Master's Thesis in Theoretical Physics - Universiteit Utrecht

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AbstractIn this thesis we consider the nonminimal inflationary scenario, where the scalar inflatonfield is coupled to the Ricci scalar R through a nonminimal coupling ξ. We show that in thelimit of strong negative coupling chaotic inflation with a quartic potential is successful inthis model. Moreover, the quartic self-coupling λ must be extraordinary small in the minimalmodel in order to agree with the observed spectrum of density perturbations, but inthe nonminimally coupled model the constraint on λ can to a large extent be relaxed if ξ issufficiently large.This allows the Higgs boson to be the inflaton and excludes the need to introduce any exoticnew particles to explain inflation. We show that we can make a transformation to theEinstein frame where the Higgs boson is not coupled to gravity, but where the potentialis modified. The potential reduces to the familiar Higgs potential for small values of theHiggs field, but becomes asymptotically flat for large values of the field, making sure thatslow-roll inflation is successful. We introduce the two-Higgs doublet model and show thatinflation also works in this model. The extra phase degree of freedom in this model is asource for CP violation and a possible source for baryogenesis.Special attention is made to the quantization of the nonminimally coupled inflaton in aFLRW universe. In an expanding universe the vacuum choice is not unique and thereforethe notion of a particle is not well defined. In quasi de Sitter space there is natural vacuumstate, called the Bunch-Davies vacuum that corresponds to zero particles in the infinitepast. With the choice of this vacuum state the scalar propagator in quasi de Sitter spacecan be calculated.The Higgs boson interacts with the Standard Model fermions and therefore effects on thedynamics of fermions during inflation. It is shown that in the two-Higgs doublet model theadditional phase degree of freedom gives rise to an axial vector current for the fermionsthat violates CP and might be converted into a baryon asymmetry through sphaleron processes.The effect of the Higgs inflaton on the dynamics of massles fermions is derived bycalculating the one-loop fermion self-energy. It is shown that the Higgs boson effectivelygenerates a mass for the massless fermions that is proportional to the Hubble parameterH.v
Page 1: INFLATION AND BARYOGENESIS THROUGH
Page 7 and 8: ContentsAbstractv1 Introduction 12
Page 9 and 10: Chapter 1IntroductionCosmology is i
Page 11 and 12: Chapter 2Cosmology2.1 The Cosmologi
Page 13 and 14: Table 2.1: Scaling of the energy de
Page 15 and 16: andδR = δ(g µν R µν )= R µν
Page 17 and 18: Chapter 3Cosmological Inflation3.1
Page 19 and 20: If we consider the evolution of the
Page 21 and 22: solution to the homogeneity puzzle.
Page 23 and 24: In general, we can define the so-ca
Page 25 and 26: Figure 3.2: WMAP measurements of th
Page 27 and 28: Chapter 4Nonminimal inflationIn thi
Page 29 and 30: where G µν = R µν − 1 2 R g
Page 31 and 32: and the equation of motion for φ f
Page 33 and 34: 0.41200.310080Φt0.2N60400.1200.000
Page 35 and 36: 0.00010.00010.000080.00008Ht0.00006
Page 37 and 38: such that the kinetic term transfor
Page 39 and 40: We now consider a chaotic inflation
Page 41 and 42: ΛM P44Ξ 2VΧΛv 44VΧ00 v(a) Effe
Page 43 and 44: 4.4 The two-Higgs doublet modelIn t
Page 45 and 46: Implicitly we have defined two new
Page 47 and 48: such that the potential term is giv
Page 49 and 50: 0.50.80.40.6Φ1t0.30.20.1Φ2t0.40.2
Page 51: N12001000800600400200Ht0.000350.000
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great triumphs of inflation is that
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We now define the vacuum state that
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of motion (5.4). If we now substitu
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This allows us to write the field e
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We could also use the conformal FLR
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5.2.1 Adiabatic vacuumSuppose now w
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expanding universe with ɛ ≪ 1 th
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(5.61), we will find a nonzero prop
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Note that for D = 4, the factor Γ(
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When we now look at the scalar prop
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Note that this is a matrix equation
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The functions Φ (1)kand in 4 dimen
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small quantum fluctuation. We quant
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In section 6.2.1 we calculate the p
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Thus, the mass term of the fermion
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and satisfy therefore {γ µ ,γ ν
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to obtain the solution for the Feyn
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This term is precisely the derivati
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Table 6.1: Feynman rules for the sc
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Note that this term is proportional
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Σ ren (x + ; x − ′ ), which co
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( )We can now rewrite ln|µ 2 (∆
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is the retarded Green function of t
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of the two Higgs bosons can be coup
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drives inflation is called the infl
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asymptotic past.In the Bunch-Davies
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AcknowledgementsFirst of all I woul
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Appendix BGeneral Relativity in an
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B.3 General Relativity in a conform
Page 117 and 118:
Bibliography[1] A. D. Sakharov, Pis
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Master's Thesis in Theoretical Physics - Universiteit Utrecht

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