Geodesic
Cosmological models with integrable equations of state
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2018), pp. 5-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a class of cosmological models with two components of matter in the Universe, which denoted as dust matter and dark energy. We investigate various equations of state for dark energy, which allow analytical dependence of its density $\rho_d$ on the scale factor $a$ or redshift. In comparison with the standard model $\Lambda$CDM we study its generalization $w$CDM with the dependence $\rho_d\sim a^{-3B}$, and also suggest a new equation of state with the dark component density $\rho_d=const/(A+a^{3B})$. For this class of models we estimated optimal values of the parameters and limitations on their acceptable deviations from the best description of observational data for type Ia supernovae, baryon acoustic oscillations and the Hubble parameter $H(z)$ estimations. The scenario with the new equation of state appears to be the most successful in minimization of the function $\chi^2$ measuring correspondence between a model and an observational data, however the small number of parameters makes the $\Lambda$CDM model more effective from the point of view of the Akaike information criterion.
Keywords: cosmological model, equation of state, Hubble parameter. 
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E. G. Vorontsova; G. S. Sharov. Cosmological models with integrable equations of state. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2018), pp. 5-26. http://geodesic.mathdoc.fr/item/VTPMK_2018_2_a0/

[1] Riess A. G. et al., “Observational evidence from Supernovae for an accelerating Universe and a cosmological constant”, The Astronomical Journal, 116:3 (1998), 1009-1038, arXiv: astro-ph/9805201 | DOI

[2] Perlmutter S. et al., “Measurements of omega and lambda from 42 high redshift supernovae”, The Astrophysical Journal, 517:2 (1999), 565-586, arXiv: astro-ph/9812133 | DOI

[3] Weinberg D. H. et al., “Observational probes of cosmic acceleration”, Physics Reports, 530:2 (2013), 87-255, arXiv: 1201.2434 | DOI

[4] Eisenstein D. J. et al., “Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies”, The Astrophysical Journal, 633:2 (2005), 560-574, arXiv: astro-ph/0501171 | DOI

[5] Hinshaw G. et. al., “Nine-year Wilkinson microwave anisotropy probe (WMAP) observations: cosmological parameters results”, The Astrophysical Journal Supplement, 208:2 (2013), 19, 25 pp., arXiv: 1212.5226 | DOI

[6] Ade P. A. R. et al., “Planck 2015 results. XIII. Cosmological parameters”, Astronomy and Astrophysics, 594 (2016), A13, 63 pp., arXiv: 1502.01589 | DOI

[7] Simon J., Verde L., Jimenez R., “Constraints on the redshift dependence of the dark energy potential”, Physical Review D, 71:12 (2005), 123001, arXiv: astro-ph/0412269 | DOI

[8] Stern D. et al., “Cosmic chronometers: constraining the equation of state of dark energy. I: $H(z)$ measurements”, Journal of Cosmology and Astroparticle Physics, 2010, no. 2, 008, arXiv: 0907.3149 | DOI

[9] Moresco M. et al., “Improved constraints on the expansion rate of the Universe up to $z\sim1.1$ from the spectroscopic evolution of cosmic chronometers”, Journal of Cosmology and Astroparticle Physics, 2012, no. 8, 006, arXiv: 1201.3609 | DOI

[10] Zhang C. et al., “Four new observational H(z) data from luminous red galaxies Sloan Digital Sky Survey Data Release seven”, Research in Astronomy and Astrophysics, 14:10 (2014), 1221-1233, arXiv: 1207.4541 | DOI

[11] Moresco M., “Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at $z\sim2$”, Monthly Notices of the Royal Astronomical Society: Letters, 450:1 (2015), L16-L20, arXiv: 1503.01116 | DOI

[12] Moresco M. et al., “A 6% measurement of the Hubble parameter at $z \sim 0.45$: direct evidence of the epoch of cosmic re-acceleration”, Journal of Cosmology and Astroparticle Physics, 2016, no. 5, 014, arXiv: 1601.01701 | DOI

[13] Ratsimbazafy A. L. et al., “Age-dating luminous red galaxies observed with the Southern African Large Telescope”, Monthly Notices of the Royal Astronomical Society, 467:3 (2017), 3239-3254, arXiv: 1702.00418 | DOI

[14] Gazta naga E., Cabre A., Hui L., “Clustering of Luminous Red Galaxies IV: Baryon Acoustic Peak in the Line-of-Sight Direction and a Direct Measurement of $H(z)$”, Monthly Notices of the Royal Astronomical Society, 399:3 (2009), 1663-1680, arXiv: 0807.3551 | DOI

[15] Blake C. et al., “The WiggleZ Dark Energy Survey: joint measurements of the expansion and growth history at $z 1$”, Monthly Notices of the Royal Astronomical Society, 425:1 (2012), 405-414, arXiv: 1204.3674 | DOI

[16] Busca N. G. et al., “Baryon acoustic oscillations in the Ly$\alpha$ forest of BOSS quasars”, Astronomy and Astrophysics, 552 (2013), A96, 18 pp., arXiv: 1211.2616 | DOI

[17] Chuang C. H., Wang Y., “Modeling the anisotropic two-point galaxy correlation function on small scales and improved measurements of $H(z)$, $D_A(z)$, and $f(z)\sigma_8(z)$ from the Sloan Digital Sky Survey DR7 Luminous Red Galaxies”, Monthly Notices of the Royal Astronomical Society, 435:1 (2013), 255-262, arXiv: 1209.0210 | DOI

[18] Chuang C. H. et al., “The clustering of galaxies in the SDSS-III baryon oscillation spectroscopic survey: single-probe measurements and the strong power of $f(z)\sigma_8(z)$ on constraining dark energy”, Monthly Notices of the Royal Astronomical Society, 433:4 (2013), 3559-3571, arXiv: 1303.4486 | DOI

[19] Anderson L. et al., “The clustering of galaxies in the SDSS-III baryon oscillation spectroscopic survey: measuring $D_A$ and $H$ at $z = 0.57$ from the baryon acoustic peak in the data release 9 spectroscopic galaxy sample”, Monthly Notices of the Royal Astronomical Society, 439:1 (2014), 83-101, arXiv: 1303.4666 | DOI

[20] Anderson L. et al., “The clustering of galaxies in the SDSS-III baryon oscillation spectroscopic survey: baryon acoustic oscillations in the data releases 10 and 11 galaxy samples”, Monthly Notices of the Royal Astronomical Society, 441:1 (2014), 24-62, arXiv: 1312.4877 | DOI

[21] Oka A. et al., “Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample”, Monthly Notices of the Royal Astronomical Society, 439:3 (2014), 2515-2530, arXiv: 1310.2820 | DOI

[22] Font-Ribera A. et al., “Quasar-Lyman $\alpha$ forest cross-correlation from BOSS DR11: baryon acoustic oscillations”, Journal of Cosmology and Astroparticle Physics, 2014, no. 5, 027, arXiv: 1311.1767 | DOI

[23] Alam S. et al., “The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample”, Monthly Notices of the Royal Astronomical Society, 470:3 (2017), 2617-2652, arXiv: 1607.03155 | DOI

[24] Wang Y. et al., “The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in configuration space”, Monthly Notices of the Royal Astronomical Society, 469:3 (2017), 3762-3774, arXiv: 1607.03154 | DOI

[25] Bautista J. E. et al., “Measurement of baryon acoustic oscillation correlations at $z = 2.3$ with SDSS DR12 Ly$\alpha$-Forests”, Astronomy and Astrophysics, 603 (2017), A12, 23 pp., arXiv: 1702.00176 | DOI

[26] Delubac T. et al., “Baryon acoustic oscillations in the Ly$\alpha$ forest of BOSS DR11 quasars”, Astronomy and Astrophysics, 574 (2015), A59, 17 pp., arXiv: 1404.1801 | DOI

[27] Sharov G. S., Vorontsova E. G., “Cosmological model with generalized Chaplygin gas and recent astronomical observations”, Vestnik TvGU. Seriya: Prikladnaya matematika [Herald of Tver State University. Series: Applied Mathematics], 2014, no. 1, 21-38 (in Russian)

[28] Clifton T., Ferreira P. G., Padilla A., Skordis C., “Modified Gravity and Cosmology”, Physics Reports, 513:1 (2012), 1-189, arXiv: 1106.2476 | DOI

[29] Bamba K., Capozziello S., Nojiri S., Odintsov S. D., “Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests”, Astrophysics and Space Science, 342:1 (2012), 155-228, arXiv: 1205.3421 | DOI

[30] Chimento L. P., “Linear and nonlinear interactions in the dark sector”, Physical Review D, 81:4 (2010), 043525, arXiv: 0911.5687 | DOI

[31] Pan S., Bhattacharya S., Chakraborty S., “An analytic model for interacting dark energy and its observational constraints”, Monthly Notices of the Royal Astronomical Society, 452:3 (2015), 3038-3046, arXiv: 1210.0396 | DOI

[32] Caldwell R. R., “A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state”, Physics Letters B, 545:1-2 (2002), 23-29, arXiv: astro-ph/9908168 | DOI

[33] Sharov G. S., Vorontsova E. G., “Parameters of cosmological models and recent astronomical observations”, Journal of Cosmology and Astroparticle Physics, 2014, no. 10, 057, arXiv: 1407.5405 | DOI

[34] Vorontsova E. G., Sharov G. S., “Recent estimations of astrophysical parameters and forecast of the model with modified Chaplygin gas”, Vestnik TvGU. Seriya: Prikladnaya matematika [Herald of Tver State University. Series: Applied Mathematics], 2015, no. 2, 7-24 (in Russian)

[35] Suzuki N. et al., “The Hubble Space Telescope Cluster Supernova Survey. V. Improving the Dark-energy Constraints above z > 1 and Building an Early-type-hosted Supernova Sample”, The Astrophysical Journal, 746:1 (2012), 85, 24 pp. , arXiv: http://supernova.lbl.gov/Union/1105.3470 | DOI

[36] Sharov G. S., “Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state”, Journal of Cosmology and Astroparticle Physics, 2016, no. 6, 023, arXiv: 1506.05246 | DOI

[37] Sharov G. S. et al., “A new interacting two fluid model and its consequences”, Monthly Notices of the Royal Astronomical Society, 466:3 (2017), 3497-3506, arXiv: 1701.00780 | DOI

[38] Pan S., Sharov G. S., “A model with interaction of dark components and recent observational data”, Monthly Notices of the Royal Astronomical Society, 472:4 (2017), 4736-4749, arXiv: 1609.02287 | DOI

[39] Odintsov S. D., Saez-Gomez D., Sharov G. S., “Is exponential gravity a viable description for the whole cosmological history?”, The European Physical Journal C - Particles and Fields, 77:12 (2017), 862, arXiv: 1709.06800

[40] Percival W. J. et al., “Baryon acoustic scillations in the Sloan Digital Sky Survey Data Release 7 galaxy sample”, Monthly Notices of the Royal Astronomical Society, 401:4 (2010), 2148-2168, arXiv: 0907.1660 | DOI

[41] Blake C. et al., “The WiggleZ dark energy survey: mapping the distance redshift relation with baryon acoustic oscillations”, Monthly Notices of the Royal Astronomical Society, 418:3 (2011), 1707-1724, arXiv: 1108.2635 | DOI