Built on

T. Aoki, M. Hirasawa, Y. Ito, J. Nishimura and A. Tsuchiya, “On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model,” PTEP 2019
Original
1904
Earlier work this paper cites.
A. Bedroya and C. Vafa, “Trans-Planckian Censorship and the Swampland,” JHEP 2009
Original
1909
Earlier work this paper cites.
A. Bedroya, R. Brandenberger, M. Loverde and C. Vafa, “Trans-Planckian Censorship and Inflationary Cosmology,” Phys. Rev. D 101
Original
1909
Earlier work this paper cites.
Y. Ito, J. Nishimura and A. Tsuchiya, “Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model,” JHEP 1511
Original
1911
Earlier work this paper cites.
R. Hagedorn, “Statistical thermodynamics of strong interactions at high-energies,” Nuovo Cim. Suppl. 3
1965
Earlier work this paper cites.
A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23
1981
Earlier work this paper cites.
N. Weiss, “Constraints on Hamiltonian Lattice Formulations of Field Theories in an Expanding Universe,” Phys. Rev. D 32
1985
Earlier work this paper cites.
D. Z. Freedman, G. W. Gibbons and M. Schnabl, “Matrix cosmology,” AIP Conf. Proc. 743
1987
Earlier work this paper cites.
J.Hoppe, Quantum Theory of a Massless Relativistic Surface, MIT Ph.D. Thesis 1982, http://dspace.mit.edu/handle/1721.1/15717; B. de Wit, J. Hoppe and H. Nicolai, “On the Quantum Mechanics of Supermembranes,” Nucl. Phys. B 305
1988
Earlier work this paper cites.
R. H. Brandenberger and C. Vafa, “Superstrings In The Early Universe,” Nucl. Phys. B 316
1989
Earlier work this paper cites.
S. R. Das and A. Jevicki, “String Field Theory and Physical Interpretation of D = 1 D=1 Strings,” Mod. Phys. Lett. A 5
1990
Earlier work this paper cites.
N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, “A Large N reduced model as superstring,” Nucl. Phys. B 498
1997
Earlier work this paper cites.

Similar

T. Banks, W. Fischler, S. H. Shenker and L. Susskind, “M theory as a matrix model: A Conjecture,” Phys. Rev. D 55
1997
Cited alongside, same era.
R. Dijkgraaf, E. P. Verlinde and H. L. Verlinde, “Matrix string theory,” Nucl. Phys. B 500
1997
Cited alongside, same era.
H. Aoki, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, “Space-time structures from IIB matrix model,” Prog. Theor. Phys. 99
1998
Cited alongside, same era.
T. Hotta, J. Nishimura and A. Tsuchiya, “Dynamical aspects of large N reduced models,” Nucl. Phys. B 545
1999
Cited alongside, same era.
L. Smolin, “M theory as a matrix extension of Chern-Simons theory,” Nucl. Phys. B 591
Original
2000
Cited alongside, same era.

Then

R. H. Brandenberger, “String Gas Cosmology,” String Cosmology, J.Erdmenger (Editor). Wiley, 2009. p.193-230 [arXiv:0808.0746 [hep-th]]
Original
2009
Later among the works it cites.
P. Agrawal, S. Gukov, G. Obied and C. Vafa, “Topological Gravity as the Early Phase of Our Universe,” arXiv:2009.10077 [hep-th]
Original
2009
Later among the works it cites.
W. Siegel, “Two vierbein formalism for string inspired axionic gravity,” Phys. Rev. D 47
Original
2009
Later among the works it cites.
S. W. Kim, J. Nishimura and A. Tsuchiya, “Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions,” Phys. Rev. Lett. 108
Original
2012
Later among the works it cites.
S. W. Kim, J. Nishimura and A. Tsuchiya, “Late time behaviors of the expanding universe in the IIB matrix model,” JHEP 10

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2022

Emergent Metric Space-Time from Matrix Theory

Brahma, Suddhasattwa, Brandenberger, Robert, Laliberte, Samuel

Understand

The IKKT matrix model yields an emergent space-time.

We further develop these ideas and give a proposal for an emergent metric.
Based on previous numerical studies of this model, we provide evidence that the emergent space-time is continuous and infinite in extent, both in space and in time, and that the metric is spatially flat.
The time evolution describes the transition from a string-theoretic emergent phase to a phase in which the $SO(9)$ symmetry of the model is spontaneously broken to $SO(6) \times SO(3)$, with three dimensions of space expanding, becoming classical and at later times evolving like in a radiation-dominated universe, and the remaining six dimensions of space stabilized at the string scale.

Built on

T. Aoki, M. Hirasawa, Y. Ito, J. Nishimura and A. Tsuchiya, “On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model,” PTEP 2019
Original
1904
Earlier work this paper cites.
A. Bedroya and C. Vafa, “Trans-Planckian Censorship and the Swampland,” JHEP 2009
Original
1909
Earlier work this paper cites.
A. Bedroya, R. Brandenberger, M. Loverde and C. Vafa, “Trans-Planckian Censorship and Inflationary Cosmology,” Phys. Rev. D 101
Original
1909
Earlier work this paper cites.
Y. Ito, J. Nishimura and A. Tsuchiya, “Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model,” JHEP 1511
Original
1911
Earlier work this paper cites.
R. Hagedorn, “Statistical thermodynamics of strong interactions at high-energies,” Nuovo Cim. Suppl. 3
1965
Earlier work this paper cites.
A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23
1981
Earlier work this paper cites.
N. Weiss, “Constraints on Hamiltonian Lattice Formulations of Field Theories in an Expanding Universe,” Phys. Rev. D 32
1985
Earlier work this paper cites.
D. Z. Freedman, G. W. Gibbons and M. Schnabl, “Matrix cosmology,” AIP Conf. Proc. 743
1987
Earlier work this paper cites.
J.Hoppe, Quantum Theory of a Massless Relativistic Surface, MIT Ph.D. Thesis 1982, http://dspace.mit.edu/handle/1721.1/15717; B. de Wit, J. Hoppe and H. Nicolai, “On the Quantum Mechanics of Supermembranes,” Nucl. Phys. B 305
1988
Earlier work this paper cites.
R. H. Brandenberger and C. Vafa, “Superstrings In The Early Universe,” Nucl. Phys. B 316
1989
Earlier work this paper cites.
S. R. Das and A. Jevicki, “String Field Theory and Physical Interpretation of D = 1 D=1 Strings,” Mod. Phys. Lett. A 5
1990
Earlier work this paper cites.
N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, “A Large N reduced model as superstring,” Nucl. Phys. B 498
1997
Earlier work this paper cites.

Similar

T. Banks, W. Fischler, S. H. Shenker and L. Susskind, “M theory as a matrix model: A Conjecture,” Phys. Rev. D 55
1997
Cited alongside, same era.
R. Dijkgraaf, E. P. Verlinde and H. L. Verlinde, “Matrix string theory,” Nucl. Phys. B 500
1997
Cited alongside, same era.
H. Aoki, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, “Space-time structures from IIB matrix model,” Prog. Theor. Phys. 99
1998
Cited alongside, same era.
T. Hotta, J. Nishimura and A. Tsuchiya, “Dynamical aspects of large N reduced models,” Nucl. Phys. B 545
1999
Cited alongside, same era.
L. Smolin, “M theory as a matrix extension of Chern-Simons theory,” Nucl. Phys. B 591
Original
2000
Cited alongside, same era.

Then

R. H. Brandenberger, “String Gas Cosmology,” String Cosmology, J.Erdmenger (Editor). Wiley, 2009. p.193-230 [arXiv:0808.0746 [hep-th]]
Original
2009
Later among the works it cites.
P. Agrawal, S. Gukov, G. Obied and C. Vafa, “Topological Gravity as the Early Phase of Our Universe,” arXiv:2009.10077 [hep-th]
Original
2009
Later among the works it cites.
W. Siegel, “Two vierbein formalism for string inspired axionic gravity,” Phys. Rev. D 47
Original
2009
Later among the works it cites.
S. W. Kim, J. Nishimura and A. Tsuchiya, “Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions,” Phys. Rev. Lett. 108
Original
2012
Later among the works it cites.
S. W. Kim, J. Nishimura and A. Tsuchiya, “Late time behaviors of the expanding universe in the IIB matrix model,” JHEP 10

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

D. E. Berenstein, J. M. Maldacena and H. S. Nastase, “Strings in flat space and pp waves from N=4 superYang-Mills,” JHEP 04

2001

Cited alongside, same era.

J. Nishimura and G. Vernizzi, “Spontaneous breakdown of Lorentz invariance in IIB matrix model,” JHEP 0004

2002

Cited alongside, same era.

J. Nishimura, “New perspectives on the emergence of (3+1)D expanding space-time in the Lorentzian type IIB matrix model,” PoS CORFU 2019

Original

2006

Cited alongside, same era.

A. Nayeri, R. H. Brandenberger and C. Vafa, “Producing a scale-invariant spectrum of perturbations in a Hagedorn phase of string cosmology,” Phys. Rev. Lett. 97

2006

Cited alongside, same era.

H. Bernardo, R. Brandenberger and G. Franzmann, “String cosmology backgrounds from classical string geometry,” Phys. Rev. D 103

Original

2007

Cited alongside, same era.

B. Craps, S. Sethi and E. P. Verlinde, “A Matrix big bang,” JHEP 10

Original

2008

Cited alongside, same era.

J. Cotler and A. Strominger, “The Universe as a Quantum Encoder,” [arXiv:2201.11658 [hep-th]]

Original