JCAP04(2007)005 hysics $30.00 18 P 4 [email protected] stroparticle stroparticle and A and K Freese 3 , 2 a degli Studi di Ferrara, I-44100 Ferrara, , 1 [email protected] , hep-ph/0612018 , A D Dolgov 2 , In models with the fundamental gravity scale in the TeV range, extra dimensions, baryon asymmetry 1 osmology and and osmology stacks.iop.org/JCAP/2007/i=04/a=005 [email protected] C Dipartimento di Fisica, Universit` Institute of Theoretical andMichigan Experimental Center Physics, for 113259, Theoretical Moscow, Physics, Russia Physics Department, University of Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, I-44100 Ferrara, Italy early cosmology is quite differentmust from have the arisen standard at picture, a becauseprobably much the never lower universe restored. temperature and In this theif context, electroweak baryogenesis the symmetry appears was physics to benon-conserving involved problematic: baryon is number essentially processestemperatures. that are of completely the negligibleasymmetry In standard at model, of this such ‘conventional’ the low papermass universe particles: we may showtheir such be mass that objects is generated of the canthey the by can be same observed gravitational quickly order out matter–antimatter decay ofsymmetries, decay through of magnitude in of as a equilibrium the particular, black TeV of true after hole baryon quantum the intermediate inflation number. gravity state, fact scale, and, violatingsatisfied In that with global if this the a low context, ‘Sakharov fundamental we conditions’ scale take of for gravity. advantage baryogenesis can be more easily Keywords: ArXiv ePrint: doi:10.1088/1475-7516/2007/04/005 Abstract. CBambi 1 2 3 4 Received 16 January 2007 Accepted 16 March 2007 Published 10 April 2007 Online at Michigan, Ann Arbor, MIE-mail: 48109, USA Italy
ournal of ournal
An IOP and SISSA journal 2007 IOP Publishing Ltd and SISSA 1475-7516/07/04005+ c scale gravity of TeV particles in theories with low Baryogenesis from gravitational decay J JCAP04(2007)005 2 2 5 6 7 16 16 17 GeV, ) 19 10 ∼ GeV, which is Pl 3 M 10 ...... 10 ∼ ...... 12 EW ], but at present there is 1 ...... 11 M CP ...... 15 and stacks.iop.org/JCAP/2007/i=04/a=005 C ...... 13 ved matter–antimatter asymmetry in the t fundamental energy scales in nature which ily satisfied with a low fundamental scale of e.g. time variation of fundamental constants, 04 (2007) 005 ( ...... 12 , in the TeV range. As we shall see in what follows, ∗ M tter–antimatter asymmetry Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity 4.3.1. Chain inflation. 4.3.2. Production of heavy particles. We will consider baryogenesis scenarios based on low scale gravity with the In the standard framework of general relativity, there is probably no realistic Acknowledgments References 4.1. ‘First Sakharov4.2. condition’: baryon ‘Second number Sakharov violating4.3. condition’: decays violation ‘Third of Sakharov condition’: out-of-equilibrium criterion 4.4. Generation of a ma 5. Conclusion Journal of Cosmology and Astroparticle Physics fundamental Planck mass, universe is an openthe problem in standard modern model. cosmologyno and Many experimental a evidence possibilities clear in sign havemodels favour of been of are new one proposed often physics model [ beyond such based over high another. on energies In assumptions as addition, difficult to unluckily, to be the unreachable test, in since future the laboratories involved on physics the is Earth. at The mechanism of generation of the obser 1. Introduction 2. TeV gravity models 3. Early universe in theories4. with low Mechanism scale of gravity baryogenesis 1. Introduction Contents the baryogenesis scenarios inproblems, models because with of atherefore, an low gravity additional expected scale exotic very encounter low assumptions, some reheating additional temperature of the universe, and, are usually needed.conditions’ In for this baryogenesis context, can on be the more other eas hand, we will show that the ‘Sakharov are different by many orders of magnitude, namely, the Planck mass possibility to everthe observe fact gravitational that interactions there are in apparently particle two distinc physics. This is due to gravity. In addition, theknown mechanism quarks) may operate or with with the a minimal minor particle extension content to (only low energy supersymmetry. accessible in lepton and hadron colliders. which sets the energyelectroweak scale when of gravity becomes the comparable standard to model gauge of interactions, particle and physics, the JCAP04(2007)005 , 3 2 ) (Φ). The RV ]. The scenario cm. However, all 10 33 − ]. It is assumed that 7 10 ]and[ 9 ∼ Pl L 300 GeV never took place in the early stacks.iop.org/JCAP/2007/i=04/a=005 as two fundamental energy scales may ∼ EW ble in the context of the standard model. d create the matter–antimatter asymmetry s distorted after particle propagation in the ) conservation below the electroweak phase ynthesis, there are no direct contradictions is based on the non-trivial assumption that M nly for temperatures below the fundamental ndard theory and this seemingly forbids any B EWSB the decays are mediated by virtual black holes ) it may reach the asymptotic Planck value, t cm. M and 04 (2007) 005 ( 28 Pl violation, a departure from thermal equilibrium is M –10 ] and considered in detail in [ 2 8 − CPT (Φ) is supposed to be in electroweak scale, i.e. about (TeV) ]. In these scenarios, gravity becomes phenomenologically V 6 Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity ] on the basis that BH evaporation produces a thermal equilibrium 11 ] the true fundamental gravity scale can be as low as a few TeV, and the 5 . ]–[ 2 Pl 2 M )= ∞ However, the interpretation of Another suggestion to explain the electroweak–gravitational hierarchy in a natural Loopholes have been found in recent years. For example, in models with extra While TeV gravity is a fascinating possibility from the point of view of particle The possibility that BH evaporation coul On the contrary, a low fundamental scale of gravity opens a new possibility for (Φ -conservation. In this paper we consider gravitational decays of heavy particles as a (1) quantum numbers including baryonic charge. initial value of the function way in the four-dimensional world was recently put forward in [ interesting for highphenomena at energy future physics colliders. and we may observe andthere study exists a quantum scalar gravity field Φ with non-minimal coupling to the curvature, dimensions [ large Planck mass isFor then a merely recent an effective review long-distance see four-dimensional parameter. [ Journal of Cosmology and Astroparticle Physics phenomenology, its cosmologythat may in be such models problematic. thesince maximum the temperature In concept of fact of the spacetime we universe never itself can exceeded exists reasonably a o few expect TeV, gravity scale.significantly In lower. factlow Consequently, we that ordinary electroweak often symmetry cosmology breaking find commenced the at temperatures reheating so temperature after inflation to be be incorrect becausegravity the behaviour previous is assertion unchanged down to the Planck length we know from experimental testsdistances, of that gravity is is its in force the at range the 10 present time on macroscopic (BHs), which (according toU common belief) can decay/evaporate with violation of global state; yet, in the absence of TeV scale baryogenesis, becauseB the gravitational interaction itself can naturally break universe. Since at theit moment was we 1 have no s reliable old, information i.e. about the before universe primordial before nucleos transition is completely negligiblerealistic in baryogenesis the scenario sta in the case of low scale gravity. mechanism for low temperature baryogenesis.irrelevant. The Instead, details the of key the feature heavy is particle that decays are was criticized in [ needed in ordercriticism, to although produce the an particleindeed excess emission thermal, of due the particles equilibrium to over distribution Hawking antiparticles. i radiation at In the response BH to horizon this is with the assumptionmodels, of because TeV to gravity.and this presently However, end we baryogenesis aIn do is particular, not mechanism quite violation know working of difficult anything at baryon suita in relatively number these ( low energies is needed while due toV dynamical evolution of Φ( of the universe was suggested in [ JCAP04(2007)005 4 ]. 14 ) ). In the first t ( we present our violation, which Pl ]. In any case, in 4 9 M CP . In section be realized only for ‘large’ BHs. ]. We stress that these conditions 3 15 f gravity. The first criterion, baryon stacks.iop.org/JCAP/2007/i=04/a=005 variation of the quark masses and their y gravitationally via intermediate BHs; n oscillations challenge the hypothesis and possible ways for realization of fundamental he resultant matter–antimatter asymmetry. ee, the standard scenario of baryogenesis in ntially quantum gravity phenomena, with a and quark masses. However, it may be just amplified by a much faster Hubble rate, which on from thermal equilibrium, which is normally Pl violation can be introduced by time variation of M ] and their mutual interactions [ 04 (2007) 005 ( does not encounter these problem because now we 12 CP N ity scales. The second criterion, G rd ‘Sakharov conditions’ [ . 5 ) or what comes to the same the Planck mass, Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity t ], a semiclassical process that can ( N 13 G to satisfy with a low fundamental scale o and the related early cosmology in section 2 We would like to stress that we do not introduce any new hypothesis for our The basic idea of the baryogenesis scenarios considered here is that TeV mass particles A larger, than standard model, The content of the paper is as follows. We briefly review TeV gravity models in easier is negligible atin high temperatures TeV gravity infew models. the hundred minimal MeV, standard First, andmixing model, second, the angles. we may effective The consider be third temperatures time criterion, much deviati can larger be quite small, about a gravity scale in TeV range:coupling either constant higher dimensions or time variation of the gravitational baryogenesis scenario.references All to them. they For example are there are considered two in the literature and we make proper negligible at electroweak energies, mightin be turn is enhanced bybaryogenesis a at very relatively small low Planck mass. energies. These features may lead to very efficient Journal of Cosmology and Astroparticle Physics are gravitational field of the parent BH [ (the mass of the fundamental gravity scale) deca this paper we considerHawking decay radiation rather [ than BHInstead, evaporation. the We will decays notsmall considered number deal here of with final are thermal particlesarise esse not if, emitted believing with in a the thermalnumber information spectrum. preserving is Other BHs not criticisms picture, may one violated.reasonable were arguments to However, suggest argue a that that baryon rigorous global proof quantum numbers is are lacking not and, be on conserved the [ these contrary, very decays violatescenarios are baryon the three number. standa The essentialnumber violation, ingredients is mediated of bysuch these virtual gravitational BHs effects baryogenesis which are canstronger inversely violate related for global to quantum low numbers; the fundamental effective grav Planck mass and hence are have normal Planckbaryon scale non-conservation gravity, was while facilitated. it was in TeV range in the early universe and opposite: if one massthat varies all with time, the thewe masses other have may were done. vary in as After TeV well. that, range It as is at one natural can the to easily early expect s time. This is the assumption that section heavy particle decays very well operates at TeV energies. the Yukawa coupling constantsin of quarks the with literature. theis Higgs One unnatural boson, may to which object have is to variation also of this considered both additional assumption, on the ground that it case the proton decayspecial and efforts neutron–antineutro should be madeHowever, to at avoid TeV contradiction temperatures with the experiment processesunsuppressed. at with zero baryon Time temperature. non-conservation could variation be of easily baryogenesis model and giveWe an conclude estimate in of section t JCAP04(2007)005 5 (1) (3) (2) cm 13 ) 10 ∼ 1TeV,we R ]). From the ∼ ∗ 19 , M 18 becomes an effective long- . ]. Interesting variations of Pl )-dimensional bulk, with the 16 BH n M ) we would obtain . Semiclassical arguments, valid M 2 s . If we assume √ hese extra dimensions are ‘large’, EW ≈ stacks.iop.org/JCAP/2007/i=04/a=005 M BH discussed for TeV scale gravity: (1) large re experiments in high energy physics. In M ian gravity at solar system distances would ane, while gravity is allowed to propagate on to the perplexing hierarchy problem in tion in collision of two particles with centre rchy problem of high energy physics, where ck mass. We briefly review these ideas and e relation with the fundamental gravity scale y that hadron colliders (such as LHC) will be ], criticisms can be found in [ 04 (2007) 005 ( 17 ]. Motivated by string theory, the observable universe 3 An alternative origin of a fundamental TeV scale for , cm but much smaller than the four-dimensional universe . 2 17 , scenarios, the Planck mass ) cm , In 1998 Antoniadis, Arkani-Hamed, Dimopoulos and Dvali − m and nowadays we have no experimental evidence against n μ 17 BH 10 R − n ) M ∼ ( 100 /n 2+ ∗ cm, then the fundamental gravity scale can be as low as a few TeV Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity 2 BH (30 M 33 TeV − 10 / R , if these particles approach each other so closely that they happen to ∼ πR s 10 ) is the horizon radius of a BH of mass 2 ∼ Pl 2, ≈ = 1 is excluded because from equation ( √ , predict the BH production cross-section ∼ ∗ M σ R BH n ≥ ]. 1 5 M M n − Pl ( is the size of the extra dimensions. If t M BH R R BH Large extra dimensions. The case Time-varying Planck mass. If gravitational interactions become strong at the TeV scale, quantum gravity is given by R M ∗ Journal of Cosmology and Astroparticle Physics the observed weakness oflarge gravity compact (at extra dimensions long [ distances) would be related to the presence of their experimental consequences. proposed a ‘geometric’ solution to the hiera There has beenespecially a great since deal they of may interest provide recently a in resoluti models with a low scale for gravity, 2. TeV gravity models particle physics. Twoextra possibilities dimensions have and been (2) time-varying Plan and therefore of the same order of magnitude as size. gravity involves a time-varying Planck mass. The idea that the value of the Planck mass i.e. where where In this approach, however,from the the hierarchy hierarchy problem in is energiesmuch larger to not than a really 1 hierarchy solved in but the shifted size instead of the extra dimensions which are be inside the event horizon of a BH with mass for and therefore strong deviations from Newton result. For a modification of gravitational forces in such a regime [ distance four-dimensional parameter andM th find: would be astandard four-dimensional model brane particles embeddedthroughout confined in the bulk. to a the In (4 + such br of mass energy these models can lowerdimensions the [ fundamental gravity scale with the use of non-compact extra particular, there is a fascinating possibilit classical point of view, we expect BH produc phenomena are in the accessible range of futu BH factories (for a review, see e.g. [ JCAP04(2007)005 6 (4) ]andin ) 21 (Φ) a dimensionless f , at which point quantum could ensure the required 2 Pl 2 − M 10 ∼ ∼ R λ we observe today is explained with stacks.iop.org/JCAP/2007/i=04/a=005 EW ]. These models have been extensively M the electroweak phase transition. Early 22 articular, the next generation of colliders easonable to expect that the universe has del, which is described by the Friedmann ] has it been stressed that they are capable ) in the four-dimensional spacetime. As a 7 t s such as the horizon and flatness problems, and ible quantum gravity effects might be effective. and curvature Pl culminated in the Brans–Dicke theory [ 04 (2007) 005 ( ] the authors take M Pl 7 M ∼ ]. This idea was then developed by other authors as a . A reasonably small 4 (Φ)] (5) T 20 ] we can consider, for example, an exponential potential ) , 7 W /μ (Φ) ] was introduced. Inflation requires a superluminal expansion f (Φ exp[ 2 ∗ , then gravitational interactions should be negligible in particle λ 23 0 Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity M V − EW 2 ∼ ) M is the only fundamental scale of the theory and /μ (Φ) (Φ) = EW V V Pl M =(Φ M ∼ W ∗ M If the true fundamental gravity scale is in the TeV range, the maximum conceivable If the Planck mass depends on the value of a scalar field Φ and today has its usual large with e.g. where temperature oftemperature the is universe probably is too of low to the allow same for order of magnitude and the reheating rate of thenot very want early to be universeof abundant followed in overclosing by the the present-day a universe universe)diluted. period (such must On as of the be superheavy other reheating. objectsmust produced hand, capable take before events place All which inflation, after must the have inflation. so left relics they traces we (such can do as be the baryogenesis) strongly universe cosmology isasymmetry becomes deeply a modified real and challenge. the Popular generation scenarios, of operating at the the matter–antimatter GUT scale, Journal of Cosmology and Astroparticle Physics complete field theory of gravitationmore and general scalar–tensor theories of gravity [ has evolved with time,his and ‘large was much number lower hypothesis’ in [ the early universe, goes back to Dirac and studied in the literature,of but solving only the recently hierarchy problem. [ In [ equation, as we lookto backwards common in belief, time, suchwhen the we equations, reach universe obtained the temperature was from hotter classical and general hotter. relativity, break According down According to the standard hot big bang mo 3. Early universe in theories with low scale gravity will not beyet able evolved to to its produce presentBaryogenesis, value, BHs. in non-neglig particular, Nevertheless, could take in place the as early is described universe, in when the Φ present has paper. not physics today, as in the standard theory. In p a temporal evolution of the scalar field Φ( modification of the model of [ function of Φ. The huge gap between gravity phenomena becomenever important: exceeded it these values isin of r curvature the and Robertson–Walker temperaturethe metric and big that is the bang, a initialthe in drawback singularity inflation order of paradigm to the [ resolve classical difficultie theory. Supplementing value with hierarchy of 16plan orders to of present elsewherecorresponding magnitude a cosmology. between detailed the study of Planck the and evolution electroweak of scales. Φ and the We features of the JCAP04(2007)005 7 (6) ]). A 29 ) 10 MeV. ∼ TeV, cannot ]). The most T ∼ 26 10 GeV. At such T 1MeV,weobtain . In fact, at high ∗ ∼ M invariance and require max bbn T T CPT violating operators in an effective B (charge conjugation combined with stacks.iop.org/JCAP/2007/i=04/a=005 ]. =7leadsto , the situation is even worse, because 27 n CP osynthesis. The analysis of light elements with a time variable Planck mass. The value: the allowed deviation from the value nergies, are needed. We note that chain upper bound for the reheating temperature ]. We note that some alternative ideas for res of baryogenesis with a low gravity scale, nsional spacetime remains baryon symmetric 28 . 04 (2007) 005 ( ]: +2) 15 ], where an effective baryon number violation on our n ( 30 / ]. 1 32 , 10 MeV, whereas Pl bbn 31 , M T 1 ∗ max Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity M T (charge conjugation) and ] C 25 max GeV, or at the electroweak symmetry breaking with T 16 ] with the QCD axion also leads to a low reheat temperature, 10 24 ∼ =2weobtain As for models with large extra dimensions parity) symmetries, In this paper we will investigate baryogenesis with TeV gravity scales and low Constraints on the time variation of the Planck mass can be derived from different n GUT (3) deviation from thermal equilibrium. (1) baryon number non-conservation, (2) violation of In ordersymmetric to universe, generate usual baryogenesis a scenarios cosmological assume matter–antimatter asymmetry in an initially 4. Mechanism of baryogenesis different picture is consideredbrane in could [ result fromin baryon brane evaporation collisions, into soand ‘baby the that branes’ matter the or dominated higher from universe baryon dime is exchange reduced to a peculiar feature of our brane. the so-called ‘Sakharov conditions’ [ baryogenesis at extremely low temperatures have been considered earlier (see e.g. [ based on enumeration of possible non-renormalizable reheating temperature inmodels a model with independent extra way, rather dimensions than from distinguishing models between essential physics is the same. Generallow featu energy Lagrangian, are described in [ inflation [ the reheating temperature is usually expected to be well below work. New mechanisms, efficient at lower e Journal of Cosmology and Astroparticle Physics M For a discussion, see e.g. [ that we measure today should be less than 5% [ production requires thatmass when had the to universe be essentially temperature frozen was at its around present 1 MeV the Planck stringent bound comes from the big bang nucle For a maximum temperature (usuallyafter assumed inflation) as [ cosmological and astrophysical considerations (for a review, see e.g. [ low temperatures standard scenarios of baryogenesis are impossible. temperatures a copiousthe production cosmological of gravitons expansionelements into rate created the compatible when bulk the with took temperature the place; of observations if the we of universe require primordial was light JCAP04(2007)005 8 (8) (7) ) . 5 − 12 odd phase in 10 /T × CP CP 3 J ) ≈ 2 d m is the CP δ ional effects that violate − 2 s CP sin δ m 13 )( θ 2 d ss the original scenario of out-of- violation to allow for successful m ssed. For example the reheating sin odd effects of the same order of − time dependent quark masses and 23 2 b n-relativistic decaying particles at a CP θ stacks.iop.org/JCAP/2007/i=04/a=005 m CP leads to more effective baryon violation. sin )( . Such a small magnitude surely demands present also a more detailed realization of 2 s too strong non-conservation of baryons to 19 12 t hard to imagine, they may e.g. be created a possible supersymmetric extension which θ m − s mechanism in models with a fundamental er hand, this feature of an enhanced baryon Here we focus on out-of-equilibrium decays of − 10 sin 2 b -meson decays. ≈ 13 , appropriately modified to the case of TeV scale m 04 (2007) 005 ( θ B X )( 2 CP 2 u In this paper we use gravitat m cos -or 23 K − θ 2 c m cos )( 100 GeV, -non-conservation in the minimal standard model is known to 2 u 12 θ m ∼ Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity CP − T . violation may arise if quark masses were in the 100 GeV–TeV range violation is possible assuming 2 t ) might not be so strongly suppre =cos 7 m in the TeV range. In particular we discu )( CP is much larger in TeV gravity than in the usual Planck scale one. Indeed, 2 c CP CP ∗ J m T M violation is the Jarlskog invariant − 2 t are mixing angles between different generations and CP m Baryon number violation. CP Deviation from thermal equilibrium. ( J ij θ in equation ( Here we consider a possible baryogenesi 1. 2. 3. On the other hand, if the temperature after inflation were much smaller than 100 GeV, Enhanced The deviation from thermal equilibrium of no ≈ CP CP gravity scale Journal of Cosmology and Astroparticle Physics equilibrium decay of heavy particles, Here temperature in the MeV range would lead to some modification of the standard mechanism of where the mass matrix. For the three conditions in a concrete model. baryon number and we focus onBHs. the Since role such of baryon gravitationalPlanck number effects violating mass, are processes a inversely mediated smaller proportional by fundamental to gravity a scale power of the effective number violation is favourable for cosmological baryogenesis. gravity. In this section wethe briefly advantages of describe TeV the scale main gravitybaryogenesis in features model. satisfying of the the We ‘Sakharov scenario will conditions’physics and required try emphasize for as to any possible, be as thoughmay close make we to baryogenesis do more the not efficient. minimal reject standard We will model in particle Thus a strongmodels. non-conservation In of fact, baryonic carekeep charge should protons is be reasonably a taken stable. to generic avoid On feature the of oth TeV gravity magnitude as those observed in mixings. Large in the earlyvalues universe, of with the themixing masses. mass angles differences It between of quarks isthe the also natural early same changed universe, to order and becauseof expect might of the both that possibly same magnitude mixings mass simultaneously be as and matrixby with of which assumption the masses the has the the are different quark order masses, entries determined massesmixings unity in the were by should the in of diagonalization be early the universe also same and of magnitude today. in the Since the same early magnitude universe, and all quite the probably close to unity. baryogenesis. be very weak. At high temperatures it is proportional to temperature TeV scale particles as responsiblecosmological for the abundance generation of of such the particles baryon is asymmetry. no A sufficient during reheating after inflation as described further below. JCAP04(2007)005 9 (9) (10) (12) (11) to the and the ) depends ρ H Pl M -particles to lighter X a possible bulk cosmological bulk might be easily of the order of unity. . stacks.iop.org/JCAP/2007/i=04/a=005 6 is ∗ neq nstein equations, i.e. the square of the δ tion in the first-order electroweak phase al equilibrium commonly considered for X M 2 the effective four-dimensional Friedmann Pl 3 ) m mental gravity scale in TeV range: here the luded by a heavy Higgs boson, if the mass deviation from equilibrium. The first-order M π ≈ f the extra dimension, we find that one of the (8 , ]. In the case of electroweak masses and with 3 T ∗ 33 is the coupling constant of 04 (2007) 005 ( bulk πM g . 1. Hence, for example, in the standard cosmology Λ Λ=6 . being the cosmological energy density, the parameter 48 0 . 4 + ρ X l Friedmann equation becomes T 2Λ ∼ 2 Pl and is negligibly small. On the other hand, if m 3 ∗ , see e.g. [ 2 ∼ 2 ,where M g 3 15 ∗ 2 . Hence, in order to recover the standard cosmology at low 1+ ρ neq π − 10 πM Λ δ 2 can be split into the energy density of ordinary matter / 10 πM brane 48 ∼ 2 Pl 2 brane X ρ Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity ρ πρ 48 ∼ − M Γ m 8 H 3 ,with 2 brane = ∝ g ρ neq Pl ≡ ] ∼ ∼ δ 2 ], ) ∼ 2 2 bulk 35 neq , 36 /a ρ/M H δ Λ H 1 TeV, the universe expansion rate is compatible with the big bang a is the total energy density on the brane and Λ 34 √ GeV, ∼ 19 brane ∗ 10 H ρ M ∼ As for the braneworlds models, the situation is a little more subtle, since the related Another mechanism for breaking of therm Pl Journal of Cosmology and Astroparticle Physics reaction rate Γ the deviation is determined by the ratio of the universe’s expansion rate One can check thatdecays the is magnitude proportional of the to baryon asymmetry generated in heavy particle equation is [ cosmology can beone quite extra different dimension from compactified the on standard a one. circle, For example, in the case of Thus a low fundamentaltemperatures. gravity scale leads to out-of-equilibrium decays at much lower where where For describing deviation from equilibrium at brane cosmological constant Λ (whichrequire can be interpreted as the tension of the brane) and temperatures [ constant. Because of thedominant compact terms nature of o the 00-component of the Ei logarithmic derivative of theis scale factor equal with to respect ( to the extra dimension coordinate, nucleosynthesis, but itfavourable is for faster baryogenesis. than the standard one at higher temperature, which is In this case the four-dimensiona M on time and was a few TeV in the early universe, decay products. Normally of the latteruseful is for the baryogenesis same in models today with and a funda in the early universe, and in any case it cannot be electroweak phase transition is probably exc electroweak baryogenesis is duetransition. to We bubble note forma antransition advantage of is our not model, necessary that to such create a first-order a electroweak large phase JCAP04(2007)005 ] 10 19 [ (13) ) et al GeV; for discussion 16 –10 = 0 should be noticeably 10 B cannot form a BH, because its charge stacks.iop.org/JCAP/2007/i=04/a=005 Pl f the event horizon. Therefore, following ollisions at the end of ‘chain inflation’ as f particles with non-zero spin and/or electric it is in agreement with experimental bounds. ck mass BHs would induce proton instability neutron oscillations and anomalous decays of violating decays may be noticeably enhanced. m
ξ/λ ]. The field tunnels from one high hould take care that this field would stacks.iop.org/JCAP/2007/i=04/a=005 24 , take place. While these bubble collisions 42 , and the coupling to light quarks is not too sis is that the universe be out-of-equilibrium ϕ e ratio of the trace of the matter energy– tion. We discuss both possibilities here. nflation and (2) out-of-equilibrium decays of are first order, with bubbles of true vacuum actions to destroy the baryons that have been 04 (2007) 005 ( R. 2 2 | out-of-equilibrium criterion χ | = 0 is unstable and the expectation value of ξ GeV χ + ξ λ λ. 4 T, | 2 80 χ In chain inflation, a series of tunnelling events takes place, e.g., − | 2 Pl Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity π λ 8 10 ξR/ M = − )= ≈
χ = 2 2 ( χ χ
R U
is more strongly coupled to quarks one s χ 0 the vacuum with Since ξR < particles produced during reheating in infla Journal of Cosmology and Astroparticle Physics so that any baryon number thatInflationary is cosmology created is offers not two immediatelyto ways wiped to out a by achieve other first-order this reactions. criterion: phase (1) transition bubble in collisions chain due i 4.3.1. Chain inflation. The ‘third Sakharov condition’ for baryogene 4.3. ‘Third Sakharov condition’: TeV range only inbe the all early about universe, TeV. Such the unusual quark behaviour can mass be differences achieved and e.g. their if masses could could be absent or much milder. achievable, thanks toenergy the density. possibility In of thistheir picture, a the standard much quark late mixing lower time angles effective values should Planck and be mass the also very suppression and different due from a to high the Jarlskog determinant ( in a potential that looks like a tilted cosine [ nucleating inside the dewhen Sitter bubble space. collisions Reheating ofare occurs the taking final at true the place,take vacuum last the place few universe without tunnelling is events, allowing the out reverse of re thermal equilibrium, so that baryogenesis may energy minimum of theenergy potential minimum to a untila lower it energy fraction one, reaches of andtunnelling zero thence an events. energy. to e-folding, yet The another adding At lower phase up each transitions to stage a the total universe of inflates sixty by e-folds after several hundred If in the universe today we have Since the curvaturemomentum tensor is to proportional the square to of the th Planck mass non-minimal coupling to curvature: which is negligible for any reasonable value of the ratio not contradict the precise electroweak data. It may be probably achieved if of magnitude heavier thanstrong. the usual Higgs, vacuum state would be the early universe, before the radiation dominated epoch, JCAP04(2007)005 13 CP (18) -non- B ) s that were discussed eV to obtain density ], such period provides 10 ], so that a TeV Planck − 43 44 10 [ . 2 5 ∼ − σ 2 m φ 10 2 2 μ ∼ stacks.iop.org/JCAP/2007/i=04/a=005 extra dimensions, where inflation (at rk. One of the examples considered + with different probabilities, due to 2 φ ¯ l ll as perturbative, non-perturbative, and δρ/ρ e collision mechanism 2 her hand, such a situation is not formally er and thermalize, converting the universe q ass of the inflaton. As usual it is assumed ition be first order). In addition, the energy , there is the preheating period, where the 3¯ m 1 2 → + φ 2 04 (2007) 005 ( . ) 4 2 could perturbatively decay into particles if the sum The period of exponential expansion of the universe, φ and λσ TeV − ql ∼ 2 3 ∗ M ( → ), oscillates, producing all the particles it couples to; then, t V φ 1 ( 4 φ Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity The inflaton GeV scale widths and GUT scale heights in order to produce the )= 19 . If the mass of the inflaton is that high, it could decay via ∗ φ, σ ( M V ∼ ]), where smaller mass scales can wo λ 45 √ Inflaton decay. / ∗ ] is a hybrid inflation model with compact 1. Another option is hybrid inflation or models with many scalar fields (e.g. assisted 46 μM least its lateststabilized stage) (though occurs a only previouscertainly in period needed). our of The 3-brane inflation potential both and of the in the model the extra is bulk dimensions and are on already our brane was appropriate amplitude of density fluctuations Journal of Cosmology and Astroparticle Physics 4.3.2. Production of heavy particles. created. This mechanism is similar to the bubbl difference between minima canheight be of arbitrary, the ininflation, potential this Heavy case is particles a constrained can fractionhave to be baryon of be violating produced a decays below TeV, during (again, if reheating, the out the and TeV of total these Planck thermal can scale equilibrium). subsequently at the time of for electroweak baryogenesis (should this trans known as inflation, endsfavourable up conditions with for ‘reheating’.be possible As abundantly baryogenesis. suggested created, inslow Many even and [ weakly very lifetime interacting heavy sufficientlythe particles long, ones. universe can allowing a them In net toproceeds addition, baryon decay through number. their out three of In reaction different equilibrium standard rates and stages: rolling can to models first be give the of inflation, produced the particles reheating the (if previous two heavy stages and interact with unstable) each decay; oth last, particles produced during classical inflaton field, from a coldcan and be low created entropy duringoscillations. state reheating, Specific even into mechanisms withas a include masses described hot tunnelling larger in and models than the high of frequency previous inflation of entropy subsection) (chain the one. as inflation, inflaton we Heavy particles gravitational particle production in rolling models as discussed below. inflation [ in [ conserving channels, e.g. mass makes such modelsexcluded untenable. and inflation On might thethan start ot the with effective the Planck potential scale, energy of the inflaton much smaller The mass of the inflaton field before inflation must be perturbations in agreementis with observations. After inflation the mass of the inflaton of their masses isthat smaller the than energy the densitymass of effective gravity the m scale, the inflaton heightthe is of TeV smaller the scale. than potential the at Mostpotentials the Planck rolling with beginning one. models 10 of Hence, of inflation for must inflation be a with below TeV the usual Planckian gravity require violation, and thus the inflaton decays might generate cosmological baryon asymmetry. JCAP04(2007)005 14 (21) (20) (19) ], but implies ) 52 ], which 4 Pl 48 , M ] and during ]. If so, only 47 ≤ 49 ] and facilitate , 47 ) 50 φ 47 ( )[ t U ( φ , is not too small in comparison The non-perturbative approach H stacks.iop.org/JCAP/2007/i=04/a=005 passes through zero [ φ re after thermalization. Thus the created te and particle production begins when ay be significant if non-perturbative effects ) there exists a ‘normal’ mass of the created tion of particles coupled to the inflaton field re)-heating. On the other hand, the effective . A natural upper bound 19 4 . 2 λφ λφ 04 (2007) 005 ( b, mplitude of the inflaton oscillations † √ rate in the case of wide resonance [ Gravitational particle production in time variable b )= 2 φ = ( . ]. 2 ) λφ U δ ω 53 ] where it was shown that the production rate that vanishes + ∼ t 48 2 φ , Pl , the production would be strongly, exponentially, suppressed m 47 2 and | /M b ], despite a large effective mass of the produced particles introduced 4 Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity | b TeV. The particles produced by external gravitational field should cos( 47 λφ 0 m ∼ φ = ¯ ∗ ff or 2 = are respectively fermionic and bosonic fields, would be only mildly, (as M . Inflation should stop when the effective inflaton mass or frequency of hφ φ H b 4 ¯ / ff ∼ 1 f ] is efficient only when the Hubble parameter, m H /λ and . It means that the particles with masses up to the Planck mass can be created Gravitational production. 51 Pl is large in comparison with the characteristic frequency of Non-perturbative particle production by inflaton. Pl f ), suppressed [ 0 M M f,b 2. In the case of production of bosons parametric resonance is possible [ 3. All the mechanisms described here allow for production of particles with masses which For models with a time dependent Planck mass, gravitational particle production may φ ≤ √ m ∼ / was pioneered in papers [ are taken into account.as In particular, produc in the lowest orders of perturbation theory m by such coupling in the case of large a this (short) time thethe mass effective mass of induced the by produced the particles coupling ( vanishes. However, if in addition to particles Journal of Cosmology and Astroparticle Physics by the inflaton. massive particles may be out of equilibrium if their lifetimemetric is [ longer than the Hubble time. may be much larger than the universe temperatu can strongly enhance theproduction production of particles with masses exceeding the mass of inflaton. oscillations is of the order of the Hubble parameter, i.e. light particles wouldtransition be took created place after butfrequency the they can universe be (pre/ may large acquirecan for be masses a realized large if for amplitude the the of potential the electroweak formally phase massless inflaton field, which if In other wordsω the inflaton starts to oscilla φ The particles are predominantly produced when where with the particleconformally invariant mass. massless fermions and Due vector to bosons would conformal not be flatness created of [ the cosmological FRW metric, quantum conformal anomaly eliminates this exclusionof and even allows for massless noticeable gauge production bosons [ be significant. At the endare of both inflation, the time dependent Planck mass and expansion rate have energies and/or massesparticles in the is same model TeVof range. dependent the The and, gravity fraction in scale of particular, the from produced it TeV heavy to depends the upon asymptotic the Planck law value. of relaxation If the time dependence 1 JCAP04(2007)005 , , ∗ 15 rh .If M 5 /T − . X ∼ ) X 10 m H ∼ T/m , production. is a reasonable ∼ X =0) 3 γ odd effects in the − /n T ( 10 X ) may be easily and 1 GeV this factor is CP t n CP ≥ ∼ with a constant factor of tot 2 ) rh /n T Pl , are to be produced. Their X . n , we find X /M 3 ) is determined by the potential T t X = T ( ∗ m X ∼ M r stacks.iop.org/JCAP/2007/i=04/a=005 γ due to necessity of rescattering in the n density was initially small in comparison 3 on factor due to annihilation of massive violation depends upon the quark mixing may be produced after inflation by several ment of the production and their relative − g angles may be large in the early universe onal field at the end of inflation their energy X and andard model of particle physics. We argued l factors give the suppression of the baryon er density at production is model dependent he non-minimal coupling of a scalar field Φ, –10 CP constant ( 2 X − ∼ m 10 X 04 (2007) 005 ( is expected to be in the GeV to MeV range. This tot n , depending upon the model. As we have argued at ∼ 7 T /ρ = − X ). The effective frequency of Φ( X ρ ρ α/π –10 ,R violation arises from the interference of loop diagrams with 6 − , heavy particles ]as (Φ CP U the amplitude of 51 , the rate of evolution of 2 4 .Since 4.3.2 -non-conserving decays of TeV mass particles. which is small in comparison with the expansion rate, Φ 4 Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity B T X ξR m ∼ ], 01 X . 54 ρ 0 , 7 ∼ X may be of order unity both at low and at high αm CP The estimates presented above are of course very approximate and model dependent As shown in section One should also keep in mind that the lifetime of the created heavy particles is large There should also be the entropy suppressi would be diluted by the entropy released in the inflaton decay by the factor (Φ) or, more generally, X but they show that a model with TeV scale gravity and time-varying quark masses is quite Journal of Cosmology and Astroparticle Physics As is argued in thebaryogenesis previous in subsections, a TeV slightly scale modified gravity minimal looks st favourable for low energy 4.4. Generation of a matter–antimatter asymmetry that all three ‘Sakharov conditions’of are gravity. more easily satisfied with a low fundamental scale of the Newtonian constant is generated by t to curvature [ the beginning of section angles and in low temperature baryogenesis it should be about species in thermal equilibrium universe into photons. If in comparison with the Hubble time at the mo energy density risesrelativistic in species. the This would course somewhat of increase expansion the effect. with respect to the energy density of and quark masses vary with cosmic time, the mixin order unity. Thusr this fraction may be close to one. The ratio of the number densities, final state (remember that the tree graph).asymmetry Taken in together, the these interval smal 10 about 0.1. Another smallbranching factor ratio comes at from the the suppression level of of the reasonable mechanisms. Their relativebut numb in all the casesto it not is overclose not negligibly the small universe (and with in heavy fact in objects): some cases we should take care If they are predominantly createddensity by can gravitati be estimated [ guess. This result depends upon the concrete scenario of heavy particle, U where the (re)heating temperature simplified estimate follows fromheavy the and made thermalized above particles, statementmagnitude, that created i.e. the by energy the density inflaton of decays, the are of the same order of they may become dominant, even if their energy with the energy density ofbaryogenesis relativistic through particles. These features could lead to very efficient naturally in the same TeV range and heavy particles, number fraction mayabout be noticeable, even close to unity. Moreover, if their lifetime is JCAP04(2007)005 ]: 16 55 CP (22) ) is at the level of a few ∗ M allows for a much larger T GeV and superheavy particles 19 10 stacks.iop.org/JCAP/2007/i=04/a=005 natives to black holes as intermediate ∼ these same black holes, then a possible gher dimensional objects, such as string Pl e and testable candidate for cosmological M ] is true, the lifetime of the LSP might still be , can be easily equal to the measured value [ 39 β 04 (2007) 005 ( . 10 − ther large extra dimensions or time-varying Planck mass. 10 × Baryogenesis from gravitational decay of TeV particles in theories with low scale gravity =6 γ B n n = β is in the TeV range. Here, baryon number can be violated by gravitational ∗ -branes, or black branes may serve as alter p M We would like to stress that a low reheating temperature which possibly excludes a If SUSY particles were unstable to decay via We also mention the possibility that other hi Our model requires a minimal extension of the particle content of the standard model. The value of the baryon asymmetry is model dependent and cannot be predicted Journal of Cosmology and Astroparticle Physics efficient in creating cosmologicalexpect baryon that the asymmetry. baryon Taking to all photon ratio, the factors together we violation from the Cabibbo–Kobayashi–Maskawa (CKM)cannot matrix. work In with fact, the our standard mechanism Planck mass period of unbroken electroweak symmetry isof not a the problem here model, butwashing a out favourable since ingredient previously created it asymmetry. prevents Moreover, low dangerous electroweak sphaleron processes capable of decays of TeVand particles, quickly which decay are throughmatter–antimatter produced asymmetry. a out black of hole thermal intermediate state, equilibrium generating after the inflation cosmological We have consideredscale baryogenesis scenarios in models where the true quantum gravity 5. Conclusion TeV and heavy elementaryor particles to exist, accept) one the can model possibly in the test next (and generation therefore of to hadron reject colliders. negative consequence of the modelparticle would (LSP), be the which instabilitydark may of matter. exclude the However, lightest a if supersymmetric our very conjecture nic [ We thank F Urban for useful comments and suggestions. Acknowledgments states responsible forprocesses. baryogenesis, though we have not computed any rates for such The scenario may operatemodels which with may the provide a standardgravitational resolution set scales, to of the due hierarchy quarks. problem to between ei We electroweak considered and TeV gravity precisely since it dependsimplicit) upon in many all unknowns other but scenarios the of same baryogenesis. shortcoming is explicit (or long enough to providemass the of dark the matter, LSP. depending upon the quantum numbers and the One variation we considered requirescreated time by variation some of new the scalar Planck mass fields. and quark masses balls, with masses of the same order of magnitude. 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