Thick Brane Models In F(t) Gravity

Is our world a four-dimensional spacetime?This problem has been plagued by physicists for a long time.With the introduction of various extra-dimensional theories and successfully explained various problems in physics,including the cosmological constant problem,the gauge hierarchy problem,the third-generation fermion problem,etc.,the extra-dimensional theory has been extensively studied.On the other hand,despite the great success of general relativity,there are still many signs that it is not the ultimate theory of gravity.Including that it is not consistent with quantum theory,without introducing dark matter and dark energy it can not explain the dynamics of galaxy and the accelerated expansion of the universe,etc.So,modified gravity is an important approach in modern physics.In this thesis,we mainly study the problem of the thick brane world models in f(T)gravity.In the first chapter,we introduce the research background of extra dimensions and the motivations of various extra dimension models.On the other hand,we show the basic knowledge of general relativity,and point out some problems that general relativity can not solve,as well as the motivation to modify gravity.The basic dynamic field in general relativity is the metric,and the torsion of spacetime is considered to be zero.But apart from simplicity,there is no reason to make this assumption.In teleparallel gravity and the generalized f(T)gravity,the basic dynamic quantity is the tetrad,and the spacetime is flat,that is,the curvature is zero but the torsion is not zero.In Chapter 2,we introduce several extra-dimensional theory models.We show the background of each extra dimension model and their respective defects.Among them,the thick brane model,as a combination of the domain wall model and the RS-2 model,has been extensively studied.In the thick brane model,since the matter fields are in five-dimensional spacetime,the localization of matter on the four-dimensional brane is an important issue.Next,in Chapter 3,we briefly introduce the basic knowledge of teleparallel gravity.The basic dynamic field in teleparallel gravity is the tetrad embedded in the tangent space at each spacetime point.The resulting Weitzenb?k manifold has only torsion but zero curvature.However,because the action of teleparallel gravity differs from the Einstein Hilbert action in general relativity only by one boundary term,the field equations of motion are equivalent.But f(T)gravity generalized by teleparallel gravity and f(R)gravity generalized by general relativity are no longer equivalent.In Chapter 4,we mainly introduce how to construct a thick brane model in f(T)gravity.We find that thick brane models can be obtained for both canonical scalar fields and non-canonical scalar fields.In both cases,the thick brane will split due to the effect of torsion.But for the thick brane generated by the non-canonical scalar field,when f(T)is taken as the polynomial form of T,the thick brane will split more obviously.And the number of sub-branes correspond to the number of terms in the polynomial.That is,the thick brane generated by the non-canonical scalar field will produce a richer internal structure.In Chapter 5,we introduce the localization of various fields in the f(T)thick brane model.Since the localization of the scalar field and the vector field only depends on the form of the warp factor and not on the gravity theory,they are the same as the results in general relativity.That is,for a free massless scalar field in five-dimensional spacetime,as long as gravity can be localized in general relativity,it can also be localized on the brane.For a free massless vector field in five-dimensional spacetime,because the zero-mode integral does not converge,it cannot be localized on the brane,but the vector zero-mode can also be localized on the brane after introducing some other localization mechanisms.The localization of fermions and gravity depends on the gravity theory,so we just investigate the localization problem in f(T)gravity.For the fermions in the five-dimensional spacetime,the zero mode can be localized on the brane under the condition of Yukawa coupling with the background scalar field.For the more important gravitational field,we analyze the tensor fluctuation of the tetrad field and find that the thick branes generated by the canonical scalar field and the non-canonical scalar field are stable under the linear tensor fluctuation,that is,there is no m~2<0 tachyon states are generated,and the zero mode of graviton can also be localized on the brane.In addition,corresponding to the splitting of the brane,the zero mode of graviton will also split.In Chapter 6,we apply the mimetic method to f(T)gravity and analyze how to construct the thick brane in this situation.Unlike the thick brane model generated by the matter field,in the mimetic f(T)gravity,since the scalar field in this case is a degree of freedom isolated from the metric,it is a geometric quantity.We found that the thick brane model generated by geometry can not only generate thick brane but also get richer inner brane structure.Based on this,we studied the gravitational resonant state and found that a lot of gravitational resonant states will be generated at this time.In the end,we give the conclusion and discussion in Chapter 7.