本論文包含兩部分。在第一部分研究真空泡泡動力學和高階修正的接面條件，並且顯示在四階重力理論很難得到接面條件的運動方程。接著研究了五維真真空泡泡在Einstein-Gauss-Bonnet 理論的動力學，找到了新的束縛解。在第二部分回顧了膜暴漲模型和D3-DBI膜的暴漲模型之後，提出D4-DBI膜暴漲模型。接著研究其吸引子行為和計算宇宙背景輻射的功率譜。

This thesis consists two parts. In part I we study the
dynamics of vacuum bubble and junction condition with higher order correction and show that it is difficult to obtain the equation of motion in the fourth order theory of gravity. Then we study the five dimensional true vacuum bubble in Einstein-Gauss-Bonnet's theory of gravity. We find a new trapped solution. In part II we review brane inflation model and D3 brane DBI inflation models. We propose a D4 DBI inflation model. We study its attractor behavior and calculate the spectral indices and tensor-to-scalar ratio.

S.~K.~Blau, E.~I.~Guendelman and A.~H.~Guth,
``The Dynamics of False Vacuum Bubbles,''
Phys.\ Rev.\ D {\bf 35} (1987) 1747.

L.~Susskind,
``The anthropic landscape of string theory,''
arXiv:hep-th/0302219.

B.~Freivogel and L.~Susskind,
``A Framework for the Landscape,''
Phys.\ Rev.\ D {\bf 70} (2004) 126007
[arXiv:hep-th/0408133].

E.~Farhi and A.~H.~Guth,
``AN OBSTACLE TO CREATING A UNIVERSE IN THE LABORATORY,''
Phys.\ Lett.\ B {\bf 183} (1987) 149.

E.~Farhi, A.~H.~Guth and J.~Guven,
``IS IT POSSIBLE TO CREATE A UNIVERSE IN THE LABORATORY BY QUANTUM TUNNELING?,''
Nucl.\ Phys.\ B {\bf 339} (1990) 417.

W.~Fischler, D.~Morgan and J.~Polchinski,
``QUANTUM NUCLEATION OF FALSE VACUUM BUBBLES,''
Phys.\ Rev.\ D {\bf 41} (1990) 2638.

W.~Fischler, D.~Morgan and J.~Polchinski,
``QUANTIZATION OF FALSE VACUUM BUBBLES: A HAMILTONIAN TREATMENT OF GRAVITATIONAL TUNNELING,''
Phys.\ Rev.\ D {\bf 42} (1990) 4042.

A.~H.~Guth,
``The Inflationary Universe: A Possible Solution To The Horizon And Flatness Problems,''
Phys.\ Rev.\ D {\bf 23} (1981) 347.

S.~Kachru, R.~Kallosh, A.~Linde and S.~P.~Trivedi,
``De Sitter vacua in string theory,''
Phys.\ Rev.\ D {\bf 68} (2003) 046005
[arXiv:hep-th/0301240].

R.~Bousso and J.~Polchinski,
``Quantization of four-form fluxes and dynamical neutralization of the cosmological constant,''
JHEP {\bf 0006} (2000) 006
[arXiv:hep-th/0004134].

S.~R.~Coleman,
``The Fate Of The False Vacuum. 1. Semiclassical Theory,''
Phys.\ Rev.\ D {\bf 15} (1977) 2929
[Erratum-ibid.\ D {\bf 16} (1977) 1248].

C.~G.~.~Callan and S.~R.~Coleman,
``The Fate Of The False Vacuum. 2. First Quantum Corrections,''
Phys.\ Rev.\ D {\bf 16} (1977) 1762.

S.~R.~Coleman and F.~De Luccia,
``Gravitational Effects On And Of Vacuum Decay,''
Phys.\ Rev.\ D {\bf 21} (1980) 3305.

W.~Israel,
``Singular hypersurfaces and thin shells in general relativity,''
Nuovo Cim.\ B {\bf 44S10} (1966) 1
[Erratum-ibid.\ B {\bf 48} (1967\ NUCIA,B44,1.1966) 463].

N.~Deruelle, M.~Sasaki and Y.~Sendouda,
``Junction Conditions in f(R) Theories of Gravity,''
Prog.\ Theor.\ Phys.\ {\bf 119} (2008) 237
[arXiv:0711.1150 [gr-qc]].

A.~Balcerzak and M.~P.~Dabrowski,
``Generalized Israel Junction Conditions for a Fourth-Order Brane World,''
Phys.\ Rev.\ D {\bf 77} (2008) 023524
[arXiv:0710.3670 [hep-th]].

S.~C.~Davis,
``Generalised Israel junction conditions for a Gauss-Bonnet brane world,''
Phys.\ Rev.\ D {\bf 67} (2003) 024030
[arXiv:hep-th/0208205].

D.~G.~Boulware and S.~Deser,
``String Generated Gravity Models,''
Phys.\ Rev.\ Lett.\ {\bf 55} (1985) 2656.

I.~P.~Neupane,
``Black hole entropy in string-generated gravity models,''
Phys.\ Rev.\ D {\bf 67} (2003) 061501
[arXiv:hep-th/0212092].

M.~G.~Richarte and C.~Simeone,
``Thin-shell wormholes supported by ordinary matter in
Einstein--Gauss--Bonnet gravity,''
Phys.\ Rev.\ D {\bf 76} (2007) 087502
[arXiv:0710.2041 [gr-qc]].

A.~D.~Linde,
``Inflation with variable Omega,''
Phys.\ Lett.\ B {\bf 351} (1995) 99
[arXiv:hep-th/9503097].

A.~D.~Linde and A.~Mezhlumian,
``Inflation with Omega not = 1,''
Phys.\ Rev.\ D {\bf 52} (1995) 6789
[arXiv:astro-ph/9506017].

E.~Komatsu {\it et al.} [WMAP Collaboration],
``Five-Year Wilkinson Microwave Anisotropy Probe (WMAP\altaffilmark 1 )
Observations:Cosmological Interpretation,''
Astrophys.\ J.\ Suppl.\ {\bf 180} (2009) 330
[arXiv:0803.0547 [astro-ph]].

G.~R.~Dvali and S.~H.~H.~Tye,
``Brane inflation,''
Phys.\ Lett.\ B {\bf 450} (1999) 72
[arXiv:hep-ph/9812483].

S.~Kachru, R.~Kallosh, A.~Linde, J.~M.~Maldacena, L.~P.~McAllister and S.~P.~Trivedi,
``Towards inflation in string theory,''
JCAP {\bf 0310} (2003) 013
[arXiv:hep-th/0308055].

E.~Silverstein and D.~Tong,
``Scalar Speed Limits and Cosmology: Acceleration from D-cceleration,''
Phys.\ Rev.\ D {\bf 70} (2004) 103505
[arXiv:hep-th/0310221].

X.~H.~Meng and P.~Wang,
``Cosmological dynamics of D-cceleration,''
Class.\ Quant.\ Grav.\ {\bf 21} (2004) L101
[arXiv:astro-ph/0406476].

E.~Witten,
``Anti-de Sitter space, thermal phase transition, and confinement in gauge theories,''
Adv.\ Theor.\ Math.\ Phys.\ {\bf 2} (1998) 505
[arXiv:hep-th/9803131].

X.~Chen, M.~x.~Huang, S.~Kachru and G.~Shiu,
``Observational signatures and non-Gaussianities of general single field inflation,''
JCAP {\bf 0701} (2007) 002
[arXiv:hep-th/0605045].

L.~Kofman and S.~Mukohyama,
``Rapid roll Inflation with Conformal Coupling,''
Phys.\ Rev.\ D {\bf 77} (2008) 043519
[arXiv:0709.1952 [hep-th]].

B.~Underwood,
``Brane Inflation is Attractive,''
Phys.\ Rev.\ D {\bf 78} (2008) 023509
[arXiv:0802.2117 [hep-th]].

M.~Alishahiha, E.~Silverstein and D.~Tong,
``DBI in the sky,''
Phys.\ Rev.\ D {\bf 70} (2004) 123505
[arXiv:hep-th/0404084].