Parametrization of the deceleration parameter in a flat FLRW universe: constraints and comparative analysis with the \(\Lambda\)CDM paradigm. (English) Zbl 07853668
Summary: The constraint of the deceleration parameter associated with dark energy stands as one of the most captivating subjects in the present cosmological framework. This study centers on the parametric reconstruction of the deceleration parameter in a flat Friedmann-Robertson-Walker (FLRW) Universe that encompasses radiation, dark energy, and pressure-less dark matter. In this context, we thoroughly investigate a highly motivated parametrization of \(q(z)\), which offers an evolutionary scenario from deceleration to the acceleration phase of the Universe. The crucial task of estimating the parametrization of the Hubble parameter is accomplished through its incorporation into the Friedmann equation. The free parameters are subsequently constrained utilizing a comprehensive set of observational data, including \(H(z)\), type Ia supernovae (SNIa), Baryon Acoustic Oscillation (BAO), Gamma Ray Burst (GRB), and Quasar (Q) measurements. Implementing the Markov Chain Monte Carlo (MCMC) technique and the \(H(z)\) + BAO + SNIa + GRB + Q dataset, we derive the best-fit values for the model parameters. Consequently, we provide a graphical analysis of the cosmographic parameters such as deceleration, jerk, and snap parameters by applying these optimized model parameter values. Finally, we compare our results with those of the standard \(\Lambda\)CDM paradigm to evaluate the viability of our proposed models.
MSC:
| 83F05 | Relativistic cosmology |
| 83C56 | Dark matter and dark energy |
| 83B05 | Observational and experimental questions in relativity and gravitational theory |
Keywords:
Friedmann-Lemaître-Robertson Walker universe; Friedmann equation; dark energy; accelerating universeReferences:
| [1] | Riess, AG, Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J., 116, 1009-1038 (1998) · doi:10.1086/300499 |
| [2] | Perlmutter, S., Measurements of the cosmological parameters Omega and Lambda from the first 7 supernovae at z \(> = 0.35\), Astrophys. J., 483, 565 (1997) · doi:10.1086/304265 |
| [3] | Perlmutter, S., Measurements of \(\Omega\) and \(\Lambda\) from 42 high redshift supernovae, Astrophys. J., 517, 565-586 (1999) · Zbl 1368.85002 · doi:10.1086/307221 |
| [4] | Vollick, DN, 1/R curvature corrections as the source of the cosmological acceleration, Phys. Rev. D, 68 (2003) · doi:10.1103/PhysRevD.68.063510 |
| [5] | Nojiri, S.; Odintsov, SD, Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration, Phys. Rev. D, 68 (2003) · doi:10.1103/PhysRevD.68.123512 |
| [6] | Tonry, JL, Cosmological results from high-z supernovae, Astrophys. J., 594, 1-24 (2003) · doi:10.1086/376865 |
| [7] | Riess, AG, Type Ia supernova discoveries at z \(> 1\) from the Hubble Space Telescope: evidence for past deceleration and constraints on dark energy evolution, Astrophys. J., 607, 665-687 (2004) · Zbl 1369.85001 · doi:10.1086/383612 |
| [8] | Clocchiatti, A., Hubble space telescope and ground-based observations of type Ia supernovae at redshift 0.5: cosmological implications, Astrophys. J., 642, 1-21 (2006) · doi:10.1086/498491 |
| [9] | Caldwell, RR; Komp, W.; Parker, L.; Vanzella, DAT, A sudden gravitational transition, Phys. Rev. D, 73 (2006) · doi:10.1103/PhysRevD.73.023513 |
| [10] | Sahni, V.; Starobinsky, AA, The Case for a positive cosmological Lambda term, Int. J. Mod. Phys. D, 9, 373-444 (2000) · doi:10.1142/S0218271800000542 |
| [11] | Padmanabhan, T., Cosmological constant: the weight of the vacuum, Phys. Rep., 380, 235-320 (2003) · Zbl 1027.83544 · doi:10.1016/S0370-1573(03)00120-0 |
| [12] | Peebles, PJE; Ratra, B., The cosmological constant and dark energy, Rev. Mod. Phys., 75, 559-606 (2003) · Zbl 1205.83082 · doi:10.1103/RevModPhys.75.559 |
| [13] | Copeland, EJ; Sami, M.; Tsujikawa, S., Dynamics of dark energy, Int. J. Mod. Phys. D, 15, 11, 1753-1935 (2006) · Zbl 1203.83061 · doi:10.1142/S021827180600942X |
| [14] | Amendola, L.; Tsujikawa, S., Dark Energy: Theory and Observations (2010), Cambridge: Cambridge University Press, Cambridge · Zbl 1200.85001 · doi:10.1017/CBO9780511750823 |
| [15] | Steinhardt, PJ; Wang, L.; Zlatev, I., Cosmological tracking solutions, Phys. Rev. D, 59, 12 (1999) · doi:10.1103/PhysRevD.59.123504 |
| [16] | Weinberg, S., The cosmological constant problem, Rev. Mod. Phys., 61, 1-23 (1989) · Zbl 1129.83361 · doi:10.1103/RevModPhys.61.1 |
| [17] | Bouali, A.; Albarran, I.; Bouhmadi-López, M.; Ouali, T., Cosmological constraints of phantom dark energy models, Phys. Dark Univ., 26 (2019) · doi:10.1016/j.dark.2019.100391 |
| [18] | Bouali, A.; Albarran, I.; Bouhmadi-Lopez, M.; Errahmani, A.; Ouali, T., Cosmological constraints of interacting phantom dark energy models, Phys. Dark Univ., 34 (2021) · doi:10.1016/j.dark.2021.100907 |
| [19] | Mhamdi, D.; Bargach, F.; Dahmani, S.; Bouali, A.; Ouali, T., Comparing phantom dark energy models with various diagnostic tools, Gen. Relativ. Gravit., 55, 1, 11 (2023) · Zbl 1528.83053 · doi:10.1007/s10714-022-03055-7 |
| [20] | Dahmani, S.; Bouali, A.; El Bojaddaini, I.; Errahmani, A.; Ouali, T., Constraining neutrino properties and smoothing the Hubble tension via the LSBR model, Gen. Relativ. Gravit., 55, 1, 22 (2023) · Zbl 1528.83046 · doi:10.1007/s10714-023-03066-y |
| [21] | Dahmani, S., Bouali, A., Bojaddaini, I.E., Errahmani, A., Ouali, T.: Smoothing the \(H_0\) tension with a dynamical dark energy model. arXiv:2301.04200 · Zbl 1528.83046 |
| [22] | Bouali, A., Chaudhary, H., Mehrotra, A., Pacif, S.K.J.: Model-independent study for a quintessence model of dark energy: analysis and observational constraints. arXiv:2304.02652 |
| [23] | Capozziello, S.; Cardone, VF; Elizalde, E.; Nojiri, S.; Odintsov, SD, Observational constraints on dark energy with generalized equations of state, Phys. Rev. D, 73 (2006) · doi:10.1103/PhysRevD.73.043512 |
| [24] | Escamilla-Rivera, C.; Capozziello, S., Unveiling cosmography from the dark energy equation of state, Int. J. Mod. Phys. D, 28, 12, 1950154 (2019) · doi:10.1142/S0218271819501542 |
| [25] | Debnath, U., Gravitational waves for variable modified Chaplygin gas and some parametrizations of dark energy in the background of FRW universe, Eur. Phys. J. Plus, 135, 2, 135 (2020) · doi:10.1140/epjp/s13360-020-00219-9 |
| [26] | del Campo, S.; Duran, I.; Herrera, R.; Pavon, D., Three thermodynamically-based parameterizations of the deceleration parameter, Phys. Rev. D, 86 (2012) · doi:10.1103/PhysRevD.86.083509 |
| [27] | Cunha, J.; Lima, JAS, Transition redshift: new kinematic constraints from supernovae, Mon. Not. R. Astron. Soc., 390, 1, 210-217 (2008) · doi:10.1111/j.1365-2966.2008.13640.x |
| [28] | Cunha, JV, Kinematic constraints to the transition redshift from SNe Ia union data, Phys. Rev. D, 79 (2009) · doi:10.1103/PhysRevD.79.047301 |
| [29] | Riess, AG, Type Ia supernova discoveries at z \(> 1\) from the Hubble Space Telescope: evidence for past deceleration and constraints on dark energy evolution, Astrophys. J., 607, 665-687 (2004) · Zbl 1369.85001 · doi:10.1086/383612 |
| [30] | Xu, L-I; Zhang, C-W; Chang, B-R; Liu, H-Y, Constraints to deceleration parameters by recent cosmic observations, Mod. Phys. Lett. A, 23, 1939-1948 (2008) · Zbl 1145.83373 · doi:10.1142/S0217732308025991 |
| [31] | Xu, L.; Lu, J., Cosmic constraints on deceleration parameter with Sne Ia and CMB, Mod. Phys. Lett. A, 24, 369-376 (2009) · Zbl 1170.83513 · doi:10.1142/S0217732309027212 |
| [32] | Nair, R.; Jhingan, S.; Jain, D., Cosmokinetics: a joint analysis of standard candles, rulers and cosmic clocks, J. Cosmol. Astropart. Phys., 2012, 1, 018 (2012) · doi:10.1088/1475-7516/2012/01/018 |
| [33] | Akarsu, O.; Dereli, T.; Kumar, S.; Xu, L., Probing kinematics and fate of the Universe with linearly time-varying deceleration parameter, Eur. Phys. J. Plus, 129, 22 (2014) · doi:10.1140/epjp/i2014-14022-6 |
| [34] | Santos, B.; Carvalho, JC; Alcaniz, JS, Current constraints on the epoch of cosmic acceleration, Astropart. Phys., 35, 1, 17-20 (2011) · doi:10.1016/j.astropartphys.2011.04.002 |
| [35] | Gong, Y-G; Wang, A., Reconstruction of the deceleration parameter and the equation of state of dark energy, Phys. Rev. D, 75 (2007) · doi:10.1103/PhysRevD.75.043520 |
| [36] | Turner, MS; Riess, AG, Do SNe Ia provide direct evidence for past deceleration of the universe?, Astrophys. J., 569, 18 (2002) · doi:10.1086/338580 |
| [37] | Al Mamon, A.; Das, S., A divergence free parametrization of deceleration parameter for scalar field dark energy, Int. J. Mod. Phys. D, 25, 3, 1650032 (2016) · Zbl 1336.83044 · doi:10.1142/S0218271816500322 |
| [38] | Gadbail, GN; Mandal, S.; Sahoo, PK, Parametrization of deceleration parameter in f (q) gravity, Physics, 4, 4, 1403-1412 (2022) · doi:10.3390/physics4040090 |
| [39] | Bouali, A.; Shukla, BK; Chaudhary, H.; Tiwari, RK; Samar, M.; Mustafa, G., Cosmological tests of parametrization \(q = \alpha -\beta H\) in f(Q) FLRW cosmology, Int. J. Geom. Methods Mod. Phys. (2023) · doi:10.1142/s0219887823501529 |
| [40] | Khurana, M., Chaudhary, H., Mumtaz, S., Pacif, S., Mustafa, G.: Analyzing a higher order \(q (t)\) model and its implications in the late evolution of the universe using recent observational datasets. arXiv preprint arXiv:2309.14222 |
| [41] | Bouali, A., Chaudhary, H., Debnath, U., Sardar, A., Mustafa, G.: Data analysis of three parameter models of deceleration parameter in frw universe. arXiv preprint arXiv:2304.13137 |
| [42] | Bouali, A., Chaudhary, H., Mehrotra, A., Pacif, S.: Model-independent study for a quintessence model of dark energy: analysis and observational constraints. arXiv preprint arXiv:2304.02652 |
| [43] | Arora, D., Chaudhary, H., Pacif, S.K.J.: Diagnostic and comparative analysis of dark energy models with \(q (z)\) parametrizations. Available at SSRN 4543124 |
| [44] | Shekh, S.; Chaudhary, H.; Bouali, A.; Dixit, A., Observational constraints on teleparallel effective equation of state, Gen. Relativ. Gravit., 55, 8, 95 (2023) · Zbl 1532.83097 · doi:10.1007/s10714-023-03140-5 |
| [45] | Chaudhary, H., Arora, D., Debnath, U., Mustafa, G., Maurya, S.K.: A new cosmological model: exploring the evolution of the universe and unveiling super-accelerated expansion. arXiv preprint arXiv:2308.07354 |
| [46] | Shukla, BK; Bouali, A.; Chaudhary, H.; Tiwari, RK; San Martin, M., Cosmographic studies of \(q= \alpha - \beta\) h parametrization in f (t) framework, Int. J. Geom. Methods Mod. Phys. (2023) · Zbl 1537.83137 · doi:10.1142/S0219887824500075 |
| [47] | Chaudhary, H.; Bouali, A.; Debnath, U.; Roy, T.; Mustafa, G., Constraints on the parameterized deceleration parameter in frw universe, Phys. Scr., 98, 9 (2023) · doi:10.1088/1402-4896/acea02 |
| [48] | Bouali, A.; Chaudhary, H.; Mumtaz, S.; Mustafa, G.; Maurya, S., Observational constraining study of new deceleration parameters in frw universe, Fortschr. Phys. (2023) · Zbl 1543.83002 · doi:10.1002/prop.202300033 |
| [49] | Bouali, A.; Shukla, B.; Chaudhary, H.; Tiwari, RK; Samar, M.; Mustafa, G., Cosmological tests of parametrization \(q= \alpha - \beta\) h in f (q) flrw cosmology, Int. J. Geom. Methods Mod. Phys. (2023) · Zbl 1533.83076 · doi:10.1142/S0219887823501529 |
| [50] | Chaudhary, H.; Kaushik, A.; Kohli, A., Cosmological test of \(\sigma \theta\) as function of scale factor in f (r, t) framework, New Astron., 103 (2023) · doi:10.1016/j.newast.2023.102044 |
| [51] | Khurana, M., Chaudhary, H., Debnath, U., Molla, N.U., Mustafa, G.: Cosmological test of dark energy parametrizations in Horava-Lifshitz gravity. arXiv preprint arXiv:2310.07410 |
| [52] | Mamon, AA; Das, S., A parametric reconstruction of the deceleration parameter, Eur. Phys. J. C, 77, 7, 495 (2017) · doi:10.1140/epjc/s10052-017-5066-4 |
| [53] | Jamil, M.; Momeni, D.; Myrzakulov, R., Observational constraints on non-minimally coupled Galileon model, Eur. Phys. J. C, 73, 3, 2347 (2013) · doi:10.1140/epjc/s10052-013-2347-4 |
| [54] | Bouali, A., Chaudhary, H., Debnath, U., Roy, T., Mustafa, G.: Constraints on the parameterized deceleration parameter in FRW universe. arXiv:2301.12107 |
| [55] | Shekh, SH; Bouali, A.; Mustafa, G.; Pradhan, A.; Javed, F., Observational constraints in accelerated emergent \(f(Q)\) gravity model, Class. Quantum Gravity, 40, 5 (2023) · Zbl 1518.83073 · doi:10.1088/1361-6382/acb631 |
| [56] | Gadbail, G.N., Harshita, Bouali, A., Sahoo, P.K.: Statistical and cosmological analysis of Weyl-type \(f(Q,T)\) models using Pantheon+ dataset. arXiv:2305.11190 |
| [57] | Barboza, E. Jr; Alcaniz, J.; Zhu, Z-H; Silva, R., Generalized equation of state for dark energy, Phys. Rev. D, 80, 4 (2009) · doi:10.1103/PhysRevD.80.043521 |
| [58] | Kundu, R.; Debnath, U.; Pradhan, A., Studying the optical depth behaviour of parametrized deceleration parameter in non-flat universe, Int. J. Geom. Methods Mod. Phys., 20, 2350110 (2023) · Zbl 1538.83017 · doi:10.1142/S0219887823501104 |
| [59] | Bandyopadhyay, T.; Debnath, U., Fluid accretion upon higher-dimensional wormhole and black hole for parameterized deceleration parameter, Int. J. Geom. Methods Mod. Phys., 19, 12, 2250182 (2022) · Zbl 1537.83150 · doi:10.1142/S0219887822501821 |
| [60] | Foreman-Mackey, D.; Hogg, DW; Lang, D.; Goodman, J., emcee: the MCMC hammer, Publ. Astron. Soc. Pac., 125, 925, 306 (2013) · doi:10.1086/670067 |
| [61] | Brooks, SP; Gelman, A., General methods for monitoring convergence of iterative simulations, J. Comput. Graph. Stat., 7, 4, 434-455 (1998) |
| [62] | Lewis, A.; Bridle, S., Cosmological parameters from CMB and other data: a Monte Carlo approach, Phys. Rev. D, 66, 10 (2002) · doi:10.1103/PhysRevD.66.103511 |
| [63] | Gilks, WR; Richardson, S.; Spiegelhalter, D., Markov Chain Monte Carlo in Practice (1995), Boca Raton: CRC Press, Boca Raton · Zbl 0832.00018 · doi:10.1201/b14835 |
| [64] | Metropolis, N.; Rosenbluth, AW; Rosenbluth, MN; Teller, AH; Teller, E., Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 6, 1087-1092 (1953) · Zbl 1431.65006 · doi:10.1063/1.1699114 |
| [65] | Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications · Zbl 0219.65008 |
| [66] | Gelman, A.; Carlin, JB; Stern, HS; Dunson, DB; Vehtari, A.; Rubin, DB, Bayesian Data Analysis (2013), Boca Raton: CRC Press, Boca Raton · Zbl 1279.62004 · doi:10.1201/b16018 |
| [67] | Verde, L.; Peiris, H.; Spergel, D.; Nolta, M.; Bennett, C.; Halpern, M.; Hinshaw, G.; Jarosik, N.; Kogut, A.; Limon, M., First-year Wilkinson microwave anisotropy probe (wmap)* observations: parameter estimation methodology, Astrophys. J. Suppl. Ser., 148, 1, 195 (2003) · doi:10.1086/377335 |
| [68] | Trotta, R., Applications of Bayesian model selection to cosmological parameters, Mon. Not. R. Astron. Soc., 378, 1, 72-82 (2007) · doi:10.1111/j.1365-2966.2007.11738.x |
| [69] | Gaztanaga, E.; Bonvin, C.; Hui, L., Measurement of the dipole in the cross-correlation function of galaxies, J. Cosmol. Astropart. Phys., 2017, 1, 032 (2017) · doi:10.1088/1475-7516/2017/01/032 |
| [70] | Stern, D.; Jimenez, R.; Verde, L.; Kamionkowski, M.; Stanford, SA, Cosmic chronometers: constraining the equation of state of dark energy. I: H (z) measurements, J. Cosmol. Astropart. Phys., 2010, 2, 008 (2010) · doi:10.1088/1475-7516/2010/02/008 |
| [71] | Lee, S.: Constraining minimally extended varying speed of light by cosmological chronometers. arXiv preprint arXiv:2301.06947 |
| [72] | Gaztanaga, 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), Mon. Not. R. Astron. Soc., 399, 1663-1680 (2009) · doi:10.1111/j.1365-2966.2009.15405.x |
| [73] | Chimento, L.; Forte, MI, Unified model of baryonic matter and dark components, Phys. Lett. B, 666, 205-211 (2008) · doi:10.1016/j.physletb.2008.07.064 |
| [74] | Oka, A.; Saito, S.; Nishimichi, T.; Taruya, A.; Yamamoto, K., Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample, Mon. Not. R. Astron. Soc., 439, 2515-2530 (2014) · doi:10.1093/mnras/stu111 |
| [75] | Wang, Y., BOSS, Mon. Not. R. Astron. Soc., 469, 3, 3762-3774 (2017) · doi:10.1093/mnras/stx1090 |
| [76] | Moresco, M.; Cimatti, A.; Jimenez, R.; Pozzetti, L.; Zamorani, G.; Bolzonella, M.; Dunlop, J.; Lamareille, F.; Mignoli, M.; Pearce, H., Improved constraints on the expansion rate of the universe up to z 1.1 from the spectroscopic evolution of cosmic chronometers, J. Cosmol. Astropart. Phys., 2012, 8, 006 (2012) · doi:10.1088/1475-7516/2012/08/006 |
| [77] | 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 \(\beta (z)\) from the Sloan digital sky survey DR7 luminous red galaxies, Mon. Not. R. Astron. Soc., 435, 255-262 (2013) · doi:10.1093/mnras/stt1290 |
| [78] | Alam, S., BOSS, Mon. Not. R. Astron. Soc., 470, 3, 2617-2652 (2017) · doi:10.1093/mnras/stx721 |
| [79] | Blake, C., The WiggleZ Dark Energy Survey: joint measurements of the expansion and growth history at z \(< 1\), Mon. Not. R. Astron. Soc., 425, 405-414 (2012) · doi:10.1111/j.1365-2966.2012.21473.x |
| [80] | Zhang, C.; Zhang, H.; Yuan, S.; Liu, S.; Zhang, T-J; Sun, Y-C, Four new observational h (z) data from luminous red galaxies in the Sloan digital sky survey data release seven, Res. Astron. Astrophys., 14, 10, 1221 (2014) · doi:10.1088/1674-4527/14/10/002 |
| [81] | Chuang, C-H; Prada, F.; Cuesta, AJ; Eisenstein, DJ; Kazin, E.; Padmanabhan, N.; Sánchez, AG; Xu, X.; Beutler, F.; Manera, M., 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, Mon. Not. R. Astron. Soc., 433, 4, 3559-3571 (2013) · doi:10.1093/mnras/stt988 |
| [82] | Moresco, M.; Pozzetti, L.; Cimatti, A.; Jimenez, R.; Maraston, C.; Verde, L.; Thomas, D.; Citro, A.; Tojeiro, R.; Wilkinson, D., A 6 · doi:10.1088/1475-7516/2016/05/014 |
| [83] | Lee, S.: Cosmic distance duality as a probe of minimally extended varying speed of light. arXiv preprint arXiv:2108.06043 |
| [84] | Delubac, T.; Bautista, JE; Rich, J.; Kirkby, D.; Bailey, S.; Font-Ribera, A.; Slosar, A.; Lee, K-G; Pieri, MM; Hamilton, J-C, Baryon acoustic oscillations in the ly \(\alpha\) forest of boss dr11 quasars, Astron. Astrophys., 574, A59 (2015) · doi:10.1051/0004-6361/201423969 |
| [85] | Bautista, JE; Guy, J.; Rich, J.; Blomqvist, M.; Des Bourboux, HDM; Pieri, MM; Font-Ribera, A.; Bailey, S.; Delubac, T.; Kirkby, D., Measurement of baryon acoustic oscillation correlations at z= 2.3 with sdss dr12 ly \(\alpha \)-forests, Astron. Astrophys., 603, A12 (2017) · doi:10.1051/0004-6361/201730533 |
| [86] | Font-Ribera, A.; Kirkby, D.; Busca, N.; Miralda-Escude, J.; Ross, NP; Slosar, A.; Rich, J.; Aubourg, E.; Bailey, S.; Bhardwaj, V., Quasar-Lyman \(\alpha\) forest cross-correlation from boss dr11: baryon acoustic oscillations, J. Cosmol. Astropart. Phys., 2014, 5, 027-027 (2014) · doi:10.1088/1475-7516/2014/05/027 |
| [87] | Ratsimbazafy, AL; Loubser, SI; Crawford, SM; Cress, CM; Bassett, BA; Nichol, RC; Väisänen, P., Age-dating luminous red galaxies observed with the Southern African large telescope, Mon. Not. R. Astron. Soc., 467, 3, 3239-3254 (2017) · doi:10.1093/mnras/stx301 |
| [88] | Scolnic, DM; Jones, D.; Rest, A.; Pan, Y.; Chornock, R.; Foley, R.; Huber, M.; Kessler, R.; Narayan, G.; Riess, A., The complete light-curve sample of spectroscopically confirmed SNe Ia from pan-starrs1 and cosmological constraints from the combined pantheon sample, Astrophys. J., 859, 2, 101 (2018) · doi:10.3847/1538-4357/aab9bb |
| [89] | Conley, A.; Guy, J.; Sullivan, M.; Regnault, N.; Astier, P.; Balland, C.; Basa, S.; Carlberg, R.; Fouchez, D.; Hardin, D., Supernova constraints and systematic uncertainties from the first three years of the supernova legacy survey, Astrophys. J. Suppl. Ser., 192, 1, 1 (2010) · doi:10.1088/0067-0049/192/1/1 |
| [90] | Demianski, M.; Piedipalumbo, E.; Sawant, D.; Amati, L., Cosmology with gamma-ray bursts-II. Cosmography challenges and cosmological scenarios for the accelerated universe, Astron. Astrophys., 598, A113 (2017) · doi:10.1051/0004-6361/201628911 |
| [91] | Roberts, C., Horne, K., Hodson, A.O., Leggat, A.D.: Tests of \(\lambda\) cdm and conformal gravity using grb and quasars as standard candles out to \(z \sim 8\). arXiv preprint arXiv:1711.10369 |
| [92] | Percival, WJ; Reid, BA; Eisenstein, DJ; Bahcall, NA; Budavari, T.; Frieman, JA; Fukugita, M.; Gunn, JE; Ivezi’c, Z.; Knapp, GR, Baryon acoustic oscillations in the Sloan digital sky survey data release 7 galaxy sample, Mon. Not. R. Astron. Soc., 401, 4, 2148-2168 (2010) · doi:10.1111/j.1365-2966.2009.15812.x |
| [93] | Beutler, F.; Blake, C.; Colless, M.; Jones, DH; Staveley-Smith, L.; Campbell, L.; Parker, Q.; Saunders, W.; Watson, F., The 6df galaxy survey: baryon acoustic oscillations and the local hubble constant, Mon. Not. R. Astron. Soc., 416, 4, 3017-3032 (2011) · doi:10.1111/j.1365-2966.2011.19250.x |
| [94] | Delubac, T.; Rich, J.; Bailey, S.; Font-Ribera, A.; Kirkby, D.; Le Goff, J-M; Pieri, MM; Slosar, A.; Aubourg, É.; Bautista, JE, Baryon acoustic oscillations in the ly \(\alpha\) forest of boss quasars, Astron. Astrophys., 552, A96 (2013) · doi:10.1051/0004-6361/201220724 |
| [95] | Anderson, L.; Aubourg, E.; Bailey, S.; Bizyaev, D.; Blanton, M.; Bolton, AS; Brinkmann, J.; Brownstein, JR; Burden, A.; Cuesta, AJ, The clustering of galaxies in the SDSS-III baryon oscillation spectroscopic survey: baryon acoustic oscillations in the data release 9 spectroscopic galaxy sample, Mon. Not. R. Astron. Soc., 427, 4, 3435-3467 (2012) · doi:10.1111/j.1365-2966.2012.22066.x |
| [96] | Seo, H-J; Ho, S.; White, M.; Cuesta, AJ; Ross, AJ; Saito, S.; Reid, B.; Padmanabhan, N.; Percival, WJ; De Putter, R., Acoustic scale from the angular power spectra of SDSS-III dr8 photometric luminous galaxies, Astrophys. J., 761, 1, 13 (2012) · doi:10.1088/0004-637X/761/1/13 |
| [97] | Ross, AJ; Samushia, L.; Howlett, C.; Percival, WJ; Burden, A.; Manera, M., The clustering of the SDSS dr7 main galaxy sample-I. A 4 per cent distance measure at z= 0.15, Mon. Not. R. Astron. Soc., 449, 1, 835-847 (2015) · doi:10.1093/mnras/stv154 |
| [98] | Tojeiro, R.; Ross, AJ; Burden, A.; Samushia, L.; Manera, M.; Percival, WJ; Beutler, F.; Brinkmann, J.; Brownstein, JR; Cuesta, AJ, The clustering of galaxies in the SDSS-III baryon oscillation spectroscopic survey: galaxy clustering measurements in the low-redshift sample of data release 11, Mon. Not. R. Astron. Soc., 440, 3, 2222-2237 (2014) · doi:10.1093/mnras/stu371 |
| [99] | Bautista, JE; Vargas-Magaña, M.; Dawson, KS; Percival, WJ; Brinkmann, J.; Brownstein, J.; Camacho, B.; Comparat, J.; Gil-Marín, H.; Mueller, E-M, The SDSS-IV extended baryon oscillation spectroscopic survey: baryon acoustic oscillations at redshift of 0.72 with the dr14 luminous red galaxy sample, Astrophys. J., 863, 1, 110 (2018) · doi:10.3847/1538-4357/aacea5 |
| [100] | De Carvalho, E.; Bernui, A.; Carvalho, G.; Novaes, C.; Xavier, H., Angular baryon acoustic oscillation measure at z= 2.225 from the SDSS quasar survey, J. Cosmol. Astropart. Phys., 2018, 4, 064 (2018) · doi:10.1088/1475-7516/2018/04/064 |
| [101] | Ata, M.; Baumgarten, F.; Bautista, J.; Beutler, F.; Bizyaev, D.; Blanton, MR; Blazek, JA; Bolton, AS; Brinkmann, J.; Brownstein, JR, The clustering of the SDSS-IV extended baryon oscillation spectroscopic survey dr14 quasar sample: first measurement of baryon acoustic oscillations between redshift 0.8 and 2.2, Mon. Not. R. Astron. Soc., 473, 4, 4773-4794 (2018) · doi:10.1093/mnras/stx2630 |
| [102] | Abbott, T.; Abdalla, F.; Alarcon, A.; Allam, S.; Andrade-Oliveira, F.; Annis, J.; Avila, S.; Banerji, M.; Banik, N.; Bechtol, K., Dark energy survey year 1 results: Measurement of the baryon acoustic oscillation scale in the distribution of galaxies to redshift 1, Mon. Not. R. Astron. Soc., 483, 4, 4866-4883 (2019) · doi:10.1093/mnras/sty3351 |
| [103] | Molavi, Z.; Khodam-Mohammadi, A., Observational tests of Gauss-Bonnet like dark energy model, Eur. Phys. J. Plus, 134, 6, 254 (2019) · doi:10.1140/epjp/i2019-12723-x |
| [104] | Benisty, D.; Staicova, D., Testing late-time cosmic acceleration with uncorrelated baryon acoustic oscillation dataset, Astron. Astrophys., 647, A38 (2021) · doi:10.1051/0004-6361/202039502 |
| [105] | Kazantzidis, L.; Perivolaropoulos, L., Evolution of the f \(\sigma 8\) tension with the Planck \(15/ \lambda\) CDM determination and implications for modified gravity theories, Phys. Rev. D, 97, 10 (2018) · doi:10.1103/PhysRevD.97.103503 |
| [106] | Hogg, NB; Martinelli, M.; Nesseris, S., Constraints on the distance duality relation with standard sirens, J. Cosmol. Astropart. Phys., 2020, 12, 019 (2020) · Zbl 1484.83129 · doi:10.1088/1475-7516/2020/12/019 |
| [107] | Martinelli, M.; Martins, CJAP; Nesseris, S.; Sapone, D.; Tutusaus, I.; Avgoustidis, A.; Camera, S.; Carbone, C.; Casas, S.; Ilić, S., Euclid: forecast constraints on the cosmic distance duality relation with complementary external probes, Astron. Astrophys., 644, A80 (2020) · doi:10.1051/0004-6361/202039078 |
| [108] | Sahni, V.; Saini, TD; Starobinsky, AA; Alam, U., Statefinder: a new geometrical diagnostic of dark energy, J. Exp. Theor. Phys. Lett., 77, 201-206 (2003) · doi:10.1134/1.1574831 |
| [109] | Visser, M., Jerk, snap and the cosmological equation of state, Class. Quantum Gravity, 21, 11, 2603 (2004) · Zbl 1054.83046 · doi:10.1088/0264-9381/21/11/006 |
| [110] | Luongo, O., Dark energy from a positive jerk parameter, Mod. Phys. Lett. A, 28, 1350080 (2013) · doi:10.1142/S0217732313500806 |
| [111] | Dunajski, M.; Gibbons, G., Cosmic jerk, snap and beyond, Class. Quantum Gravity, 25, 23 (2008) · Zbl 1155.83014 · doi:10.1088/0264-9381/25/23/235012 |
| [112] | Sahni, V.; Saini, TD; Starobinsky, AA; Alam, U., Statefinder: a new geometrical diagnostic of dark energy, J. Exp. Theor. Phys. Lett., 77, 201-206 (2003) · doi:10.1134/1.1574831 |
| [113] | Alam, U.; Sahni, V.; Deep Saini, T.; Starobinsky, A., Exploring the expanding universe and dark energy using the statefinder diagnostic, Mon. Not. R. Astron. Soc., 344, 4, 1057-1074 (2003) · doi:10.1046/j.1365-8711.2003.06871.x |
| [114] | Sami, M.; Shahalam, M.; Skugoreva, M.; Toporensky, A., Cosmological dynamics of a nonminimally coupled scalar field system and its late time cosmic relevance, Phys. Rev. D, 86, 10 (2012) · doi:10.1103/PhysRevD.86.103532 |
| [115] | Myrzakulov, R.; Shahalam, M., Statefinder hierarchy of bimetric and Galileon models for concordance cosmology, J. Cosmol. Astropart. Phys., 2013, 10, 047 (2013) · doi:10.1088/1475-7516/2013/10/047 |
| [116] | Aviles, A.; Klapp, J.; Luongo, O., Toward unbiased estimations of the statefinder parameters, Phys. Dark Univ., 17, 25-37 (2017) · doi:10.1016/j.dark.2017.07.002 |
| [117] | Sahni, V.; Shafieloo, A.; Starobinsky, AA, Two new diagnostics of dark energy, Phys. Rev. D, 78, 10 (2008) · doi:10.1103/PhysRevD.78.103502 |
| [118] | Zunckel, C.; Clarkson, C., Consistency tests for the cosmological constant, Phys. Rev. Lett., 101, 18 (2008) · doi:10.1103/PhysRevLett.101.181301 |
| [119] | Shahalam, M.; Pathak, S.; Verma, M.; Khlopov, MY; Myrzakulov, R., Dynamics of interacting quintessence, Eur. Phys. J. C, 75, 1-9 (2015) · doi:10.1140/epjc/s10052-015-3608-1 |
| [120] | Agarwal, A.; Myrzakulov, R.; Pacif, S.; Shahalam, M., Cosmic acceleration from coupling of baryonic and dark matter components: analysis and diagnostics, Int. J. Mod. Phys. D, 28, 6, 1950083 (2019) · Zbl 1432.83055 · doi:10.1142/S0218271819500834 |
| [121] | Schwarz, G., Estimating the dimension of a model, Ann. Stat., 6, 461-464 (1978) · Zbl 0379.62005 · doi:10.1214/aos/1176344136 |
| [122] | Liddle, AR, How many cosmological parameters, Mon. Not. R. Astron. Soc., 351, 3, L49-L53 (2004) · doi:10.1111/j.1365-2966.2004.08033.x |
| [123] | Nesseris, S.; Garcia-Bellido, J., Is the Jeffreys’ scale a reliable tool for Bayesian model comparison in cosmology?, J. Cosmol. Astropart. Phys., 2013, 8, 036 (2013) · doi:10.1088/1475-7516/2013/08/036 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
