Many cosmological measurements today suggest that the Universe is expanding at a constant rate. This is inferred from the observed age versus redshift relationship and various distance indicators, all of which point to a cosmic equation of state (EoS) p = −ρ/3, where ρ and p are, respectively, the total energy density and pressure of the cosmic fluid. It has recently been shown that this result is not a coincidence and simply confirms the fact that the symmetries in the Friedmann–Robertson–Walker (FRW) metric appear to be viable only for a medium with zero active mass, i.e., ρ+ 3p = 0. In their latest paper, however, Kim, Lasenby and Hobson (2016) have provided what they believe to be a counter argument to this conclusion. Here, we show that these authors are merely repeating the conventional mistake of incorrectly placing the observer simultaneously in a comoving frame, where the lapse function gtt is coordinate dependent when ρ+ 3p≠0, and a supposedly different, freefalling frame, in which gtt = 1, implying no time dilation. We demonstrate that the Hubble flow is not inertial when ρ+ 3p≠0, so the comoving frame is generally not in free fall, even though in FRW, the comoving and free-falling frames are supposed to be identical at every spacetime point. So this confusion of frames not only constitutes an inconsistency with the fundamental tenets of general relativity but, additionally, there is no possibility of using a gauge transformation to select a set of coordinates for which gtt = 1 when ρ+ 3p≠0.
. [J]. Frontiers of Physics, 2017, 12(1): 129802.
Fulvio Melia. The zero active mass condition in Friedmann–Robertson–Walker cosmologies. Front. Phys. , 2017, 12(1): 129802.
C. L. Bennett, R. S. Hill, G. Hinshaw, M. R. Nolta, N. Odegard, L. Page, D. N. Spergel, J. L. Weiland, E. L. Wright, M. Halpern, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, G. S. Tucker, and E. Wollack, First-Year Wilkinson Microwave Anisotropy Probe (WMAP)Observations: Foreground Emission,Astrophys. J. Suppl. 148(1), 97 (2003)
https://doi.org/10.1086/377252
2
D. N. Spergel, L. Verde, H. V. Peiris, E. Komatsu, M. R. Nolta, C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright, First-Year Wilkinson Microwave Anisotropy Probe (WMAP)Observations: Determination of cosmological parameters,Astrophys. J. Suppl. 148(1), 175 (2003)
https://doi.org/10.1086/377226
3
P. A. R. Ade, (Planck Collaboration), Planck 2013 results. XXIII. Isotropy and statistics of the CMB,A&A 571, A23 (2014)
4
F. Melia, The Edge of Infinity: Supermassive Black Holes in the Universe, Cambridge: Cambridge University Press, 1972, p. 119
D. Y. Kim, A. N. Lasenby, and M. P. Hobson, Friedmann–Robertson–Walker models do not require zero active mass, Mon. Not. R. Astron. Soc. 460(1), L119 (2016), arXiv: 1601.07890
10
S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, New York: Wiley, 1972
M. Carrera and D. Giulini, Influence of global cosmological expansion on local dynamics and kinematics, Rev. Mod. Phys. 82, 169 (2010), arXiv: 0810.2712v2
https://doi.org/10.1103/RevModPhys.82.169
13
H. Liu, Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys. 28(11), 1920 (1987)
https://doi.org/10.1063/1.527751
14
H. Liu, Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys. 28(11), 1924 (1987)
https://doi.org/10.1063/1.527751
D. Y. Kim, A. N. Lasenby, and M. P. Hobson, Spherically-symmetric solutions in general relativity, Phys. Rev. D (2016) (submitted), arXiv: 1604.06365
17
B. O. J. Tupper, Tetrad field equations and a generalized Friedmann equation, Astrophys. Space Sci. 28(1), 225 (1974)
https://doi.org/10.1007/BF00642252
18
P. van Oirschot, J. Kwan, and G. F. Lewis, Through the looking glass: Why the “Cosmic Horizon” is not a horizon, Mon. Not. R. Astron. Soc. 404, 1633 (2010), arXiv: 1001.4795
https://doi.org/10.1111/j.1365-2966.2010.16398.x
O. Bikwa, F. Melia, and A. S. H. Shevchuk, Photon geodesics in Friedmann–Robertson–Walker cosmologies, Mon. Not. R. Astron. Soc. 421(4), 3356 (2012)
https://doi.org/10.1111/j.1365-2966.2012.20560.x
21
F. Melia, The cosmic horizon for a universe with Phantom energy, J. Cosmol. Astropart. Phys. 09, 029 (2012)
22
F. Melia, Proper size of the visible Universe in FRW metrics with a constant space-time curvature, Class. Quantum Gravity 30(15), 155007 (2013)
https://doi.org/10.1088/0264-9381/30/15/155007