References
- Bonanos, A.Z., et al. 2006, The First DIRECT Distance Determination to a Detached Eclipsing Binary in M33, Astrophys. J., 652, 313-322. https://doi.org/10.1086/508140
- Clocchiatti, A., et al. 2006, Hubble Space Telescope and Ground-based Observations of Type Ia Supernovae at Redshift 0.5: Cosmological Implications, Astrophys. J., 642, 1-21. https://doi.org/10.1086/498491
- Colberg, J.M., et al. 2000, Clustering of galaxy clusters in cold dark matter universes, Mon. Not. R. Astron. Soc., 319, 209-214. https://doi.org/10.1046/j.1365-8711.2000.03832.x
- Cole, S., et al. 2005, The 2dF Galaxy Redshift Survey: power-spectrum analysis of the final data set and cosmological implications, Mon. Not. R. Astron. Soc., 362, 505-534. https://doi.org/10.1111/j.1365-2966.2005.09318.x
- Dubrovin, B.A., Fomenko, A.T., and Novikov, S.P. 1984, Modern Geometry - Methods and Applications. Part I. The Geometry of Surfaces, Transformation Groups, and Fields (Springer-Verlag, New York).
- Dunkley, J., et al. 2009, Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data, Astrophys. J. Suppl., 180, 306-329. https://doi.org/10.1088/0067-0049/180/2/306
- Einstein, A. 1917, Kosmologische Betrachtungen zur allgemeinen Relativittstheorie, Sitzungsberichte der Preussischen Akad. d. Wiss., 1917, 142-152.
- Einstein, A. 1922, The Meaning of Relativity (Princeton University Press), 98-108.
- Eisenstein, D.J., et al. 2005, Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies, Astrophys. J., 633, 560-574. https://doi.org/10.1086/466512
- Freedman, W.L., et al. 2001, Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant, Astrophys. J., 553, 47-72. https://doi.org/10.1086/320638
- Friedmann, A.A. 1922, Uber die Krummung des Raumes, Z. Phys., 10, 377-386. https://doi.org/10.1007/BF01332580
- Friedmann, A.A. 1924, Uber die Moglichkeit einer Welt mit konstanter negativer Krmmung des Raumes, Z. Phys., 21, 326-332. https://doi.org/10.1007/BF01328280
- Guth, A.H. 1981, Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D, 23, 347-356. https://doi.org/10.1103/PhysRevD.23.347
- Hinshaw, G., et al. 2007, Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis, Astrophys. J. Suppl., 170, 288-334. https://doi.org/10.1086/513698
- Hinshaw, G., et al. 2009, Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results, Astrophys. J. Suppl., 180, 225-245. https://doi.org/10.1088/0067-0049/180/2/225
- Hwang, J.-c., and Noh, H. 2006, Why Newtonian gravity is reliable in large-scale cosmological simulations, Mon. Not. R. Astron. Soc., 367, 1515-1520. https://doi.org/10.1111/j.1365-2966.2006.10067.x
- Jackson, J.C., and Jannetta, A.L. 2006, Legacy data and cosmological constraints from the angular-size/redshift relation for ultracompact radio sources, Journal of Cosmology and Astroparticle Physics, 0611, 002. https://doi.org/10.1088/1475-7516/2006/11/002
- Kolb, E.W. 1989, A coasting cosmology, Astrophys. J., 344, 543-550. https://doi.org/10.1086/167825
-
Kolb, E.W., and Turner, M.S. 1990, The Early Universe (Addison-Wesley Publishing Company),
$\S$ 3.3. - Landau, L.D., and Lifshitz, E.M. 1975, The Classical Theory of Fields (4th ed., Pergamon Press Ltd).
- Mach, E. 1893, The Science of Mechanics (6th ed., The Open Court Publishing Company), Chapter II.
- Macri, L.M., Stanek, K.Z., Bersier, D., Greenhill, L.J., and Reid, M.J. 2006, A New Cepheid Distance to the Maser-Host Galaxy NGC 4258 and Its Implications for the Hubble Constant, Astrophys. J., 652, 1133-1149. https://doi.org/10.1086/508530
- Mather, J.C., Fixsen, D.J., Shafer, R.A., Mosier, C., and Wilkinson, D.T. 1999, Calibrator Design for the COBE Far-Infrared Absolute Spectrophotometer (FIRAS), Astrophys. J., 512, 511-520. https://doi.org/10.1086/306805
- McCrea, W.H., and Milne, E.A. 1934, Newtonian Universes and the Curvature of Space, Quart. J. Math., 5, 73-80. https://doi.org/10.1093/qmath/os-5.1.73
- Milne, E.A. 1934, A Newtonian Expanding Universe, Quart. J. Math., 5, 64-72. https://doi.org/10.1093/qmath/os-5.1.64
- Misner, C.W., Thorne, K.S., and Wheeler, J.A. 1973, Gravitation (W.H. Freeman and Company, San Francisco).
- Page, L., et al. 2007, Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis, Astrophys. J. Suppl., 170, 335-376. https://doi.org/10.1086/513699
- Park, C., Kim, J., and Gott, J.R. 2005, Effects of Gravitational Evolution, Biasing, and Redshift Space Distortion on Topology, Astrophys. J., 633, 1-10. https://doi.org/10.1086/452621
- Park, C.-G., 2012, Introduction to Relativistic Cosmology, Journal of Science Education Chonbuk National University, 37, 57-71.
-
Park, C.-G. and Ratra, B., 2018a, Observational constraints on the tilted spatially-flat and the untilted nonflat
$\varphi$ CDM dynamical dark energy inflation models, Astrophys. J. 868, 83 [arXiv:1807.07421 [astro-ph.CO]]. https://doi.org/10.3847/1538-4357/aae82d - Park, C.-G. and Ratra, B., 2019a, Using the tilted flat- ΛCDM and the non-flat ΛCDM inflation models to measure cosmological parameters from a compilation of observational data, Astrophys. J. in press [arXiv:1801.00213 [astro-ph.CO]].
- Park, C.-G. and Ratra, B., 2019b, Observational constraints on the tilted flat-XCDM and the untilted nonflat XCDM dynamical dark energy inflation parameterizations, Astrophys. Space Sci. 364, 82 [arXiv:1803.05522 [astroph. CO]]. https://doi.org/10.1007/s10509-019-3567-3
- Park, C.-G. and Ratra, B., 2019c, Measuring the Hubble constant and spatial curvature from supernova apparent magnitude, baryon acoustic oscillation, and Hubble parameter data, Astrophys. Space Sci. 364, 134 [arXiv: 1809.03598 [astro-ph.CO]]. https://doi.org/10.1007/s10509-019-3627-8
-
Peebles, P.J.E. 1980, The Large-Scale Structure of the Universe (Princeton University Press),
$\S$ 6. - Planck Collaboration, 2018a, Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209 [astro-ph.CO].
- Planck Collaboration, 2018b, Planck 2018 results: Cosmological Parameter Tables.
-
Riess, A.G., et al. 2007, New Hubble Space Telescope Discoveries of Type Ia Supernovae at z
$\geq$ 1: Narrowing Constraints on the Early Behavior of Dark Energy, Astrophys. J., 659, 98-121. https://doi.org/10.1086/510378 - Robertson, H.P. 1929, On the Foundations of Relativistic Cosmology, Proc. Natl. Acad. Sci. U. S. A., 15, 822-829. https://doi.org/10.1073/pnas.15.11.822
- Sandage, A., Tammann, G.A., Saha, A., Reindl, B., Macchetto, F.D., and Panagia, N. 2006, The Hubble Constant: A Summary of the Hubble Space Telescope Program for the Luminosity Calibration of Type Ia Supernovae by Means of Cepheids, Astrophys. J., 653, 843-860. https://doi.org/10.1086/508853
- Spergel, D.N., et al. 2007, Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology, Astrophys. J. Suppl., 170, 377-408. https://doi.org/10.1086/513700
- Tegmark, M., et al. 2004, The Three-Dimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey, Astrophys. J., 606, 702-740. https://doi.org/10.1086/382125
- Tegmark, M., et al. 2006, Cosmological constraints from the SDSS luminous red galaxies, Phys. Rev. D, 74, 123507. https://doi.org/10.1103/PhysRevD.74.123507
- Walker, A.G. 1935, On Riemannian Spaces with Spherical Symmetry about a Line and the Conditions for Isotropy in General Relativity, Quart. J. Math., 6, 81-93. https://doi.org/10.1093/qmath/os-6.1.81
- Warren, J.S., et al. 2005, Cosmic-Ray Acceleration at the Forward Shock in Tycho's Supernova Remnant: Evidence from Chandra X-Ray Observations, Astrophys. J., 634, 376-389. https://doi.org/10.1086/496941
- Weinberg, S. 1972, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley & Sons, Inc.), Chapter 13.
- Weyl, H. 1923, Zur allgemeinen Relativittstheorie, Z. Phys., 24, 230-232.
- Wood-Vasey, M., et al. 2007, Observational Constraints on the Nature of Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey, Astrophys. J., 666, 694-715. https://doi.org/10.1086/518642
- Wright, E.L. 2007, Constraints on Dark Energy from Supernovae, Gamma-Ray Bursts, Acoustic Oscillations, Nucleosynthesis, Large-Scale Structure, and the Hubble Constant, Astrophys. J., 664, 633-639. https://doi.org/10.1086/519274