Gravitational Potential And Shortcut In Braneworld Theories

Higher-dimensional theories usually allow a spacetime with its dimension larger than four.In the theories,the introduction of extra spatial dimensions will result in the existence of particles beyond the Standard Model of particle physics.Moreover,the gravity in the theories could deviate from the general relativity either in the cosmologi-cal scale or under the submillimeter scale.Therefore,the existence of extra dimensions is usually regarded as a new physics beyond the Standard Model.In addition,since the first proposal of the higher-dimensional theory at the beginning of 20th century,grad-ually in-depth researches on extra dimensions showed that higher-dimensional theories have the opportunity to unifying gravitational interaction with the other fundamental in-teractions.Obviously,investigating whether extra dimensions exist could help to build a new viewpoint of the spacetime.On the other hand,it also helps us to understand our real Universe.It then becomes so important to find the clues of extra dimensions in our Universe.In higher-dimensional theories,particles beyond the Standard Model can participate in the interactions in our Universe.Based on this,people expect to find the contributions of these particles to the high-energy particle collision experiments and the Cavendish torsion balance experiments.Since the first detection of the gravitational wave（GW）event in 2016,we are now in a new era of gravitational wave astronomy,and the GW observation is becoming a new approach to studying extra dimensions.In this thesis,we will focus on the braneworld theory and investigate the theory through the modified Newtonian potential and the shortcut.In the first chapter,we will briefly review the history of extra dimensions from the perspective of the introduction,development,and tests of extra dimensions.Therein,we will first introduce the early discussions on the nature of the spacetime by Chinese and foreign philosophers.Then,we will review the attempts to unify the four fundamental interactions with extra dimensions.After that,we will show the thoughts to solve the hierarchy problem and the corresponding models,which are proposed by physicists from the early 1990s to around 2000.Note that we will give a further study on the construction of those models and show their characteristics in the next chapter.At the end of this chapter,we will finally give a brief introduction to the traditional experiments on testing extra dimensions.We will also show the idea of using the GW as a probe of extra dimensions.All these tests are based on the new physics results from the extra dimensions.In the second chapter,we will introduce the Kaluza-Klein theory,domain wall,Arkani-Hamed-Dimopoulos-Dvali model,Randall-Sundrum-1（RS-1）model,and RS-2 model in order.Giving the theoretical construction of these theories,we will further study the development of the physicists’understanding on the relation between extra di-mensions and the four-dimensional Universe from the beginning of 1990s to nowadays.Besides,we will also refer to how the braneworld theory solves the hierarchy problem.In the third chapter,we will investigate the structure of the spacetime in a five-dimensional extended Eddington-inspired Born-Infeld（Ei BI）theory,the socalled f（?）theory.Therein,the traditional approach we employ to test extra dimensions is based on the fact that extra dimensions could affect the Newtonian potential on the Universe which is one of the clues.In this chapter,we will first give a brief review on how extra spatial dimensions affect the interaction on the brane.For simplicity,we will consider that the interaction is mediated by a scalar field in the higher-dimensional spacetime.We then briefly introduce the idea and characteristic of the four-dimensional Ei BI theory and its extension,the f（?）theory.We should note that it is meaningful to investigate the structure of the higher-dimensional spacetime under the description of the Ei BI the-ory and its extension,since these theories can well avoid the singular problems,such as the big bang singularity and black hole singularity.Taking advantage of this,we will further construct f（?）thick branes in the five-dimensional spacetime and anal-yse their stability.We will also give the corrected Newtonian potential in the model.By comparing our results with the torsion balance experiment under the submillimeter scale,we will finally constrain the structure of extra dimensions in our model.Extra dimensions allow the existence of the shortcut of GWs,which could result in the time delay in the observations.This is one of the clues of extra dimensions.Based on this,we will investigate scale of extra dimensions in the fourth chapter.In this chapter,we first briefly review the conception of the shortcut and the corresponding scenario.We then try to embed our four-dimensional Universe in the five-dimensional de-Sitter（d S）spacetime.Further,we will derive the gravitational horizon radius and photon horizon radius on the brane.With the joint GW observations of the event GW170817and its electromagnetic counterpart GRB 170817A,we will finally constrain the d S₅radius.Comparing with the case in the five-dimensional Anti de-Sitter（Ad S）spacetime,our result indicates that the five-dimensional d S spacetime would have an extremely different structure.In the fifth chapter,we will still investigate the structure of extra dimensions through the shortcut.Unlike the case in the last chapter,we will concern the contribution from the sixth dimension.Moreover,we will give a constraint on the six-dimensional Ad S radius with the time delay reported by the LIGO/Virgo detectors.According to our expectation to the source redshift of the target event measured in the future GW obser-vations,we also generalize the previous theoretical analysis.With the goal of DECIGO and BBO,a much stronger constraint on the Ad S₆radius will be found.In the last chapter,we will give a short summary and an expectation to our future researches.