CP-violating inflation and its cosmological imprints
HHIP-2021-6/TH
CP-violating inflationand its cosmological imprints
Venus Keus ∗ , , Kimmo Tuominen † Department of Physics, University of Helsinki,P.O.Box 64, FI-00014 Helsinki, Finland Helsinki, Finland School of Physics and Astronomy, University of Southampton,Southampton, SO17 1BJ, United Kingdom
February 17, 2021
Abstract
We study models with several SU (2) scalar doublets where the inert doublets have anon-minimal coupling to gravity and play the role of the inflaton. We allow for thiscoupling to be complex, thereby introducing CP-violation - a necessary source of thebaryon asymmetry - in the Higgs–inflaton couplings. We investigate the inflationarydynamics of the model and discuss how the CP-violation of the model is imprinted on theparticle asymmetries after inflation in the hot big bang universe. ∗ E-mail: [email protected] † E-mail: [email protected] a r X i v : . [ h e p - ph ] F e b Introduction
The Standard Model (SM) of particle physics has been extensively tested and is in great agree-ment with experimental data, with its last missing particle – the Higgs boson – discovered byATLAS and CMS experiments at the CERN Large Hadron Collider (LHC) [1, 2]. Although theproperties of the observed scalar are in agreement with those of the SM-Higgs boson, it mayjust be one member of an extended scalar sector. Even though so far no signs of new physicshave been detected, it is well understood that the SM of particle physics is incomplete.Cosmological and astrophysical observations imply a large dark matter (DM) component inthe energy budget of the universe. Within the particle physics setting, this would be a particlewhich is stable on cosmological time scales, cold, non-baryonic, neutral and weakly interact-ing [3]. A particle with such characteristics does not exist in the SM. Another shortcoming ofthe SM is the lack of an explanation for the origin of the observed matter-antimatter asymmetryin the universe. One of the most promising baryogenesis scenarios is electroweak baryogene-sis (EWBG) [4], which produces the baryon excess during the electroweak phase transition(EWPT). Although the SM in principle contains all required ingredients for EWBG, it is un-able to explain the observed baryon excess due to its insufficient amount of CP-violation [5–7]and the lack of a first-order phase transition [8].Furthermore, in its current form, the SM fails to incorporate cosmic inflation in a satisfactorymanner. Inflation is a well-motivated theory predicting a period of exponential expansion in theearly universe which explains the generation of primordial density fluctuations seeding structureformation, flatness, homogeneity and isotropy of the universe [9–12]. The simplest models ofinflation in best agreement with observations are those driven by a scalar field, the inflaton ,with a standard kinetic term, slowly rolling down its smooth potential. At the end of inflation,the inflaton which naturally is assumed to have couplings with the SM- Higgs, dumps its energyinto the SM bath during the reheating process which populates the universe with SM particles.Scalars with non-minimal couplings to gravity are well-motivated inflaton candidates sincethey acquire fluctuations proportional to the inflationary scale and can drive the inflationprocess in the early universe, as in the Higgs-inflation model [13] where the SM-Higgs plays therole of the inflaton, and s -inflation models [14, 15] where the SM is extended by a singlet scalar.Extensive studies have been carried out in simple one singlet or one doublet scalar extensionsof the SM (see e.g. [16–19] and references therein). These models, however, by construction canonly partly provide a solution to the main drawbacks of the SM. For example, to incorporateboth CP-violation and DM into the model one has to go beyond simple scalar extensions of theSM [20]; see also e.g. [21–26].It is therefore theoretically appealing to have a more coherent setting where different moti-vations of beyond SM (BSM) frameworks could be simultaneously investigated. For example,in non-minimal Higgs frameworks with conserved discrete symmetries one can accommodatestabilised DM candidates. Moreover, the extended scalar potential could provide new sourcesof CP-violation and accommodate a strong first order phase transition [27]. Collider searchescan constrain these model frameworks by excluding or discovering the existence of the spectrumof new states.In this paper we introduce a model where a source of CP-violation originates from the1ouplings of the inflation. Through the process of reheating this is transmitted to an asymmetrywithin the SM and can furthermore seed the generation of an excess of matter over antimatterduring the evolution of the early universe. We describe these dynamics in the context ofa Z symmetric 3-Higgs Doublet Model (3HDM) with a CP-violating extended dark sector,which also provides a viable DM candidate, new sources of CP-violation and a strong first-order EWPT [20–25]. We study the inflationary dynamics of this set-up and outline its mainconsequences. In a future work we aim to continue to complement this study by more thoroughanalysis of EWBG and DM observables as well as a phenomenological analysis towards LHCsearches for new physics.The paper is organized as follows. In Section 2 we present the scalar potential and explorethe inflationary dynamics. In Section 3, we discuss the inflationary imprints of our novel CPviolating inflation phenomena. In Section 4, we discuss the inflaton decay into the SM particlesand possible consequences. In Section 5 we draw our conclusions and discuss the outlook forfurther work. A 3HDM scalar potential which is symmetric under a group G of phase rotations, can be writtenas the sum of two parts: V with terms symmetric under any phase rotation, and V G with termssymmetric under G [28, 29]. As a result, a Z -symmetric 3HDM can be written as : V = V + V Z , (1) V = − µ ( φ † φ ) − µ ( φ † φ ) − µ ( φ † φ )+ λ ( φ † φ ) + λ ( φ † φ ) + λ ( φ † φ ) + λ ( φ † φ )( φ † φ ) + λ ( φ † φ )( φ † φ ) + λ ( φ † φ )( φ † φ )+ λ (cid:48) ( φ † φ )( φ † φ ) + λ (cid:48) ( φ † φ )( φ † φ ) + λ (cid:48) ( φ † φ )( φ † φ ) ,V Z = − µ ( φ † φ ) + λ ( φ † φ ) + λ ( φ † φ ) + λ ( φ † φ ) + h.c. where the three Higgs doublets, φ , φ , φ , transform under the Z group, respectively, as g Z = diag ( − , − , +1) . (2)The parameters of the V part of the potential are real by construction. We allow for theparameters of V Z to be complex, using the following notation throughout the paper λ j = | λ j | e i θ j ( j = 1 , , , and µ = | µ | e i θ . (3)The composition of the doublets is as follows: φ = (cid:18) H +1 H + iA √ (cid:19) , φ = (cid:18) H +2 H + iA √ (cid:19) , φ = (cid:32) G + v + h + iG √ (cid:33) , (4) We ignore additional Z -symmetric terms that can be added to the potential, e.g., ( φ † φ )( φ † φ ) , ( φ † φ )( φ † φ ) , ( φ † φ )( φ † φ ) and ( φ † φ )( φ † φ ) , as they do not change the phenomenology of the model [23]. φ and φ are the Z -odd inert doublets, (cid:104) φ (cid:105) = (cid:104) φ (cid:105) = 0, and φ is the one Z -even active doublet, which at low energy attains a vacuum expectation value (VEV) (cid:104) φ (cid:105) = v/ √ (cid:54) = 0. The doublet φ plays the role of the SM Higgs doublet, with h being the SM Higgs bosonand G ± , G the would-be Goldstone bosons. Note that according to the Z generator in Eq. (2)the symmetry of the potential is respected by the vacuum (0 , , v/ √ ). In this paper we considerthe scenario where the components of the inert doublets act as inflation candidates and reheatthe universe at the end of inflation through their interactions with the SM-Higgs and gaugebosons. Note that at the scales relevant for inflation we can take the VEV of the active doubletto be zero, (cid:104) φ (cid:105) = 0.Furthermore, CP-violation is only introduced in the inert sector which is forbidden frommixing with the active sector by the conservation of the Z symmetry. As a result, the amountof CP-violation is not limited by electric dipole moments [21]. The lightest particle amongstthe CP-mixed neutral fields from the inert doublets is a viable DM candidate and stable due tothe unbroken Z symmetry. In this paper, we focus on the inflationary dynamics of the modeland shall not discuss DM implications of the model any further. We start by rewriting the doublets in the unitary gauge and ignore the charged scalars (sincethey do not affect the inflationary dynamics). φ = 1 √ (cid:32) h + iη (cid:33) , φ = 1 √ (cid:32) h + iη (cid:33) , φ = 1 √ (cid:32) h (cid:33) . (5)The action of the model in the Jordan frame is S J = (cid:90) d x √− g (cid:20) − M pl R − D µ φ † D µ φ − D µ φ † D µ φ − D µ φ † D µ φ (6) − V ( φ , φ , φ ) − (cid:18) ξ | φ | + ξ | φ | + ξ | φ | + ξ ( φ † φ ) + ξ ∗ ( φ † φ ) (cid:19) R (cid:21) , where R is the Ricci scalar, M pl is the reduced Planck mass and the parameters ξ i are di-mensionless couplings of the scalar doublets to gravity. Note that, in principle, ξ could be acomplex parameter for which we use the notation ξ = | ξ | e iθ . (7)In Eq. (6) the covariant derivative, D µ , contains couplings of the scalars with the gaugebosons. However, for the dynamics during the inflation, the covariant derivative is reducedto the normal derivative D µ → ∂ µ . The minus sign in the kinetic terms follows the metricconvention of ( − , + , + , +).Since we identify the two inert doublets with inflaton, we assume that the energy density of φ is sub-dominant during inflation. Therefore, the part of the potential relevant for inflationis V = − µ ( φ † φ ) − µ ( φ † φ ) + λ ( φ † φ ) + λ ( φ † φ ) (8)+ λ ( φ † φ )( φ † φ ) + λ (cid:48) ( φ † φ )( φ † φ ) − µ ( φ † φ ) + λ ( φ † φ ) + h.c. η . Such atransformation is equivalent to taking the η → S E = (cid:90) d x (cid:112) − ˜ g (cid:20) − M pl ˜ R −
12 ˜ g µν G ij ∂ µ ϕ i ∂ ν ϕ j − ˜ V (cid:21) , (9)where ˜ V = V / Ω is the potential in the Einstein frame following the conformal transformation˜ g µν = Ω g µν ,G ij = 1Ω δ ij + 32 M pl Ω ∂ Ω ∂ ϕ i ∂ Ω ∂ ϕ j , (10)where ϕ k = h , h , η , and the transformation parameterΩ = 1 + ξ M pl ( h + η ) + ξ M pl h + 2 | ξ | M pl (cid:18) h h c θ + η h s θ (cid:19) (11)using the shorthand notation c θ k = cos θ k and s θ k = sin θ k throughout the paper.The prefactor G ij in Eq. (10) leads to mixed kinetic terms. We introduce the reparametri-sation A = (cid:114) M pl log(Ω ) with ∂ Ω ∂ ϕ k = (cid:114)
23 Ω M pl dAdϕ k (12)which reduces the kinetic terms to the diagonal form˜ g µν G ij ∂ µ ϕ i ∂ ν ϕ j = Ω g µν (cid:18) δ ij Ω + ∂A∂ϕ i ∂A∂ϕ j (cid:19) ∂ µ ϕ i ∂ ν ϕ j = ∂ µ ϕ i ∂ µ ϕ i + Ω ∂ µ A ∂ µ A (13)To write the potential in the Einstein frame, we keep only terms in the potential in Eq. (8)which are quartic in h , and η . This reduces the potential to˜ V ≈
14 Ω (cid:20) λ ( h + η ) + λ h + ( λ + λ (cid:48) )( h + η ) h (14)+ 2 | λ | (cid:18) c θ (cid:0) h ( h − η ) (cid:1) + 2 s θ h h η (cid:19)(cid:21) where θ is the CP-violating phase of the λ parameter.Further, we introduce another reparametrisation η = β h , h = β h , (15)4ith β , β as field dependent values, to rewrite the potential as˜ V ≈ h (cid:20) λ (1 + β ) + λ β + (cid:18) ( λ + λ (cid:48) )(1 + β ) + 2 | λ | (cid:0) c θ (1 − β ) + 2 s θ β (cid:1)(cid:19) β (cid:21) (16)Using this reparametrisation, one can also simplify the Ω parameter in Eq. (11) asΩ = 1 + (cid:32) ξ M pl (1 + β ) + ξ M pl β + 2 | ξ | M pl β ( c θ + β s θ ) (cid:33) h ≡ BM pl h . (17)From Eq. (12), recall that Ω = exp( ˜ A ) using the shorthand notation ˜ A = (cid:113) AM pl . One canthen write the field h in terms of the reparametrised field ˜ Ah = M pl B (cid:16) e ˜ A − (cid:17) . (18)Therefore, expressing h and Ω in terms of ˜ A allows us to write the potential in Eq. (16) inthe form ˜ V ∼ (1 − e − ˜ A ) X ( β , β ) . (19)We will be interested in the effect of the non-minimal coupling ξ and the associated phase θ . Therefore, we will set ξ = ξ = 0 and assume that the initial field values are such thatΩ > V = (cid:18) M pl | ξ | (cid:19) (cid:16) − e − ˜ A (cid:17) X ( β , β ) (20)where X ( β , β ) = λ (1 + β ) + λ β + (cid:0) ( λ + λ (cid:48) )(1 + β ) + 2 | λ | (cid:0) c θ (1 − β ) + 2 s θ β (cid:1)(cid:1) β β ( c θ + β s θ ) . (21) Following the procedure in [16], to find the direction of inflation, we first minimise the X ( β , β )function with respect to β which occurs at ∂X ( β , β ) ∂β = 0 ⇒ β = (cid:114) λ λ (1 + β ) (22)The second order derivative at this point is ∂ X ( β , β ) ∂β = 2 λ ( c θ + β s θ ) (23)which is always positive provided λ >
0, as shown in the left panel in Figure 1.Using the β value in Eq. (22), we can write the X ( β , β ) function solely in terms of β , X ( β ) = (1 + β ) Λ + 2 ((1 − β ) c θ + 2 β s θ ) | λ | c θ + β s θ ) (24)5 .0 0.5 1.0 1.5 2.0 2.5 3.0 - - θ β ( ∂ X / ∂β at β min ) - - - θ θ ( ∂ X / ∂β at β min ) Figure 1: The second order derivative of the function X ( β , β ) with respect to β at theminimum ( ∂X/∂β = 0) on the left and the second order derivative of the function X ( β ) withrespect to β at the minimum ( ∂X/∂β = 0) on the right (all λ i ∼ . λ + λ (cid:48) + 2 √ λ λ .We repeat the same treatment and minimise the X ( β ) function with respect to β . ∂X ( β ) ∂β = 0 ⇒ β = (Λ + 2 | λ | c θ ) s θ − | λ | c θ s θ (Λ − | λ | c θ ) c θ − | λ | s θ s θ (25)We check the positivity of the second order derivative at the minimum point which is satisfiedfor all θ , θ values as shown in the right panel of Figure 1.Replacing the β value which minimises the X ( β ) function back into the X ( β ) functionitself, yields the form of X independent of β and β with only θ and θ as variables: X ( θ , θ ) = Λ − λ Λ − λ cos( θ − θ ) (26)The left panel in Figure 2 shows the X ( θ , θ ) function for allowed values of θ and θ . At eachpoint in the plots, one can derive the values of β and consequently β using Eq. (22) for givenvalues of θ and θ . The right panel in Figure 2 shows the values of β for varying values of θ and θ . 6 - - θ θ X ( θ , θ ) - - - θ θ Values of β - - - Figure 2: The X ( θ , θ ) function on the left and the values of β on the right for varying valuesof θ and θ (all λ i ∼ . β values tend to plus infinity approaching from the bottom and to minus infinity approachingfrom the top of the plot. θ = π / θ = π / θ = π / θ = π /
30 1 2 3 4 50.00000.00050.00100.0015 A ˜ ( ξ M p l ) V ˜ θ = π / θ = π / θ = π / θ = π /
30 1 2 3 4 50.00000.00050.00100.0015 A ˜ ( ξ M p l ) V ˜ Figure 3: The inflationary potential for different values of θ and θ (all λ i ∼ . With the procedure used in the previous section, the dynamics is essentially that of a singlefield inflation. The full inflationary potential in Eq. (20) can be written as˜ V = (cid:18) M pl | ξ | (cid:19) (cid:16) − e − ˜ A (cid:17) X ( θ , θ ) (27)Figure 3 shows the inflationary potential for different values of θ and θ . Note that the potentialis almost flat at high field values which ensures a slow roll inflation.For the usual slow roll parameters in this case the function X is irrelevant, since it cancels7n the expressions for (cid:15) and η , which are (cid:15) = 12 M pl (cid:32) V d ˜ VdA (cid:33) = 43 (cid:0) − e ˜ A (cid:1) , (28) η = M pl V d ˜ VdA = 4(2 − e ˜ A )3 (cid:0) − e ˜ A (cid:1) . (29)For field values A (cid:29) M pl (or equivalently ˜ A (cid:29) (cid:15), η (cid:28) (cid:15) (cid:39)
1. To calculate the values of A at the beginningand end of inflation, A i and A f respectively, one needs to calculate the number of e-folds N e ,i.e. the number of times the universe expanded by e times its own size. N e is calculated to be N e = 1 M pl (cid:90) A i A f ˜ V ˜ V (cid:48) dA = 34 (cid:104) ˜ A f − ˜ A i − e ˜ A f + e ˜ A i (cid:105) , (30)where ˜ V (cid:48) = d ˜ VdA and A i ( ˜ A i ) is the value of A ( ˜ A ) at the beginning of inflation and A f ( ˜ A f )is the value of A ( ˜ A ) at the end of the inflation. Since inflation ends when (cid:15) (cid:39)
1, one cancalculate A f , which yields: e ˜ A f = exp (cid:32)(cid:114) A f M pl (cid:33) (cid:39) . ⇒ ˜ A f = (cid:114) A f M pl (cid:39) . . (31)To calculate A i , one could plug in the A f value into Eq. (30) assuming N e = 60, which resultsin 34 (cid:104) − ˜ A i + e ˜ A i (cid:105) − . , ⇒ ˜ A i = (cid:114) A i M pl ≈ . h using Eq. (18).This gives h f = 1 . × (cid:112) | ξ | β ( c θ + β s θ ) , h i = 1 . × (cid:112) | ξ | β ( c θ + β s θ ) . (33)In the case of Higgs-inflation where the non-minimal coupling to gravity, ξ , is forced to be ofthe order ∼ GeV, the h field values during inflation are as large as 10 GeV or so. In ourcase the situation is similar.Having fixed N e to 60, and calculated the A field value at the start of inflation, we canderive the scalar power spectrum, P s , the tensor to scalar ratio r and the spectral index n s asfollows: P s = 112 π M pl (cid:16) ˜ V (cid:17) (cid:16) ˜ V (cid:48) (cid:17) = (cid:32) (1 − e ˜ A ) π e A (cid:33) X ( θ , θ ) | ξ | = 5 . × X ( θ , θ ) | ξ | , (34) r = 16 (cid:15) = 0 . , (35) n s = 1 − (cid:15) + 2 η = 0 . , (36)8 .0 4.2 4.4 4.6 4.845505560657075 A ˜ N e A ˜ n s A ˜ r Figure 4: The slow roll parameters: the number of e -folds N e (left), spectral index n s (center)and tensor to scalar ratio r (right) as a function of ˜ A with the grid-lines highlighting the55 < N e <
65 values.where ˜ V (cid:48) is the derivative of ˜ V with respect to A and both ˜ V and ˜ V (cid:48) are calculated at the A i . Figure 4 shows the slow roll parameters N e , n s and r with respect to ˜ A with the grid-lineshighlighting the 55 < N e <
65 values. We show the inflationary parameters over a range of N e ,since there is no reason for N e to be precisely 60. The values of r and n s are well within thePlank bounds of n s = 0 . ± . σ level and r < .
11 at 95% confidence level [31].Note that the spectral index and the tensor to scalar ratio are in agreement with the Planckbounds over the full range of N e . Figure 5 shows the 1 σ and 2 σ regions allowed by Planckobservations in the r - n s plane and the theoretical predictions of our framework for N e valuesof 55 and 65. n s r Planck 1 σ Planck 2 σ N e = N e = Figure 5: The 1 σ and 2 σ regions for n s and r from Planck observation compared to thetheoretical prediction of our framework.Observations from WMAP7 [32] constrain the scalar power spectrum which put a boundon the ξ coupling and angles θ , θ , P s = (2 . ± . × − = 5 . × X ( θ , θ ) | ξ | . (37)9 σ σ σ - - - θ θ ξ for central value P s Figure 6: Left panel: P s values for the fixed θ = π/ ξ and θ upto 3 σ standard deviation from the observed central value. Right panel: Contours of ξ in the θ - θ plane which lead to P s central values (all λ i ∼ . P s values for the fixed θ = π/ ξ and θ up to 3 σ standard deviation from the central value in Eq. (37). In the right panel,we fix P s to the WMAP7 central value for fixed values of λ i ∼ .
001 to get | ξ | = 4 . × (cid:112) X ( θ , θ ) (38)and show contours of ξ for varying values of θ and θ . Note that every point in the plot yieldsthe exact P s central value.This is a very important feature of our framework. To satisfy the bounds on the scalar powerspectrum, the function X ( θ , θ ) allows for a wide range of ξ values as shown in Figure 6. Thisis in contrast to the Higgs-inflation models where P s ∝ λ/ξ with λ the Higgs self-couplingwhich is fixed to be ∼ .
12 at the electroweak scale. Thus, for P s to agree with observationsat the inflationary scale, ξ will have to be very large O (10 ). In our set-up, a combination ofparameters λ , λ , λ , λ , λ (cid:48) appears in the X ( θ , θ ) function. The only constraint limitingthese parameters is the stability of the potential requiring λ ii > , λ ij + λ (cid:48) ij > − (cid:112) λ ii λ jj , | λ i | ≤ | λ ii | , | λ ij | , | λ (cid:48) ij | , i (cid:54) = j = 1 , , , (39)which allows for very small values of λ i ∼ .
001 which, in turn, allows for much smaller valuesof ξ , at least one order of magnitude than the ξ value in Higgs-inflation models. At the end of inflation, the energy stored in the inflaton disperses as the inflaton decays/annihilatesinto the SM particles through processes mediated by the SM-Higgs and gauge bosons in our10ase, during the so-called reheating phase [33]. There are numerous details on how the inflatondecays and creates the initial condition for the conventional hot early universe. Here our maininterest is to discuss how the CP asymmetry originating from the non-minimal coupling, istransferred to the SM degrees of freedom.For the discussion of the scalar asymmetries, let’s focus on the neutral components of the φ doublets acquiring an initial non-vanishing expectation value at the exit from inflaton. Wewrite the field fluctuations around the initial conditions as φ → φ − a e i α , φ † → φ ∗ − a e − i α φ → φ − a , φ † → φ ∗ − a φ → φ − a , φ † → φ ∗ − a (40)The phase α here is related to the CP-violating phases of inflation. Note that at the endof inflation the h field has taken a value according to Eq. (33) which is dependant on theinflationary dynamics, namely θ , β and β which are dependant on θ . Since h is the realpart of the complex field φ , its value is what feeds the a cos α component of fluctuations inEq. (40). The imaginary part of φ , represented by η , takes a value proportional to h asshown in Eq. (15), and feeds the a sin α component of the field fluctuations. Recall that onecan obtain the values of β and β for any given value of θ and θ from Eq. (22) and Eq. (25).However, to keep the present discussion more transparent, we retain a generic phase α here.To discuss the consequences of this complex phase, we now assume instant reheating. Sincethe field φ is light with respect to the inflaton degrees of freedom, we expect the latter toquickly decay to φ . The asymmetry arising from the values of the fields in Eq. (40) willmanifest in creation of unequal number of φ and φ ∗ quanta as follows.From the potential in Eq. (1), the couplings contributing to the decays of φ → φ φ ∝ a λ e i ( α + θ ) and φ ∗ → φ ∗ φ ∗ ∝ a λ e − i ( α + θ ) (41) φ → φ φ ∝ a λ e iθ and φ ∗ → φ ∗ φ ∗ ∝ a λ e − iθ (42)Such decay processes are CP-violating and result in unequal number of φ and φ ∗ states.Consequently, the relative asymmetries A CP and A CP in the decay rates are A CP ∼ a λ sin 2( α + θ ) , A CP ∼ a λ sin 2 θ . (43)This asymmetry in the scalar sector is then transferred to the fermion sector through thecouplings of the Higgs field (the φ doublet) with the fermions. For example, assuming theexistence of right-handed neutrinos, the Yukawa interactions between neutrinos and φ willgenerate an asymmetry between ν L and ¯ ν R , which would be further translated into baryonasymmetry by the electroweak sphalerons. Scalar fields which have non-minimal couplings to gravity are well-motivated inflaton candi-dates. Paradigmatic examples are the Higgs-inflation [13] and s -inflation models [15]. In this11aper we have considered a scenario where several non-minimally coupled scalars contribute tothe inflationary dynamics. In particular we investigated a model where these scalars are elec-troweak doublets and therefore generalize the Higgs inflation. We focused on a setting wherethe dominant non-minimal coupling is allowed to be complex and investigated the effect thatthis would have on CP-violation in our universe. We determined the inflationary dynamics inthe regime where the model essentially conforms to the predictions of single field inflation. Theessential difference is that the inflaton obtains a non-zero phase representing possible source ofCP-violation for subsequent post-inflationary evolution. At the end of inflation, the inflatonparticle which is naturally assumed to have couplings with the SM Higgs, dumps its energy intothe SM particle bath through the process of reheating, which populates the universe with theSM particles. We sketched how the complex value of the inflaton field leads to an asymmetryin the scalar sector decays, and how this asymmetry will further be transmitted to the fermionsector. There are numerous details in our scenario which can be investigated in more detail.These include the multi-field dynamics during the inflation as well as the details of reheatingand subsequent particle decays. Also the detailed analysis of the effects on the generation ofbaryon asymmetry need to be addressed in more detail. We will consider these in future workon the model introduced in this paper. Acknowledgements
VK acknowledges financial support from Academy of Finland projects “Particle cosmology andgravitational waves” No. 320123 and “Particle cosmology beyond the Standard Model” No.310130.
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