Built on

J. M. Bardeen, “Gauge Invariant Cosmological Perturbations,” Phys. Rev
1905
Earlier work this paper cites.
Ya. B. Zeldovich, “Gravitational instability: An Approximate theory for large density perturbations,” Astron. Astrophys
1970
Earlier work this paper cites.
L. Smarr and J. W. York, Jr., “Kinematical conditions in the construction of space-time,” Phys. Rev
1978
Earlier work this paper cites.
C. C. Dyer and R. C. Roeder, “On the transition from Weyl to Ricci focusing,” General Relativity and Gravitation
1981
Earlier work this paper cites.
V. I. Arnold, S. F. Shandarin, and I. B. Zeldovich, “The large scale structure of the universe. I - General properties One- and two-dimensional models,” Geophysical and Astrophysical Fluid Dynamics
1982
Earlier work this paper cites.
S. L. Shapiro and S. A. Teukolsky, “Relativistic stellar dynamics on the computer. I - Motivation and numerical method,” Astrophys. J
1985
Earlier work this paper cites.
T. Nakamura, K. Oohara, and Y. Kojima, “General Relativistic Collapse to Black Holes and Gravitational Waves from Black Holes,” Prog. Theor. Phys. Suppl
1987
Earlier work this paper cites.
V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, “Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions,” Phys. Rept
1992
Earlier work this paper cites.
M. Shibata and T. Nakamura, “Evolution of three-dimensional gravitational waves: Harmonic slicing case,” Phys. Rev
1995
Earlier work this paper cites.
E. Bertschinger, “Cosmological dynamics,” NASA STI/Recon Technical Report N
1995
Earlier work this paper cites.
T. W. Baumgarte and S. L. Shapiro, “On the numerical integration of Einstein’s field equations,” Phys. Rev
1999
Earlier work this paper cites.
M. Shibata, “3-D numerical simulation of black hole formation using collisionless particles: Triplane symmetric case,” Prog. Theor. Phys
1999
Earlier work this paper cites.
M. Shibata, “Fully general relativistic simulation of merging binary clusters: Spatial gauge condition,” Prog. Theor. Phys
1999
Earlier work this paper cites.
M. Alcubierre and B. Bruegmann, “Simple excision of a black hole in (3+1)-numerical relativity,” Phys. Rev
2001
Earlier work this paper cites.
A. Lewis and S. Bridle, “Cosmological parameters from CMB and other data: A Monte Carlo approach,” Phys. Rev
2002
Earlier work this paper cites.
M. D. Duez, P. Marronetti, S. L. Shapiro, and T. W. Baumgarte, “Hydrodynamic simulations in 3+1 general relativity,” Phys. Rev
2003
Earlier work this paper cites.
M. T. Gastner and M. E. J. Newman, “Diffusion-based method for producing density-equalizing maps,” Proceedings of the National Academy of Sciences
2004
Earlier work this paper cites.
International series of monographs on physics. Oxford Univ. Press, Oxford, 2008
M. Alcubierre, Introduction to 3+1 numerical relativity · 2008
Earlier work this paper cites.
S. F. Daniel, R. R. Caldwell, A. Cooray, and A. Melchiorri, “Large Scale Structure as a Probe of Gravitational Slip,” Phys. Rev
Original
2008
Earlier work this paper cites.

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Cambridge University Press, 2010
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Then

J. B. Mertens, J. T. Giblin, and G. D. Starkman, “Integration of inhomogeneous cosmological spacetimes in the BSSN formalism,” Phys. Rev
Original
2016
Later among the works it cites.
O. Hahn and R. E. Angulo, “An adaptively refined phase–space element method for cosmological simulations and collisionless dynamics,” Mon. Not. Roy. Astron. Soc
Original
2016
Later among the works it cites.
R. Hirai, H. Nagakura, H. Okawa, and K. Fujisawa, “Hyperbolic self-gravity solver for large scale hydrodynamical simulations,” Phys. Rev
Original
2016
Later among the works it cites.
P. Fleury, J. Larena, and J.-P. Uzan, “Weak gravitational lensing of finite beams,” Phys. Rev. Lett
Original
2017
Later among the works it cites.
O. Umeh, S. Jolicoeur, R. Maartens, and C. Clarkson, “A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone,” JCAP

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2018

The Limited Accuracy of Linearized Gravity

Giblin Jr, John T., Mertens, James B., Starkman, Glenn D. et al.

Understand

Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations.

In an era of precision cosmology, we should ask: are these approximate predictions sufficiently accurate for comparison to observations, and can we draw meaningful conclusions about properties of our Universe from them? In this work we examine the accuracy of linearized gravity in the presence of collisionless matter and a cosmological constant utilizing fully general relativistic simulations.
We observe the gauge-dependence of corrections to linear theory, and note the amplitude of these corrections.
For perturbations whose amplitudes are in line with expectations from the standard $\Lambda$CDM model, we find that the full, general relativistic metric is well-described by linear theory in Newtonian and harmonic gauges, while the metric in comoving-synchronous gauge is not.

Built on

J. M. Bardeen, “Gauge Invariant Cosmological Perturbations,” Phys. Rev
1905
Earlier work this paper cites.
Ya. B. Zeldovich, “Gravitational instability: An Approximate theory for large density perturbations,” Astron. Astrophys
1970
Earlier work this paper cites.
L. Smarr and J. W. York, Jr., “Kinematical conditions in the construction of space-time,” Phys. Rev
1978
Earlier work this paper cites.
C. C. Dyer and R. C. Roeder, “On the transition from Weyl to Ricci focusing,” General Relativity and Gravitation
1981
Earlier work this paper cites.
V. I. Arnold, S. F. Shandarin, and I. B. Zeldovich, “The large scale structure of the universe. I - General properties One- and two-dimensional models,” Geophysical and Astrophysical Fluid Dynamics
1982
Earlier work this paper cites.
S. L. Shapiro and S. A. Teukolsky, “Relativistic stellar dynamics on the computer. I - Motivation and numerical method,” Astrophys. J
1985
Earlier work this paper cites.
T. Nakamura, K. Oohara, and Y. Kojima, “General Relativistic Collapse to Black Holes and Gravitational Waves from Black Holes,” Prog. Theor. Phys. Suppl
1987
Earlier work this paper cites.
V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, “Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions,” Phys. Rept
1992
Earlier work this paper cites.
M. Shibata and T. Nakamura, “Evolution of three-dimensional gravitational waves: Harmonic slicing case,” Phys. Rev
1995
Earlier work this paper cites.
E. Bertschinger, “Cosmological dynamics,” NASA STI/Recon Technical Report N
1995
Earlier work this paper cites.
T. W. Baumgarte and S. L. Shapiro, “On the numerical integration of Einstein’s field equations,” Phys. Rev
1999
Earlier work this paper cites.
M. Shibata, “3-D numerical simulation of black hole formation using collisionless particles: Triplane symmetric case,” Prog. Theor. Phys
1999
Earlier work this paper cites.
M. Shibata, “Fully general relativistic simulation of merging binary clusters: Spatial gauge condition,” Prog. Theor. Phys
1999
Earlier work this paper cites.
M. Alcubierre and B. Bruegmann, “Simple excision of a black hole in (3+1)-numerical relativity,” Phys. Rev
2001
Earlier work this paper cites.
A. Lewis and S. Bridle, “Cosmological parameters from CMB and other data: A Monte Carlo approach,” Phys. Rev
2002
Earlier work this paper cites.
M. D. Duez, P. Marronetti, S. L. Shapiro, and T. W. Baumgarte, “Hydrodynamic simulations in 3+1 general relativity,” Phys. Rev
2003
Earlier work this paper cites.
M. T. Gastner and M. E. J. Newman, “Diffusion-based method for producing density-equalizing maps,” Proceedings of the National Academy of Sciences
2004
Earlier work this paper cites.
International series of monographs on physics. Oxford Univ. Press, Oxford, 2008
M. Alcubierre, Introduction to 3+1 numerical relativity · 2008
Earlier work this paper cites.
S. F. Daniel, R. R. Caldwell, A. Cooray, and A. Melchiorri, “Large Scale Structure as a Probe of Gravitational Slip,” Phys. Rev
Original
2008
Earlier work this paper cites.