# On the Phenomenology of an Accelerated Large-Scale Universe

^{1}

^{2}

^{3}

## Abstract

**:**

## 1. Introduction

## 2. Varying Ghost Sark Energy Models

#### 2.1. Cosmological Model with ${\rho}_{de}=\alpha H+\beta {a}^{m}{H}^{2}$

#### 2.1.1. Non-Interacting Model

#### 2.1.2. Interacting Model

#### 2.2. Cosmological Model with ${\rho}_{de}=\alpha H+\beta {\rho}_{dm}^{m}{H}^{2}$

#### Statefinder Hierarchy and Thermodynamics

#### 2.3. Cosmological Model with ${\rho}_{de}=\alpha {\rho}_{dm}^{m}H+\beta {H}^{2}$

#### 2.3.1. Non-Interacting Model

#### 2.3.2. Interacting Model with $Q=3bH({\rho}_{de}+{\rho}_{dm})$

#### 2.3.3. Interacting Model with $Q=3bHq({\rho}_{de}+{\rho}_{dm})$

#### 2.3.4. Interacting Model with $Q=3bH({\rho}_{dm}-{\rho}_{de})$

## 3. Alternative Look at the Problem

#### 3.1. LSU with Interacting Polytropic Gas

#### 3.1.1. Interacting Model with $Q=3Hb\left({\rho}_{p}+{\rho}_{m}+\frac{{\rho}_{m}^{2}}{{\rho}_{p}+{\rho}_{m}}\right)$

#### 3.1.2. Interacting Model with $Q=3Hb\left({\rho}_{p}+{\rho}_{m}+\frac{{\rho}_{p}^{2}}{{\rho}_{p}+{\rho}_{m}}\right)$

#### 3.1.3. Interacting Model with $Q=3Hb\left({\rho}_{p}+{\rho}_{m}+\frac{{\rho}_{p}{\rho}_{m}}{{\rho}_{p}+{\rho}_{m}}\right)$

#### 3.1.4. Sign Changeable Interactions

#### 3.2. LSU with a Varying Polytropic Gas

#### 3.2.1. Interaction $Q=3Hb{\rho}_{de}+\gamma {\dot{\rho}}_{de}$

#### 3.2.2. Interaction $Q=3Hb{\rho}_{dm}+\gamma {\dot{\rho}}_{dm}$

#### 3.2.3. Interaction $Q=3Hb({\rho}_{dm}+{\rho}_{de})+\gamma ({\dot{\rho}}_{dm}+{\dot{\rho}}_{de})$

#### 3.2.4. Interaction $Q=q\left(3Hb{\rho}_{de}+\gamma {\dot{\rho}}_{de}\right)$

#### 3.2.5. Interaction $Q=q\left(3Hb({\rho}_{dm}+{\rho}_{de})+\gamma ({\dot{\rho}}_{dm}+{\dot{\rho}}_{de})\right)$

#### 3.3. Cosmological Models with Generalized Holographic DE

#### 3.3.1. Models with $Q=3Hb({\rho}_{de}+{\rho}_{dm})$

#### 3.3.2. Models with Non-Linear Interactions

## 4. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

- Riess, A.G.; Filippenko, A.V.; Challis, P.; Clocchiatti, A.; Diercks, A.; Garnavich, P.M.; Gilliland, R.L.; Hogan, C.J.; Jha, S.; Kirshner, R.P.; et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J.
**1998**, 116, 1009–1038. [Google Scholar] [CrossRef] - Perlmutter, S.; Aldering, G.; Goldhaber, G.; Knop, R.A.; Nugent, P.; Castro, P.G.; Deustua, S.; Fabbro, S.; Goobar, A.; Groom, D.E.; et al. Measurements of Ω and Λ from 42 high-redshift supernovae. Astrophys. J.
**1999**, 517, 565–586. [Google Scholar] [CrossRef] - Tegmark, M.; Strauss, M.; Blanton, M.; Abazajian, K.; Dodelson, S.; Sandvik, H.; Wang, X.; Weinberg, D.; Zehavi, I.; Bahcall, N.; et al. Cosmological parameters from SDSS and WMAP. Phys. Rev. D
**2004**, 69, 103501. [Google Scholar] [CrossRef] - Hawkins, E.; Maddox, S.; Cole, S.; Lahav, O.; Madgwick, D.; Norberg, P.; Peacock, J.; Baldry, I.; Baugh, C.; Bland-Hawthorn, J.; et al. The 2dF Galaxy Redshift Survey: Correlation functions, peculiar velocities and the matter density of the universe. Mon. Not. Roy. Astron. Soc.
**2003**, 346, 78–96. [Google Scholar] [CrossRef] - Yoo, J.; Watanabe, Y. Theoretical Models of Dark Energy. Int. J. Mod. Phys. D
**2012**, 21, 1230002. [Google Scholar] [CrossRef] - Balakin, A.B. Electrodynamics of a Cosmic Dark Fluid. Symmetry
**2016**, 8, 56. [Google Scholar] [CrossRef] - Bradav, M.; Allen, S.W.; Treu, T.; Ebeling, H.; Massey, R.; Morris, R.G.; von der Linden, A.; Applegate, D. Revealing the Properties of Dark Matter in the Merging Cluster MACS J0025.4–1222*. Astrophys. J.
**2008**, 687, 959–967. [Google Scholar] [CrossRef] [Green Version] - Bosma, A. 21-cm line studies of spiral galaxies. II. The distribution and kinematics of neutral hydrogen in spiral galaxies of various morphological types. Astron. J.
**1981**, 86, 1825–1846. [Google Scholar] [CrossRef] - Liddle, A. An introduction to cosmological inflation. arXiv, 1999; arXiv:astro-ph/9901124. [Google Scholar]
- Andrei, L. Inflationary Cosmology after Planck 2013. arXiv, 2013; arXiv:1402.0526. [Google Scholar]
- Guth, H.; Kaiser, D.I.; Nomura, Y. Inflationary paradigm after Planck 2013. Phys. Lett. B
**2014**, 733, 112–119. [Google Scholar] [CrossRef] - Bamba, K.; Odintsov, S.D. Inflationary cosmology in modified gravity theories. Symmetry
**2015**, 7, 220–240. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Unified cosmic history in modified gravity: From F (R) theory to Lorentz non-invariant models. Phys. Rep.
**2011**, 505, 59–144. [Google Scholar] [CrossRef] - Capozziello, S.; Nojiri, S.; Odintsov, S.D. Unified phantom cosmology: Inflation, dark energy and dark matter under the same standard. Phys. Lett. B
**2006**, 632, 597–604. [Google Scholar] [CrossRef] - Velten, H.E.S.; vom Marttens, R.F.; Zimdahl, W. Aspects of the cosmological “coincidence problem”. Eur. Phys. J. C
**2014**, 74, 3160. [Google Scholar] [CrossRef] - Sivanandam, N. Is the Cosmological Coincidence a Problem? Phys. Rev. D
**2013**, 87, 083514. [Google Scholar] [CrossRef] - Martin, J. Everything you always wanted to know about the cosmological constant problem (but were afraid to ask). Comptes Rendus Phys.
**2012**, 13, 566–665. [Google Scholar] [CrossRef] - Bamba, K.; Capozziello, S.; Nojiri, S.; Odintsov, S.D. Dark energy cosmology: The equivalent description via different theoretical models and cosmography tests. Astrophys. Space Sci.
**2012**, 342, 155–228. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Is the future universe singular: Dark Matter versus modified gravity? Phys. Lett. B
**2010**, 686, 44–48. [Google Scholar] [CrossRef] [Green Version] - Garcia-Salcedo, R.; Gonzalez, T.; Quiros, I. No compelling cosmological models come out of magnetic universes which are based on nonlinear electrodynamics. Phys. Rev. D
**2014**, 89, 084047. [Google Scholar] [CrossRef] - Elizalde, E.; Nojiri, S.; Odintsov, S.D. Late-time cosmology in a (phantom) scalar-ensor theory: Dark energy and the cosmic speed-up. Phys. Rev. D
**2004**, 70, 043539. [Google Scholar] [CrossRef] - Elizalde, E.; Nojiri, S.; Odintsov, S.D.; Saez-Gomez, D.; Faraoni, V. Reconstructing the universe history, from inflation to acceleration, with phantom and canonical scalar fields. Phys. Rev. D
**2008**, 77, 106005. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Final state and thermodynamics of a dark energy universe. Phys. Rev. D
**2004**, 70, 103522. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Unifying phantom inflation with late-time acceleration: Scalar phantom– non-phantom transition model and generalized holographic dark energy. Gen. Relativ. Gravit.
**2006**, 38, 1285–1304. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Quantum deSitter cosmology and phantom matter. Phys. Lett. B
**2003**, 562, 147–152. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. The oscillating dark energy: future singularity and coincidence problem. Phys. Lett. B
**2006**, 637, 139–148. [Google Scholar] [CrossRef] - Elizalde, E.; Makarenko, A. N.; Nojiri, S.; Obukhov, V.V.; Odintsov, S.D. Multiple Λ cosmology with string landscape features and future singularities. Astrophys. Space Sci.
**2013**, 344, 479–488. [Google Scholar] [CrossRef] - Brevik, I.; Elizalde, E.; Nojiri, S.; Odintsov, S.D. Viscous little rip cosmology. Phys. Rev. D
**2011**, 84, 103508. [Google Scholar] [CrossRef] - Brevik, I.; Myrzakulov, R.; Nojiri, S.; Odintsov, S.D. Turbulence and Little Rip Cosmology. Phys. Rev. D
**2012**, 86, 063007. [Google Scholar] [CrossRef] - Astashenok, A.V.; Odintsov, S.D. Confronting dark energy models mimicking ΛCDM epoch with observational constraints: Future cosmological perturbations decay or future Rip? Phys. Lett. B
**2013**, 718, 1194–1202. [Google Scholar] [CrossRef] - Astashenok, A.V.; Nojiri, S.; Odintsov, S.D.; Scherrer, R.J. Scalar dark energy models mimicking ΛCDM with arbitrary future evolution. Phys. Lett. B
**2012**, 713, 145–153. [Google Scholar] [CrossRef] - Kahya, E.O.; Khurshudyan, M.; Pourhassan, B.; Myrzakulov, R.; Pasqua, A. Higher order corrections of the extended Chaplygin gas cosmology with varying G and λ. Eur. Phys. J. C
**2015**, 75, 43. [Google Scholar] [CrossRef] - Guo, Z.K.; Ohta, N. Parametrizations of the dark energy density energy and scalar potential. Mod. Phys. Lett. A
**2007**, 22, 883–890. [Google Scholar] [CrossRef] - Dutta, S.; Saridakis, E.N.; Scherrer, R.J. Dark energy from a quintessence (phantom) field rolling near a potential minimum (maximum). Phys. Rev. D
**2009**, 79, 103005. [Google Scholar] [CrossRef] - Saridakis, E.N.; Sushkov, S.V. Quintessence and phantom cosmology with nonminimal derivative coupling. Phys. Rev. D
**2010**, 81, 083510. [Google Scholar] [CrossRef] - Sadeghi, J.; Khurshudyan, M.; Hakobyan, M.; Farahani, H. Phenomenological Fluids from Interacting Tachyonic Scalar Fields. Int. J. Theor. Phys.
**2014**, 53, 2246–2260. [Google Scholar] [CrossRef] - Brevik, I.; Gorbunova, O.; Nojiri, S.; Odintsov, S.D. On Isotropic Turbulence in the Dark Fluid Universe. Eur. Phys. J. C
**2011**, 71, 1629. [Google Scholar] [CrossRef] - Khurshudyan, M.; Myrzakulov, R. Phase space analysis of some interacting Chaplygin gas models. arXiv, 2015; arXiv:1509.02263. [Google Scholar]
- Pourhassan, B.; Kahya, E.O. Extended Chaplygin gas model. Results Phys.
**2004**, 4, 101102. [Google Scholar] [CrossRef] - Kahya, E.O.; Pourhassan, B. The universe dominated by the extended Chaplygin gas. Mod. Phys. Lett. A
**2015**, 30, 1550070. [Google Scholar] [CrossRef] - Khurshudyan, M.; Chubaryan, E.; Pourhassan, B. Interacting Quintessence Models of Dark Energy. Int. J. Theor. Phys.
**2014**, 53, 2370–2378. [Google Scholar] [CrossRef] - Capozziello, S.; Cardone, V.F.; Elizalde, E.; Nojiri, S.; Odintsov, S.D. Observational constraints on dark energy with generalized equations of state. Phys. Rev. D
**2006**, 73, 043512. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Inhomogeneous equation of state of the universe: Phantom era, future singularity, and crossing the phantom barrier. Phys. Rev. D
**2005**, 72, 023003. [Google Scholar] [CrossRef] - Cardone, V.F.; Troisi, A.; Capozziello, S. Inflessence: A Phenomenological model for inflationary quintessence. Phys. Rev. D
**2006**, 73, 043512. [Google Scholar] - Ferreira, P.G.; Joyce, M. Structure Formation with a Self-Tuning Scalar Field. Phys. Rev. Lett.
**1997**, 79, 4740–4743. [Google Scholar] - Copeland, E.J.; Sami, M.; Tsujikawa, S. Dynamics of dark energy. Int. J. Mod. Phys. D
**2006**, 15, 1753–1936. [Google Scholar] [CrossRef] - Copeland, E.J.; Liddle, A.R.; Wands, D. Exponential potentials and cosmological scaling solutions. Phys. Rev. D
**1998**, 57, 4686–4690. [Google Scholar] [CrossRef] - Gong, Y.G.; Wang, A.; Zhang, Y.-Z. Exact scaling solutions and fixed points for general scalar field. Phys. Lett. B
**2006**, 636, 286–292. [Google Scholar] [CrossRef] - Bolotin, Y.L.; Kostenko, A.; Lemets, O.A.; Yerokhin, D.A. Cosmological Evolution With Interaction Between Dark Energy And Dark Matter. Int. J. Mod. Phys. D
**2015**, 24, 1530007. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Introduction to Modified Gravity and Gravitational Alternative for Dark Energy. Int. J. Geom. Methods. Mod. Phys.
**2007**, 4, 115–146. [Google Scholar] [CrossRef] - Clifton, T.; Ferreira, P.G.; Padilla, A.; Skordis, C. Modified Gravity and Cosmology. Phys. Rep.
**2012**, 513, 1–189. [Google Scholar] [CrossRef] - Sahni, V.; Saini, T.D.; Starobinsky, A.A.; Alam, U. Statefinder—A new geometrical diagnostic of dark energy. JETP Lett.
**2003**, 77, 201–206. [Google Scholar] [CrossRef] - Sahni, V.; Shafieloo, A.; Starobinsky, A.A. Two new diagnostics of dark energy. Phys. Rev. D
**2008**, 78, 103502. [Google Scholar] [CrossRef] - Caldwell, R.R.; Linder, E.V. Limits of Quintessence. Phys. Rev. Lett.
**2005**, 95, 141301. [Google Scholar] [CrossRef] [PubMed] - Arabsalmani, M.; Sahni, V. Statefinder hierarchy: An extended null diagnostic for concordance cosmology. Phys. Rev. D
**2011**, 83, 043501. [Google Scholar] [CrossRef] - Sahni, V.; Shafieloo, A.; Starobinsky, A.A. Model-independent evidence for dark energy evolution from baryon acoustic oscillations. Astrophys. J.
**2014**, 793, L40. [Google Scholar] [CrossRef] - Khurshudyan, M.; Khurshudyan, A.; Myrzakulov, R. Interacting varying ghost dark energy models in general relativity. Astrophys. Space Sci.
**2015**, 357, 113. [Google Scholar] [CrossRef] - Khurshudyan, M. Low redshift universe and a varying ghost dark energy. Mod. Phys. Lett. A
**2016**, 31, 1650055. [Google Scholar] [CrossRef] - Khurshudyan, M. Varying ghost dark energy and particle creation. Eur. Phys. J. Plus
**2016**, 131, 25. [Google Scholar] [CrossRef] - Khurshudyan, M.Z.; Makarenko, A.N. On a phenomenology of the accelerated expansion with a varying ghost dark energy. Astrophys. Space Sci.
**2016**, 361, 187. [Google Scholar] [CrossRef] - Zeldovich, Y.B. Simulated light scattering induced by absorption. JETP Lett.
**1970**, 12, 307. [Google Scholar] [CrossRef] - Barrow, J.D. The deflationary universe: An instability of the de Sitter universe. Phys. Lett. B
**1986**, 180, 335–339. [Google Scholar] [CrossRef] - Morikawa, M.; Sasaki, M. Entropy production in an expanding universe. Phys. Lett. B
**1985**, 165, 59–62. [Google Scholar] [CrossRef] - Padmanabhan, T.; Chitre, S.M. Viscous universes. Phys. Lett. A
**1987**, 120, 433–436. [Google Scholar] [CrossRef] - Zimdahl, W.; Pavon, D. Fluid cosmology with decay and production of particles. Gen. Relativ. Gravit.
**1994**, 26, 1259–1265. [Google Scholar] [CrossRef] - Zimdahl, W.; Schwarz, D.J.; Balakin, A.B.; Pavon, D. Cosmic anti-friction and accelerated expansion. Phys. Rev. D
**2001**, 64, 063501. [Google Scholar] [CrossRef] - Abramo, L.R.W.; Lima, J.A.S. Inflationary models driven by adiabatic matter creation. Class. Quantum Grav.
**1996**, 13, 2953–2964. [Google Scholar] [CrossRef] - Gariel, J.; le Denmat, G. Matter creation and bulk viscosity in early cosmology. Phys. Lett. A
**1995**, 200, 11–16. [Google Scholar] [CrossRef] - Lima, J.A.S.; Germano, A.S.M.; Abramo, L.R.W. FRW-type cosmologies with adiabatic matter creation. Phys. Rev. D
**1996**, 53, 4287. [Google Scholar] [CrossRef] - Parker, L. Particle Creation in Expanding Universes. Phys. Rev. Lett.
**1968**, 21, 562. [Google Scholar] [CrossRef] - Parker, L. Quantized Fields and Particle Creation in Expanding Universes. I. Phys. Rev.
**1969**, 183, 1057. [Google Scholar] [CrossRef] - Parker, L. Quantized Fields and Particle Creation in Expanding Universes. II. Phys. Rev. D
**1971**, 3, 346. [Google Scholar] [CrossRef] - Parker, L. Particle Creation in Isotropic Cosmologies. Phys. Rev. Lett.
**1972**, 28, 705. [Google Scholar] [CrossRef] - Parker, L. Conformal Energy-Momentum Tensor in Riemannian Space-Time. Phys. Rev. D
**1973**, 7, 976. [Google Scholar] [CrossRef] - Grib, A.A.; Pavlov, Y.V. Superheavy particles and the dark matter problem. Gravit. Cosmol.
**2006**, 12, 159–162. [Google Scholar] - Grishchuk, L.P. Quantum effects in cosmology. Class. Quantum Grav.
**1993**, 10, 2449–2478. [Google Scholar] [CrossRef] - Maia, M.R.G. Spectrum and energy density of relic gravitons in flat Robertson-Walker universes. Phys. Rev. D
**1993**, 48, 647–662. [Google Scholar] [CrossRef] - Maia, M.R.G.; Barrow, J.D. Cosmological graviton production in general relativity and related gravity theories. Phys. Rev. D
**1994**, 50, 6262–6296. [Google Scholar] [CrossRef] - Maia, M.R.G.; Lima, J.A.S. Graviton production in elliptical and hyperbolic universes. Phys. Rev. D
**1996**, 54, 6111–6121. [Google Scholar] [CrossRef] - Pereira, S.H.; Bessab, C.H.G.; Lima, J.A.S. Quantized fields and gravitational particle creation in f (R) expanding universes. Phys. Lett. B
**2010**, 690, 103–107. [Google Scholar] [CrossRef] - Pereira, S.H.; Aguilar, J.C.Z.; Romao, E.C. Massless particle creation in a f (R) expanding universe. arXiv, 2013; arXiv:1108.3346. [Google Scholar]
- Pereira, S.H.; Holanda, R.F.L. Particle creation in a f (R) theory with cosmological constraints. Gen. Relativ. Gravit.
**2014**, 46, 1699. [Google Scholar] [CrossRef] - Xu, Y.D.; Huang, Z.G. The sign-changeable interaction between variable generalized Chaplygin gas and dark matter. Astrophys. Space Sci.
**2013**, 343, 807–811. [Google Scholar] - Jarv, L.; Mohaupt, T.; Saueressig, F. Phase Space Analysis of Quintessence Cosmologies with a Double Exponential Potential. J. Cosmol. Astropart. Phys.
**2004**, 0408, 16. [Google Scholar] [CrossRef] - Leon, G.; Saridakis, E.N. Phase-space analysis of Horava-Lifshitz cosmology. J. Cosmol. Astropart. Phys.
**2009**, 0911, 6. [Google Scholar] [CrossRef] [PubMed] - Leon, G.; Saridakis, E.N. Dynamical analysis of generalized Galileon cosmology. J. Cosmol. Astropart. Phys.
**2013**, 1303, 025. [Google Scholar] [CrossRef] - Leon, G.; Saavedra, J.; Saridakis, E.N. Cosmological behavior in extended nonlinear massive gravity. Class. Quantum Grav.
**2013**, 30, 135001. [Google Scholar] [CrossRef] - Fadragas, C.R.; Leon, G.; Saridakis, E.N. Dynamical analysis of anisotropic scalar-field cosmologies for a wide range of potentials. Class. Quantum Grav.
**2014**, 31, 075018. [Google Scholar] [CrossRef] - Xu, C.; Saridakis, E.N.; Leon, G. Phase-space analysis of teleparallel dark energy. J. Cosmol. Astropart. Phys.
**2012**, 07, 005. [Google Scholar] [CrossRef] [PubMed] - Chen, X.; Gong, Y.; Saridakis, E.N. Phase-space analysis of interacting phantom cosmology. J. Cosmol. Astropart. Phys.
**2009**, 0904. [Google Scholar] [CrossRef] - Khurshudyan, M. Some non linear interactions in polytropic gas cosmology: Phase space analysis. Astrophys. Space Sci.
**2015**, 360, 33. [Google Scholar] [CrossRef] - Khurshudyan, M. A varying polytropic gas universe and phase space analysis. Mod. Phys. Lett. A
**2016**, 31, 1650097. [Google Scholar] [CrossRef] - Ade, P.A.R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Bartolo, N.; et al. Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys.
**2016**, 594, A13. [Google Scholar] [CrossRef] - Khurshudyan, M. On a holographic dark energy model with a Nojiri-Odintsov cut-off in general relativity. Astrophys. Space Sci.
**2016**, 361, 232. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Tsujikawa, S. Properties of singularities in (phantom) dark energy universe. Phys. Rev. D
**2015**, 71, 063004. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Oikonomou, V.K. A quantitative analysis of singular inflation with scalar-tensor and modified gravity. Phys. Rev. D
**2015**, 91, 084059. [Google Scholar] [CrossRef] - Odintsov, S.D.; Oikonomou, V.K. Inflation in exponential scalar model and finite-time singularity induced instability. arXiv, 2015; arXiv:1507.05273. [Google Scholar]
- Odintsov, S.D.; Oikonomou, V.K. Singular Inflationary Universe from F(R) Gravity. Phys. Rev. D
**2015**, 92, 124024. [Google Scholar] [CrossRef] - Oikonomou, V.K. Singular Bouncing Cosmology from Gauss-Bonnet Modified Gravity. Phys. Rev. D
**2015**, 92, 124027. [Google Scholar] [CrossRef] - Kleidis, K.; Oikonomou, V.K. Effects of Finite-time Singularities on Gravitational Waves. Astrophys. Space Sci.
**2016**, 361, 326. [Google Scholar] [CrossRef] - Cid, A.; Labran, P. Observational constraints on a cosmological model with Lagrange multipliers. Phys. Lett. B
**2012**, 717, 10–16. [Google Scholar] [CrossRef] - Farooq, M.O. Observational constraints on dark energy cosmological model parameters. arXiv, 2013; arXiv: 1309.3710. [Google Scholar]
- Cao, S.; Pan, Y.; Biesiada, M.; Godlowski, W.; Zhu, Z.-H. Constraints on cosmological models from strong gravitational lensing systems. J. Cosmol. Astropart. Phys.
**2012**, 3, 16. [Google Scholar] [CrossRef] - Chen, Y.; Geng, C.-Q.; Cao, S.; Huang, Y.-M.; Zhu, Z.-H. Constraints on a $\varphi $CDM model from strong gravitational lensing and updated Hubble parameter measurements. J. Cosmol. Astropart. Phys.
**2015**, 2, 10. [Google Scholar] [CrossRef]

**Figure 1.**Graphical behavior of the deceleration parameter q and ${\omega}_{de}$ of the varying ghost dark energy (DE), Equation (21), against redshift z. $m=0$ corresponds to the usual ghost DE.

**Figure 2.**Graphical behavior of EoS parameter of the effective fluid and ${\mathrm{\Omega}}_{i}={\rho}_{i}/3{H}^{2}$ against redshift z. Purple curve corresponds to ${\mathrm{\Omega}}_{de}$, and the orange curve corresponds to ${\mathrm{\Omega}}_{dm}$. $m=0$ corresponds to the usual ghost DE. ${\omega}_{tot}$ is defined according to Equation (23).

**Figure 4.**Graphical behavior of the $Om$ parameter against the redshift z. The blue curve represents non interacting model with $b=0$, the orange curve represents the model, when the interaction is given by $Q=3Hb({\rho}_{de}+{\rho}_{dm})$, the red curve represents the model when the interaction is given by Equation (116), the green curve represents the model with the interaction given by Equation (119), while the black curve represents the model with the interaction given by Equation (120), when ${H}_{0}=0.7$, ${\alpha}_{0}=0.15$, ${\alpha}_{1}=0.25$, $c=0.75$. The left plot corresponds to the case when $b=0.03$. The right plot represents the case when for the interacting models $b=0.05$.

**Figure 5.**Graphical behavior of the $Om3$ parameters against the redshift z. The blue curve represents non interacting model with $b=0$, the orange curve represents the model, when the interaction is given by $Q=3Hb({\rho}_{de}+{\rho}_{dm})$, the red curve represents the model when the interaction is given by Equation (116), the green curve represents the model with the interaction given by Equation (119), while the black curve represents the model with the interaction given by Equation (120), when ${H}_{0}=0.7$, ${\alpha}_{0}=0.15$, ${\alpha}_{1}=0.25$, $c=0.75$. The left plot corresponds to the case when $b=0.03$. The right plot represents the case when for the interacting models $b=0.05$. ${z}_{1}=0.3$ and ${z}_{2}=0.35$.

**Figure 6.**Graphical behavior of the ${S}_{3}$ parameters against the redshift z. The blue curve represents non interacting model with $b=0$, the orange curve represents the model, when the interaction is given by $Q=3Hb({\rho}_{de}+{\rho}_{dm})$, the red curve represents the model when the interaction is given by Equation (116), the green curve represents the model with the interaction given by Equation (119), while the black curve represents the model with the interaction given by Equation (120), when ${H}_{0}=0.7$, ${\alpha}_{0}=0.15$, ${\alpha}_{1}=0.25$, $c=0.75$. The left plot corresponds to the case when $b=0.03$. The right plot represents the case when for the interacting models $b=0.05$.

The Energy Condition | Mathematical Expression |
---|---|

Null energy condition (NEC) | $\rho +P\ge 0$ |

Dominant energy condition (DEC) | $\rho \ge 0\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}\rho \pm P\ge 0$ |

Strong energy condition (SEC) | $\rho +3P\ge 0\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}\rho +P\ge 0$ |

Weak energy condition (WEC) | $\rho \ge 0\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}\rho +P\ge 0$ |

**Table 2.**The values of EoS parameter ω allowing one to have various forms of the matter in the universe due to the barotropic fluid.

EoS Parameter | Matter |
---|---|

$\omega =0$ | dust |

$\omega =1/3$ | radiation |

$\omega \in (1/3,1)$ | hard universe |

$\omega =1$ | stiff matter |

$\omega \in (-1/3,-1)$ | quintessence |

$\omega =-1$ | cosmological constant |

$\omega <-1$ | phantom matter |

$\omega >1$ | ekpyrotic matter |

**Table 3.**Present day values of $(r,s)$, $({\omega}_{de}^{\prime},{\omega}_{de})$ and q for various values of the parameter m, when ${\mathrm{\Omega}}_{dm}\approx 0.3$, ${\mathrm{\Omega}}_{r}\approx 7\times {10}^{-5}$, while $b=0$ and ${H}_{0}=0.72$. $m=0$ corresponds to the usual ghost DE.

m | $(\mathit{r},\mathit{s})$ | $({\mathit{\omega}}_{\mathit{de}}^{\prime},{\mathit{\omega}}_{\mathit{de}})$ | q |
---|---|---|---|

1 | $(9.9,-2.937)$ | $(-5.96,-0.973)$ | $-0.51$ |

$0.5$ | $(3.854,-1.531)$ | $(-2.38,-0.605)$ | $-0.121$ |

$0.0$ | $(3.069,-2.974)$ | $(-1.68,-0.237)$ | $0.268$ |

**Table 4.**Present day values of the statefinder pair $(r,s)$, $({\omega}_{de}^{\prime},{\omega}_{de})$ and q for various values of the parameter m, when ${\mathrm{\Omega}}_{dm}\approx 0.3$, ${\mathrm{\Omega}}_{r}\approx 7\times {10}^{-5}$, while $b=0.03$ and ${H}_{0}=0.72$. $m=0$ corresponds to the usual ghost DE. $\alpha =0.3$ and $\beta =1.7$.

m | $(\mathit{r},\mathit{s})$ | $({\mathit{\omega}}_{\mathit{de}}^{\prime},{\mathit{\omega}}_{\mathit{de}})$ | q |
---|---|---|---|

1 | $(10.73,-2.827)$ | $(-6.315,-1.099)$ | $-0.648$ |

$0.5$ | $(3.838,-1.246)$ | $(-2.361,-0.732)$ | $-0.299$ |

$0.0$ | $(2.213,-1.084)$ | $(-1.29,-0.364)$ | $0.130$ |

**Table 5.**Present day values of the statefinder pair $(r,s)$, $({\omega}_{de}^{\prime},{\omega}_{de})$ and q for various values of the interaction parameter b, when ${\mathrm{\Omega}}_{dm}\approx 0.3$, ${\mathrm{\Omega}}_{r}\approx 7\times {10}^{-5}$, while $m=0.5$ and ${H}_{0}=0.72$. $\alpha =0.3$ and $\beta =1.7$.

b | $(\mathit{r},\mathit{s})$ | $({\mathit{\omega}}_{\mathit{de}}^{\prime},{\mathit{\omega}}_{\mathit{de}})$ | q |
---|---|---|---|

$0.0$ | $(3.797,-1.475)$ | $(-2.348,-0.612)$ | $-0.132$ |

$0.01$ | $(3.796,-1.382)$ | $(-2.348,-0.652)$ | $-0.174$ |

$0.03$ | $(3.838,-1.246)$ | $(-2.361,-0.732)$ | $-0.26$ |

$0.05$ | $(3.938,-1.161)$ | $(-2.393,-0.812)$ | $-0.343$ |

$0.07$ | $(4.095,-1.111)$ | $(-2.445,-0.891)$ | $-0.428$ |

**Table 6.**Present day values of $(r,s)$, $({\omega}_{de}^{\prime},{\omega}_{de})$, q and appropriate redshift transition for the various values of the parameter m, when $b=0.01$, $\alpha =0.75$ and $\beta =0.85$, ${H}_{0}=0.69$, ${\mathrm{\Omega}}_{de}\approx 0.7$, ${\mathrm{\Omega}}_{dm}\approx 0.3$ and ${\mathrm{\Omega}}_{r}\approx 0.3\times {10}^{-5}$. $m=0$ corresponds to the usual ghost DE.

m | $(\mathit{r},\mathit{s})$ | $({\mathit{\omega}}_{\mathit{de}}^{\prime},{\mathit{\omega}}_{\mathit{de}})$ | q | ${\mathit{z}}_{\mathit{tr}}$ |
---|---|---|---|---|

$0.0$ | $(2.247,-0.711)$ | $(-1.173,-0.576)$ | $-0.085$ | $0.18$ |

$-0.1$ | $(2.515,-0.745)$ | $(-1.033,-0.647)$ | $-0.177$ | $0.3$ |

$-0.15$ | $(2.852,-0.842)$ | $(-1.057,-0.707)$ | $-0.233$ | $0.38$ |

$-0.2$ | $(3.381,-0.996)$ | $(-1.171,-0.761)$ | $-0.297$ | $0.42$ |

$-0.4$ | $(8.883,-2.268)$ | $(-3.237,-1.042)$ | $-0.658$ | $0.58$ |

Critical Points | Q | x | y |
---|---|---|---|

$E.2.1$ | Equation (87) | $\frac{1+2b\pm \sqrt{1-4{b}^{2}}}{2b}$ | $-1$ |

$E.2.2$ | Equation (88) | $\frac{1\pm \sqrt{1-4b(1+b)}}{2b}$ | $-1$ |

$E.2.3$ | Equation (89) | $\frac{1}{2}(1\pm \sqrt{5})$ | 0 |

$E.2.4$ | Equation (89) | $\frac{b-1\pm \sqrt{1+(2+5b)b}}{2b}$ | $-1$ |

**Table 8.**Present day values of $({\omega}_{de}^{\prime},{\omega}_{de})$ and statefinder parameters $(r,s)$ for the cosmological model where ${H}_{0}=0.72$, ${\mathrm{\Omega}}_{de}^{0}=0.7$ and ${\mathrm{\Omega}}_{de}^{0}=0.3$, while the interaction is given by Equation (93).

b | γ | $({\mathit{\omega}}_{\mathit{de}}^{\prime},{\mathit{\omega}}_{\mathit{de}})$ | $(\mathit{r},\mathit{s})$ |
---|---|---|---|

$0.0$ | $0.0$ | $(-0.453,-0.998)$ | $(4.982,-1.266)$ |

$0.02$ | $0.0$ | $(-0.483,-0.998)$ | $(4.857,-1.226)$ |

$0.02$ | $0.01$ | $(-0.483,-0.998)$ | $(4.858,-1.226)$ |

$0.02$ | $0.02$ | $(-0.482,-0.998)$ | $(4.859,-1.227)$ |

$0.02$ | $0.03$ | $(-0.482,-0.998)$ | $(4.861,-1.228)$ |

$\mathit{Critical}\phantom{\rule{3.33333pt}{0ex}}\mathit{Points}$ | x | y | Type of Stability | Acceleration |
---|---|---|---|---|

$C.2.1$ | 1 | $-1$ | Stable node | Yes |

$C.2.2$ | 1 | 0 | Stable node | No |

**Table 10.**Present day values of $({\omega}_{de}^{\prime},{\omega}_{de})$ and statefinder parameters $(r,s)$ for the cosmological model where ${H}_{0}=0.72$, ${\mathrm{\Omega}}_{de}^{0}=0.7$ and ${\mathrm{\Omega}}_{de}^{0}=0.3$, while the interaction is given via Equation (99). The values of the parameters are due to the behavior of the cosmological parameters presented in Figure 2 of Reference [92]. $m=-2$.

b | γ | $({\mathit{\omega}}_{\mathit{de}}^{\prime},{\mathit{\omega}}_{\mathit{de}})$ | $(\mathit{r},\mathit{s})$ |
---|---|---|---|

$0.0$ | $0.0$ | $(-0.453,-0.998)$ | $(4.982,-1.266)$ |

$0.02$ | $0.0$ | $(-0.466,-0.998)$ | $(4.928,-1.249)$ |

$0.02$ | $0.01$ | $(-0.459,-0.998)$ | $(4.955,-1.258)$ |

$0.02$ | $0.03$ | $(-0.447,-0.998)$ | $(5.011,-1.227)$ |

**Table 11.**Present day values of the deceleration parameter q, $({\omega}_{de},{\omega}_{de}^{\prime})$ of interacting dark energy, $(r,s)$ statefinder parameters and the value of the transition redshift ${z}_{tr}$ for several values of the interaction parameter b, when the interaction is given by $Q=3Hb({\rho}_{de}+{\rho}_{dm})$. The best fit of the theoretical results to the recent observational data has been obtained for ${H}_{0}=0.7$, ${\alpha}_{0}=0.15$, ${\alpha}_{1}=0.25$, $c=0.75$.

b | q | $({\mathit{\omega}}_{\mathit{de}},{\mathit{\omega}}_{\mathit{de}}^{\prime})$ | $(\mathit{r},\mathit{s})$ | ${\mathit{z}}_{\mathit{tr}}$ |
---|---|---|---|---|

$0.0$ | $-0.522$ | $(-0.978,0.249)$ | $(2.86,-0.61)$ | $0.682$ |

$0.01$ | $-0.537$ | $(-0.993,0.257)$ | $(2.76,-0.57)$ | $0.728$ |

$0.03$ | $-0.567$ | $(-1.022,0.269)$ | $(2.57,-0.49)$ | $0.832$ |

$0.05$ | $-0.596$ | $(-1.051,0.279)$ | $(2.39,-0.42)$ | $0.954$ |

$0.07$ | $-0.626$ | $(-1.079,0.284)$ | $(2.23,-0.36)$ | $1.101$ |

© 2016 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Khurshudyan, M.
On the Phenomenology of an Accelerated Large-Scale Universe. *Symmetry* **2016**, *8*, 110.
https://doi.org/10.3390/sym8110110

**AMA Style**

Khurshudyan M.
On the Phenomenology of an Accelerated Large-Scale Universe. *Symmetry*. 2016; 8(11):110.
https://doi.org/10.3390/sym8110110

**Chicago/Turabian Style**

Khurshudyan, Martiros.
2016. "On the Phenomenology of an Accelerated Large-Scale Universe" *Symmetry* 8, no. 11: 110.
https://doi.org/10.3390/sym8110110