063510.arXiv:1405.7288, doi:10.1103/PhysRevD.90.063510

work page doi:10.1103/physrevd.90.063510 2014
[36]

Bl´ azquez-Salcedo, C

V. Salvatelli, N. Said, M. Bruni, A. Melchiorri, D. Wands, Indications of a late-time interaction in the dark sector, Phys. Rev. Lett. 113 (18) (2014) 181301.arXiv:1406.7297,doi:10.1103/PhysRevLett. 113.181301

work page doi:10.1103/physrevlett 2014
[38]

S. Pan, S. Bhattacharya, S. Chakraborty, An ana- lytic model for interacting dark energy and its ob- servational constraints, Mon. Not. Roy. Astron. Soc. 452 (3) (2015) 3038–3046.arXiv:1210.0396,doi: 10.1093/mnras/stv1495

work page doi:10.1093/mnras/stv1495 2015
[39]

R. C. Nunes, S. Pan, E. N. Saridakis, New constraints on interacting dark energy from cosmic chronometers, Phys. Rev. D 94 (2) (2016) 023508.arXiv:1605.01712, doi:10.1103/PhysRevD.94.023508

work page doi:10.1103/physrevd.94.023508 2016
[40]

van de Bruck, J

C. van de Bruck, J. Mifsud, J. P. Mimoso, N. J. Nunes, Generalized dark energy interactions with mul- tiple fluids, JCAP 11 (2016) 031.arXiv:1605.03834, doi:10.1088/1475-7516/2016/11/031

work page doi:10.1088/1475-7516/2016/11/031 2016
[41]

Mukherjee, N

A. Mukherjee, N. Banerjee, In search of the dark matter dark energy interaction: a kinematic approach, Class. Quant. Grav. 34 (3) (2017) 035016.arXiv:1610.04419, doi:10.1088/1361-6382/aa54c8

work page doi:10.1088/1361-6382/aa54c8 2017
[42]

van de Bruck, J

C. van de Bruck, J. Mifsud, J. Morrice, Testing coupled dark energy models with their cosmological background evolution, Phys. Rev. D 95 (4) (2017) 043513.arXiv: 1609.09855,doi:10.1103/PhysRevD.95.043513

work page doi:10.1103/physrevd.95.043513 2017
[43]

R.-G. Cai, N. Tamanini, T. Yang, Reconstructing the dark sector interaction with LISA, JCAP 05 (2017) 031. arXiv:1703.07323,doi:10.1088/1475-7516/2017/05/ 031

work page doi:10.1088/1475-7516/2017/05/ 2017
[44]

W. Yang, S. Pan, J. D. Barrow, Large-scale Stability and Astronomical Constraints for Coupled Dark-Energy Models, Phys. Rev. D 97 (4) (2018) 043529.arXiv: 1706.04953,doi:10.1103/PhysRevD.97.043529

work page doi:10.1103/physrevd.97.043529 2018
[45]

S. Pan, A. Mukherjee, N. Banerjee, Astronomical bounds on a cosmological model allowing a general in- teraction in the dark sector, Mon. Not. Roy. Astron. Soc. 477 (1) (2018) 1189–1205.arXiv:1710.03725, doi:10.1093/mnras/sty755

work page doi:10.1093/mnras/sty755 2018
[46]

Mifsud, C

J. Mifsud, C. Van De Bruck, Probing the imprints of generalized interacting dark energy on the growth of perturbations, JCAP 11 (2017) 001.arXiv:1707.07667, doi:10.1088/1475-7516/2017/11/001

work page doi:10.1088/1475-7516/2017/11/001 2017
[47]

W. Yang, S. Pan, A. Paliathanasis, Cosmological con- straints on an exponential interaction in the dark sector, Mon. Not. Roy. Astron. Soc. 482 (1) (2019) 1007–1016. arXiv:1804.08558,doi:10.1093/mnras/sty2780. 14

work page doi:10.1093/mnras/sty2780 2019
[50]

S. Pan, W. Yang, C. Singha, E. N. Saridakis, Ob- servational constraints on sign-changeable interaction models and alleviation of theH 0 tension, Phys. Rev. D 100 (8) (2019) 083539.arXiv:1903.10969,doi: 10.1103/PhysRevD.100.083539

work page doi:10.1103/physrevd.100.083539 2019
[51]

C. Li, X. Ren, M. Khurshudyan, Y.-F. Cai, Implica- tions of the possible 21-cm line excess at cosmic dawn on dynamics of interacting dark energy, Phys. Lett. B 801 (2020) 135141.arXiv:1904.02458,doi:10.1016/ j.physletb.2019.135141

work page arXiv 2020
[52]

W. Yang, S. Pan, E. Di Valentino, B. Wang, A. Wang, Forecasting interacting vacuum-energy models using gravitational waves, JCAP 05 (2020) 050.arXiv:1904. 11980,doi:10.1088/1475-7516/2020/05/050

work page doi:10.1088/1475-7516/2020/05/050 2020
[53]

W. Yang, S. Vagnozzi, E. Di Valentino, R. C. Nunes, S. Pan, D. F. Mota, Listening to the sound of dark sector interactions with gravitational wave standard sirens, JCAP 07 (2019) 037.arXiv:1905.08286,doi: 10.1088/1475-7516/2019/07/037

work page doi:10.1088/1475-7516/2019/07/037 2019
[54]

Paliathanasis, S

A. Paliathanasis, S. Pan, W. Yang, Dynamics of non- linear interacting dark energy models, Int. J. Mod. Phys. D 28 (12) (2019) 1950161.arXiv:1903.02370, doi:10.1142/S021827181950161X

work page doi:10.1142/s021827181950161x 2019
[55]

Di Valentino, A

E. Di Valentino, A. Melchiorri, O. Mena, S. Vagnozzi, Interacting dark energy in the early 2020s: A promis- ing solution to theH 0 and cosmic shear tensions, Phys. Dark Univ. 30 (2020) 100666.arXiv:1908.04281,doi: 10.1016/j.dark.2020.100666

work page doi:10.1016/j.dark.2020.100666 2020
[56]

G´ omez-Valent, V

A. G´ omez-Valent, V. Pettorino, L. Amendola, Update on coupled dark energy and theH 0 tension, Phys. Rev. D 101 (12) (2020) 123513.arXiv:2004.00610,doi:10. 1103/PhysRevD.101.123513

work page arXiv 2020
[57]

Paliathanasis, Dynamics of Chiral Cosmology, Class

A. Paliathanasis, Dynamics of Chiral Cosmology, Class. Quant. Grav. 37 (19) (2020) 195014.arXiv:2003. 05342,doi:10.1088/1361-6382/aba667

work page doi:10.1088/1361-6382/aba667 2020
[58]

Khyllep, J

W. Khyllep, J. Dutta, S. Basilakos, E. N. Saridakis, Background evolution and growth of structures in inter- acting dark energy scenarios through dynamical system analysis, Phys. Rev. D 105 (4) (2022) 043511.arXiv: 2111.01268,doi:10.1103/PhysRevD.105.043511

work page doi:10.1103/physrevd.105.043511 2022
[59]

Chatzidakis, A

S. Chatzidakis, A. Giacomini, P. G. L. Leach, G. Leon, A. Paliathanasis, S. Pan, Interacting dark energy in curved FLRW spacetime from Weyl Integrable Space- time, JHEAp 36 (2022) 141–151.arXiv:2206.06639, doi:10.1016/j.jheap.2022.10.001

work page doi:10.1016/j.jheap.2022.10.001 2022
[60]

Y. Zhai, W. Giar` e, C. van de Bruck, E. Di Valentino, O. Mena, R. C. Nunes, A consistent view of inter- acting dark energy from multiple CMB probes, JCAP 07 (2023) 032.arXiv:2303.08201,doi:10.1088/ 1475-7516/2023/07/032

work page arXiv 2023
[61]

Li, S.-J

T.-N. Li, S.-J. Jin, H.-L. Li, J.-F. Zhang, X. Zhang, Prospects for Probing the Interaction between Dark En- ergy and Dark Matter Using Gravitational-wave Dark Sirens with Neutron Star Tidal Deformation, Astro- phys. J. 963 (1) (2024) 52.arXiv:2310.15879,doi: 10.3847/1538-4357/ad1bc9

work page doi:10.3847/1538-4357/ad1bc9 2024
[62]

Y.-H. Li, X. Zhang, IDECAMB: an implementation of interacting dark energy cosmology in CAMB, JCAP 09 (2023) 046.arXiv:2306.01593,doi:10.1088/ 1475-7516/2023/09/046

work page arXiv 2023
[63]

, author Giar \`e , W

M. Forconi, W. Giar` e, O. Mena, Ruchika, E. Di Valentino, A. Melchiorri, R. C. Nunes, A double take on early and interacting dark energy from JWST, JCAP 05 (2024) 097.arXiv:2312.11074, doi:10.1088/1475-7516/2024/05/097

work page doi:10.1088/1475-7516/2024/05/097 2024
[64]

E. M. Teixeira, R. Daniel, N. Frusciante, C. van de Bruck, Forecasts on interacting dark energy with stan- dard sirens, Phys. Rev. D 108 (8) (2023) 084070.arXiv: 2309.06544,doi:10.1103/PhysRevD.108.084070

work page doi:10.1103/physrevd.108.084070 2023
[65]

Paliathanasis, Unified dark energy from Chiral- Quintom model with a mixed potential in Fried- mann–Lemaˆ ıtre–Robertson–Walker cosmology, Eur

A. Paliathanasis, Unified dark energy from Chiral- Quintom model with a mixed potential in Fried- mann–Lemaˆ ıtre–Robertson–Walker cosmology, Eur. Phys. J. C 83 (8) (2023) 756.arXiv:2308.10460, doi:10.1140/epjc/s10052-023-11946-5

work page doi:10.1140/epjc/s10052-023-11946-5 2023
[66]

Giar` e, Y

W. Giar` e, Y. Zhai, S. Pan, E. Di Valentino, R. C. Nunes, C. van de Bruck, Tightening the reins on non- minimal dark sector physics: Interacting dark energy with dynamical and nondynamical equation of state, Phys. Rev. D 110 (6) (2024) 063527.arXiv:2404.02110, doi:10.1103/PhysRevD.110.063527

work page doi:10.1103/physrevd.110.063527 2024
[67]

Mbarek and D

T.-N. Li, P.-J. Wu, G.-H. Du, S.-J. Jin, H.-L. Li, J.- F. Zhang, X. Zhang, Constraints on Interacting Dark Energy Models from the DESI Baryon Acoustic Oscil- lation and DES Supernovae Data, Astrophys. J. 976 (1) (2024) 1.arXiv:2407.14934,doi:10.3847/1538-4357/ ad87f0

work page doi:10.3847/1538-4357/ 2024
[68]

Li, G.-H

T.-N. Li, G.-H. Du, Y.-H. Li, P.-J. Wu, S.-J. Jin, J.-F. Zhang, X. Zhang, Probing the sign-changeable interac- tion between dark energy and dark matter with DESI baryon acoustic oscillations and DES supernovae data, Sci. China Phys. Mech. Astron. 69 (1) (2026) 210413. arXiv:2501.07361,doi:10.1007/s11433-025-2771-5

work page doi:10.1007/s11433-025-2771-5 2026
[69]

Y. Zhai, M. de Cesare, C. van de Bruck, E. Di Valentino, E. Wilson-Ewing, A low-redshift preference for an inter- acting dark energy model, JCAP 11 (2025) 010.arXiv: 2503.15659,doi:10.1088/1475-7516/2025/11/010

work page doi:10.1088/1475-7516/2025/11/010 2025
[70]

van der Westhuizen, D

M. van der Westhuizen, D. Figueruelo, R. Thubisi, S. Sahlu, A. Abebe, A. Paliathanasis, Compartmental- ization in the dark sector of the universe after DESI DR2 BAO data, Phys. Dark Univ. 50 (2025) 102107.arXiv: 2505.23306,doi:10.1016/j.dark.2025.102107

work page doi:10.1016/j.dark.2025.102107 2025
[71]

Li, G.-H

T.-N. Li, G.-H. Du, Y.-H. Li, Y. Li, J.-L. Ling, J.-F. Zhang, X. Zhang, Updated constraints on interacting dark energy: A comprehensive analysis using multiple CMB probes, DESI DR2, and supernovae observations (10 2025).arXiv:2510.11363

work page arXiv 2025
[72]

Y.-H. Li, X. Zhang, Cosmic Sign-Reversal: Non- Parametric Reconstruction of Interacting Dark Energy with DESI DR2 (6 2025).arXiv:2506.18477

work page arXiv 2025
[74]

A review on brain tumor segmentation based on deep learning methods with federated learning techniques

M. van der Westhuizen, A. Abebe, E. Di Valentino, II. Non-linear interacting dark energy: Analytical so- lutions and theoretical pathologies, Phys. Dark Univ. 50 (2025) 102120.arXiv:2509.04494,doi:10.1016/j. 15 dark.2025.102120

work page doi:10.1016/j 2025
[75]

Zhang, T.-N

Y.-M. Zhang, T.-N. Li, G.-H. Du, S.-H. Zhou, L.-Y. Gao, J.-F. Zhang, X. Zhang, Alleviating theH 0 tension through new interacting dark energy model in light of DESI DR2 (10 2025).arXiv:2510.12627

work page arXiv 2025
[76]

Figueruelo, M

D. Figueruelo, M. van der Westhuizen, A. Abebe, E. Di Valentino, Late-time Background Constraints on Linear and Non-linear Interacting Dark Energy after DESI DR2 (1 2026).arXiv:2601.03122

work page arXiv 2026
[77]

Paliathanasis, Phys

A. Paliathanasis, Indications of a Late-Time Transition to a Strongly Interacting Dark Sector (1 2026).arXiv: 2601.02789

work page arXiv 2026
[78]

Amendola, Scaling solutions in general nonmini- mal coupling theories, Phys

L. Amendola, Scaling solutions in general nonmini- mal coupling theories, Phys. Rev. D 60 (1999) 043501. arXiv:astro-ph/9904120,doi:10.1103/PhysRevD.60. 043501

work page doi:10.1103/physrevd.60 1999
[79]

Amendola and D

L. Amendola, D. Tocchini-Valentini, Stationary dark energy: The Present universe as a global attractor, Phys. Rev. D 64 (2001) 043509.arXiv:astro-ph/ 0011243,doi:10.1103/PhysRevD.64.043509

work page doi:10.1103/physrevd.64.043509 2001
[80]

Zimdahl, D

W. Zimdahl, D. Pavon, Interacting quintessence, Phys. Lett. B 521 (2001) 133–138.arXiv:astro-ph/0105479, doi:10.1016/S0370-2693(01)01174-1

work page doi:10.1016/s0370-2693(01)01174-1 2001
[81]

Wetterich, The Cosmon model for an asymptotically vanishing time dependent cosmological ’constant’, As- tron

C. Wetterich, The Cosmon model for an asymptotically vanishing time dependent cosmological ’constant’, As- tron. Astrophys. 301 (1995) 321–328.arXiv:hep-th/ 9408025

1995
[82]

Coupled Quintessence

L. Amendola, Coupled quintessence, Phys. Rev. D 62 (2000) 043511.arXiv:astro-ph/9908023,doi:10. 1103/PhysRevD.62.043511

work page Pith review arXiv 2000
[83]

R.-G. Cai, A. Wang, Cosmology with in- teraction between phantom dark energy and dark matter and the coincidence problem, JCAP 03 (2005) 002.arXiv:hep-th/0411025, doi:10.1088/1475-7516/2005/03/002

work page doi:10.1088/1475-7516/2005/03/002 2005
[84]

del Campo, R

S. del Campo, R. Herrera, D. Pavon, Toward a solu- tion of the coincidence problem, Phys. Rev. D 78 (2008) 021302.arXiv:0806.2116,doi:10.1103/PhysRevD.78. 021302

work page doi:10.1103/physrevd.78 2008

Showing first 80 references.