Sup ernatural InationInation from Sup ersymmetry with No Very Small Parameters by Marin Soljacic SUBMITTED TO THE DEPARTMENT OF PHYSICS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF BACHELOR OF SCIENCE IN PHYSICS AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE c Marin Soljacic All rights reserved The author hereby grants to MIT p ermission to repro duce and to distribute publicly pap er and electronic copies of this thesis do cument in whole or in part Signature of Author DepartmentofPhysics May Certied by Lisa J Randall Asso ciate Professor of Physics Thesis Sup ervisor Approved by June L Matthews Professor of Physics DepartmentofPhysics Undergraduate Thesis Co ordinator Sup ernatural InationInation from Sup ersymmetry with No Very Small Parameters by Marin Soljacic May Submitted to the Department of Physics on May in Partial Fulllment of the Requirements for the Degree of Bachelor of Science in Physics Abstract Most mo dels of ination incorp orate small inexplainable parame ters that do not exist normally in particle physics theories We de signed a mo del that avoids this it implements ination using only the parameters that already exist in the particle physics theories We succeeded this by using two coupled quantum elds instead of using only one as it is usually done Using more elds than just one makes the mo del more complicated and the analysis is harder The prop er analysis of the predictions of our mo del would therefore b e purely numerical However as we show the approximate analytical expressions we obtain are in an excellent agreement with the exact numerical solutions Therefore weusethem to analyze and calculate its predictions Thesis Sup ervisor Lisa J Randall Title Asso ciate Professor of Physics Contents BigBang Justication of BigBang mo del The problems of the old BigBang mo del The problem of the domain walls The monop ole problem The baryon asymmetry The horizon problem The atness of space Other problems and the solution Ination How do es ination do it Smallscale inhomogeneity Existing mo dels of ination and our goal Our mo dels Where do our mo dels come from Density p erturbations Mathematical analysis of the number of efolds Stage Stage Stage Total number of efolds Computer conrmation of the number of efolds Stage Stage Stage The spike in the density p erturbations Creating the plots of masses Description of the program Conclusion Acknowledgements List of Figures The numerical simulation for Stage The example wecho ose is for M mo del We pick some typical values of the parame ters M GeV andM Dierent parameters or mo del dier only quantitatively The numerical simulation for the development of and the envelop e of in Stage All the parameters are as for Figure This particular example is for the mo del with l The numerical simulation for the development of E in Stage corresp onding to the development of and shown in e Figure The numerical simulation for the development of in Stage All the parameters are as for Figure This is just a continuation of Stage here The numerical simulation for the development of E in Stage corresp onding to the development of shown in Figure This Figure presents the result of optimizing our M mo del with M at the Planck scale given the constraints of the den sity p erturbations and the constraining spike in the density p erturbations This Figure presents the result of optimizing our M mo del with M at the GUT scale given the constraints of the den sity p erturbations and the constraining spike in the density p erturbations This Figure presents the result of optimizing our M mo del with M at the intermediate scale given the constraints of the density p erturbations and the constraining spike in the densit y p erturbations This Figure presents the result of optimizing our mo del with the Yukawa coupling with given the constraints of the density p erturbations and the constraining spike in the density p erturbations Note Fol lowing a long tradition in Cosmology we set al l the constants k c and h to throughout this paper They are easy B to reintroduce later on the basis of dimensional analysis For a general review of the subject of inationary cosmology please refer to BigBang Starting in the b eginning of this centurymanycharacteristics of the observ able universe lead scientists to a conclusion that universe was created in a big explosion some billion years ago Therefore all the energy of the uni verse was once concentrated in a v ery small volume of enormous temp erature and energy density This is the essence of the socalled the Hot BigBang mo del of the creation of the universe An imp ortant thing to realize ab out the idea that the whole universe evolved from a small volume is that we are not talking ab out a purely three dimensional explosion like the explosion of a b omb A feature of an explosion which happ ens in a three dimensional space is that it has a well dened origin at which the explosion happ ened In contrast the explosion of the universe do es not have such a three dimensional origin Instead the explosion happ ens in what we can picture to be four dimen sions The universe is like a three dimensional surface of a four dimensional ballo on that is b eing blown As the volume of the ballo on increases anytwo points on its surface moveaw ay from each other the p oints that are further away move apart faster In reality this picture is slightly more complicated since we are not sure yet whether the universe is really like a ballo on or like a four dimensional hyp erb ola nevertheless the essence of the description is the same Justication of BigBang mo del In it was discovered that all observable stars are moving away from the solar system This fact was detected by measuring the radiation sp ectrum of the stars and observing that the further away a star was from us the shift its sp ectrum had The red doppler shift meant of bigger red doppler course that the star was moving away from us Of the galaxy sp ectra measured by the present day a red shift was observed in all except a very few closest galaxies This universal expansion was in a direct accord with the BigBang mo del If we are to b elieve the Hot BigBang mo del we should exp ect that at the earliest stages of the development of the universe all the particle sp ecies are in a thermal equilibrium with each other that is the whole universe was in a thermal equilibrium To solve for the energy in each particle sp ecies and the energy distribution of particles of each particle sp ecies we can use the black body mo del but with many more degrees of freedom than the black body we usually talk ab out each particle sp ecies represents a degree of freedom in which the energy can b e stored Since all particles are relativistic at temp eratures this high the energy distribution of particles in each particle sp ecies will b e the same as for a black body However as the universe adiabatically expands it co ols down the density of each sp ecies decreases and the collisions b etween the particles needed to keep the universe in a thermal equilibrium b ecome rare Dep ending on the scattering cross section of a particular sp ecies one after the other particle sp ecies decouple from the thermal equilibrium Nevertheless at the moment of the decoupling each sp ecies still has the energy distribution which follows from the black body mo del of the temp erature at the time of the decou pling After the decoupling this energy redshifts due to the expansion of the universe It turns out that the redshift do es not destroy the shap e of the energy distribution the only thing it do es is to decrease the eective tem p erature the distribution is at Consequently we exp ect to observe some background photon radiation still present from the time of the creation of the universe And indeed a cosmic microwave background radiation CMBR with the energy distribution of a black body at temp erature of K is readily observed There is many other evidence that supp orts the Hot BigBang mo del dif among the most imp ortant is lightelement abundances which are very cult to explain without employing the Hot BigBang mo del Consequently the Hot BigBang mo del is universally accepted to day and it is used to make predictions ab out the state of the universe all the way to sec after the bang The problems of the old BigBang mo del In the recent decades scientists b egan to realize signicant disadvantages of the old Big Bang mo del In fact Collins and Hawking showed that the set of initial data needed for the universe to evolveintoauniverse similar to ours is of measure zero I summarize in this section many of the problems of the old the BigBang mo del For a comprehensive discussion please see The problem of the domain walls In the b eginning the universe is at a very high temp erature Consequently the term