Evolution of sub-spaces at high and low energies

The evolution of sub-spaces in the framework of gravity with higher derivatives is studied. Numerical solutions to exact differential equations are found. It is shown that the initial conditions play crucial role in the space dynamic. Appropriate metrics describing an expanding and a stationary sub-space shed light on the well-known question: why our 3-dim space is large but an extra space is small and stable (if exists)? It is assumed that the values of parameters at high energies strongly depend on uncontrolled quantum corrections and, hence, are not equal to their values at low energies. Therefore, there is no way to trace solutions throughout the energy range, and we restrict ourselves to the sub-Planckian and the inflationary energies.

Note:

20 pages

energy: low
energy: high
derivative: high
correction: quantum
numerical calculations
differential equations
boundary condition
gravitation
stability
inflation

References(42)

Figures(6)

[1]

Quantum cosmology and higher order Lagrangian theories

Henk van Elst
(
- Queen Mary, U. of London
)
,
James E. Lidsey
(
- Fermilab
)
,
Reza K. Tavakol
(
- Queen Mary, U. of London
)

- Class.Quant.Grav. 11 (1994) 2483-2498
•
e-Print:
- gr-qc/9404044
•
DOI:
- 10.1088/0264-9381/11/10/008

[2]

Quantum creation of a universe with $\Omega \neq 1$ : Singular and nonsingular instantons

- Phys.Rev.D 58 (1998) 083503
•
e-Print:
- gr-qc/9803068
•
DOI:
- 10.1103/PhysRevD.58.083503

[3]

INTRODUCTORY LECTURES ON QUANTUM COSMOLOGY

Jonathan J. Halliwell
(
- MIT, LNS
)

•
e-Print:
- 0909.2566

[4]

Quantum creation of a universe with varying speed of light: Lambda-problem and instantons

e-Print:
- hep-th/0505034

[5]

Dynamics of Compactification in Einstein {Yang-Mills} Theories

Yu.A. Kubyshin
(
- Lebedev Inst. and
- Moscow State U.
)
,
V.A. Rubakov
(
- Lebedev Inst. and
- Moscow State U.
)
,
I.I. Tkachev
(
- Lebedev Inst. and
- Moscow State U.
)

- Int.J.Mod.Phys.A 4 (1989) 1409-1425
•
DOI:
- 10.1142/S0217751X89000595

[6]

Spontaneous creation of inflationary universes and the cosmic landscape

Hassan Firouzjahi
(
- Cornell U., LEPP
)
,
Saswat Sarangi
(
- Cornell U., LEPP
)
,
S.H.Henry Tye
(
- Cornell U., LEPP
)

- JHEP 09 (2004) 060
•
e-Print:
- hep-th/0406107
•
DOI:
- 10.1088/1126-6708/2004/09/060

[7]

Kaluza-Klein multidimensional models with Ricci-flat internal spaces: the absence of the KK particles

- Adv.High Energy Phys. 2013 (2013) 106135
•
e-Print:
- 1311.0220
•
DOI:
- 10.1155/2013/106135

[8]

The Fine-tuning Problems of Particle Physics and Anthropic Mechanisms (Cambridge University Press, Cambridge,), p. 231

J.F. Donoghue

[9]

Dynamically avoiding fine-tuning the cosmological constant: The 'Relaxed Universe'

Florian Bauer
(
- Barcelona U., ECM and
- ICC, Barcelona U.
)
,
Joan Sola
(
- Barcelona U., ECM and
- ICC, Barcelona U.
)
,
Hrvoje Stefancic
(
- Boskovic Inst., Zagreb
)

- JCAP 12 (2010) 029
•
e-Print:
- 1006.3944
•
DOI:
- 10.1088/1475-7516/2010/12/029

[10]

The Hierarchy problem and new dimensions at a millimeter

Nima Arkani-Hamed
(
- SLAC
)
,
Savas Dimopoulos
(
- Stanford U., Phys. Dept.
)
,
G.R. Dvali
(
- ICTP, Trieste
)

- Phys.Lett.B 429 (1998) 263-272
•
e-Print:
- hep-ph/9803315
•
DOI:
- 10.1016/S0370-2693(98)00466-3

[11]

Grand unification at intermediate mass scales through extra dimensions

Keith R. Dienes
(
- CERN
)
,
Emilian Dudas
(
- CERN and
- Orsay, LPT
)
,
Tony Gherghetta
(
- CERN
)

- Nucl.Phys.B 537 (1999) 47-108
•
e-Print:
- hep-ph/9806292
•
DOI:
- 10.1016/S0550-3213(98)00669-5

[12]

Neutrino masses from large extra dimensions

Nima Arkani-Hamed
(
- SLAC
)
,
Savas Dimopoulos
(
- Stanford U., Phys. Dept.
)
,
G.R. Dvali
(
- New York U. and
- ICTP, Trieste
)
,
John March-Russell
(
- CERN
)

- Phys.Rev.D 65 (2001) 024032
•
e-Print:
- hep-ph/9811448
•
DOI:
- 10.1103/PhysRevD.65.024032

[13]

Large extra dimensions and cosmological problems

Glenn D. Starkman
(
- Case Western Reserve U.
)
,
Dejan Stojkovic
(
- Case Western Reserve U.
)
,
Mark Trodden
(
- Syracuse U.
)

- Phys.Rev.D 63 (2001) 103511
•
e-Print:
- hep-th/0012226
•
DOI:
- 10.1103/PhysRevD.63.103511

[14]

Nonlinear multidimensional cosmological models with form fields: Stabilization of extra dimensions and the cosmological constant problem

U. Gunther
(
- Potsdam U., Inst. of Math. and
- Potsdam, Max Planck Inst.
)
,
P. Moniz
(
- Beira Interior U., Covilha
)
,
A. Zhuk
(
- Odessa State U. and
- Potsdam, Max Planck Inst.
)

- Phys.Rev.D 68 (2003) 044010
•
e-Print:
- hep-th/0303023
•
DOI:
- 10.1103/PhysRevD.68.044010

[15]

Inhomogeneous extra space as a tool for the top-down approach

Sergey G. Rubin
(
- Moscow Phys. Eng. Inst. and
- Kazan State U.
)

- Adv.High Energy Phys. 2018 (2018) 2767410
•
e-Print:
- 1609.07361
•
DOI:
- 10.1155/2018/2767410

[16]

Dark Energy and Stabilization of Extra Dimensions

Brian R. Greene
(
- ISCAP, New York and
- Columbia U., Dept. Math.
)
,
Janna Levin
(
- ISCAP, New York and
- Barnard Coll.
)

- JHEP 11 (2007) 096
•
e-Print:
- 0707.1062
•
DOI:
- 10.1088/1126-6708/2007/11/096

[17]

Classical stabilization of homogeneous extra dimensions

Sean M. Carroll
(
- Chicago U., EFI and
- Chicago U.
)
,
James Geddes
(
- Chicago U., EFI and
- Chicago U.
)
,
Mark B. Hoffman
(
- Chicago U., EFI and
- Chicago U.
)
,
Robert M. Wald
(
- Chicago U., EFI and
- Chicago U.
)

- Phys.Rev.D 66 (2002) 024036
•
e-Print:
- hep-th/0110149
•
DOI:
- 10.1103/PhysRevD.66.024036

[18]

Radion stabilization in compact hyperbolic extra dimensions

Salah Nasri
(
- Syracuse U.
)
,
Pedro J. Silva
(
- Syracuse U.
)
,
Glenn D. Starkman
(
- Case Western Reserve U.
)
,
Mark Trodden
(
- Syracuse U.
)

- Phys.Rev.D 66 (2002) 045029
•
e-Print:
- hep-th/0201063
•
DOI:
- 10.1103/PhysRevD.66.045029

[19]

Black Holes, Cosmology and Extra Dimensions

K.A. Bronnikov
,
S.G. Rubin

[20]

Inflation from $(R+\gamma R^n-2\Lambda)$ Gravity in Higher Dimensions

Sergei V. Ketov
(
- Tokyo Metropolitan U. and
- Tokyo U., IPMU and
- Tomsk Polytechnic U.
)
,
Hiroshi Nakada
(
- Tokyo Metropolitan U.
)

- Phys.Rev.D 95 (2017) 10, 103507
•
e-Print:
- 1701.08239
•
DOI:
- 10.1103/PhysRevD.95.103507

[21]

Dynamical Compactification and Inflation in Einstein-Yang-Mills Theory with Higher Derivative Coupling

- Phys.Rev.D 80 (2009) 066004
•
e-Print:
- 0906.4493
•
DOI:
- 10.1103/PhysRevD.80.066004

[22]

Calculation of Gauge Couplings and Compact Circumferences from Selfconsistent Dimensional Reduction

Philip Candelas
(
- Texas U.
)
,
Steven Weinberg
(
- Texas U.
)

- Nucl.Phys.B 237 (1984) 397,
- IN *APPELQUIST, T. (ED.) ET AL.: MODERN KALUZA-KLEIN THEORIES*, 375-419. (NUCL. PHYS. B237 (1984) 397) AND TEXAS UNIV. AUSTIN - UTTG-83-06 (83,REC.JUN.) 31 P. TEXAS UNIV. AUSTIN - UTTG-83-06A (83,REC.JUL.) 6 P. (SEE BOOK INDEX)
•
DOI:
- 10.1016/0550-3213(84)90001-4

[23]

On cosmology in nonlinear multidimensional gravity with multiple factor spaces

- Grav.Cosmol. 24 (2018) 2, 154-160
•
e-Print:
- 1803.04904
•
DOI:
- 10.1134/S0202289318020044

[24]

Dynamics of Dimensional Reduction

Peter G.O. Freund
(
- Chicago U., EFI
)
,
Mark A. Rubin
(
- Chicago U., EFI
)

- Phys.Lett.B 97 (1980) 233-235,
- IN *APPELQUIST, T. (ED.) ET AL.: MODERN KALUZA-KLEIN THEORIES*, 210-212. (Phys. Lett. B97 (1980) 233-235) AND CHICAGO UNIV. - EFI 80-035 (80,REC.NOV.) 7 P. (SEE BOOK INDEX),
•
DOI:
- 10.1016/0370-2693(80)90590-0

[25]

Effective Action and Cosmological Evolution of Scale Factors in Higher Dimensional Curved Space-time

M. Yoshimura
(
- KEK, Tsukuba
)

- Phys.Rev.D 30 (1984) 344
•
DOI:
- 10.1103/PhysRevD.30.344

1-25 of 42
1
2
25 / page