• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Cosmic inflation from broken conformal symmetry

    2022-10-22 08:15:06RongGenCaiYuShiHaoandShaoJiangWang
    Communications in Theoretical Physics 2022年9期

    Rong-Gen Cai,Yu-Shi Hao and Shao-Jiang Wang

    1 CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China

    2 School of Fundamental Physics and Mathematical Sciences,Hangzhou Institute for Advanced Study(HIAS),University of Chinese Academy of Sciences (UCAS),Hangzhou 310024,China

    3 School of Physical Sciences,University of Chinese Academy of Sciences(UCAS),Beijing 100049,China

    Abstract A period of rapidly accelerating expansion is expected in the early Universe implemented by a scalar field slowly rolling down along an asymptotically flat potential preferred by the current data.In this paper,we point out that this picture of the cosmic inflation with an asymptotically flat potential could emerge from the Palatini quadratic gravity by adding the matter field in such a way to break the local gauged conformal symmetry in both kinetic and potential terms.

    Keywords: Palatini gravity,modified gravity,conformal symmetry,cosmic inflation

    1.Introduction

    A simultaneous resolution for the fine-tuned horizon problem,flatness problem,and monopole problem calls for a period of rapidly accelerating expansion of spacetime[1–8]in the early Universe at least prior to the big bang nucleosynthesis.This inflationary paradigm also provides the causal productions for the primordial cosmological perturbations with a nearly scale-invariant spectrum [9–16]responsible for the observed cosmic microwave background [17,18]and large-scale structures [19,20].The standard realization for such an inflationary period usually turns to a slow-roll scalar field along with some inflationary potential [8].The most recent constraint [21]on cosmic inflation still prefers a single-field slow-roll plateau-like potential.

    There are two popular implements for such a plateau-like potential:the simplest one is the Starobinsky inflation[2]with an additional quadratic term for the Ricci scalar curvature R;the most economic one is the Higgs inflation [22]with the only known fundamental scalar field (Higgs boson) so far as the inflaton non-minimally coupled to R.It was realized in recent years that they could be all constructed in general from the cosmological attractors [23]to consist of the α-attractors[24–28](including the Starobinsky inflation as a special case[29]) and ξ-attractors [30](including the Higgs inflation and induced inflation [31–35]as special cases).

    It is then intriguing to explore the theoretical origin of these asymptotically flat potentials.The current observational data merely reveals two clues: (i) a plateau-like potential is supposed to admit an approximate shift symmetry,which should be slightly broken to protect an asymptotically flat potential against quantum corrections.(ii) A nearly scaleinvariant spectrum of primordial perturbations suggests a slightly broken scale symmetry in the very early Universe from de Sitter (dS) to quasi-dS phases.An appealing understanding of cosmic inflation should explain the roles played by these two symmetries.

    Motivated by the superconformal approach [36–38]to the Higgs-like inflation and Starobinsky inflation[39,40],the α-attractor approach is able to really appreciate the role played by the conformal(scale)symmetry.The starting point of this approach is an old observation that a single real conformal compensator(a scalar field called conformon)with the Lagrangianis equivalent to the pure Einstein gravity with a positive cosmological constant 9λ(thus a dS solution)after gauge-fixing the conformon field to some constant thanks to the local conformal symmetry of the Lagrangian.

    Although the gauge-fixing for the conformon field eliminates the concern for the presence of ghost from the wrong-sign kinetic term,the conformon field cannot be gauge-fixed if one tries to construct any nontrivial structure(namely inflation with quasi-dS phase)by explicitly breaking the local conformal symmetry.Therefore,the α-attractor approach introduces an extra scalar field with a joint global symmetry [24,25,39,40]with the conformon field but still leaves the local conformal symmetry unbroken in order to fix the gauge of the would-be-ghost conformon field.After gauge-fixing,the local conformal symmetry is spontaneously broken,and the global-symmetry-breaking potential leads to an asymptotically flat potential.However,the global symmetry for a successful inflationary implementation is restricted due to the wrong-sign kinetic term required by the local conformal symmetry.

    The introduction of the conformon field with wrong-sign kinetic term could be avoided if one dives into the Palatini formalism of gravity [41,42]where the metric and affine connection are treated as independent degrees of freedom.In the Palatini formalism,the conformon field with wrong-sign kinetic term naturally emerges as a geometric gauge degree of freedom from the R2term (see equation (14) below),which has been already derived but overlooked in [43].The focus there is mainly on the dynamical recovering of the metric Einstein gravity in the absence of matter field in the Palatini formalism of a general quadratic gravity with the local conformal symmetry.The metric Einstein gravity therefore emerges at the decoupling limit of the Weyl gauge field after eating up the dilaton field?μlnφ2with a shift symmetry inherited from the local gauged conformal symmetry of φ.See [44–46]for a similar realization in the Weyl quadratic gravity and a comparison to the Palatini quadratic gravity[47]as well as its concrete realizations in the standard model of particle physics [48]and cosmology [49].See also [50–55]for other trials.

    However,to carry out an inflationary potential in the Palatini formalism in a conformally invariant manner,it seems that a global symmetry shared with an additional scalar field is still needed to be slightly broken[56,57]similar to the α-attractor approach.Nevertheless,we will point out in this paper that,in the Palatini quadratic gravity,the presence of an additional global symmetry is not necessary as also expected from the swampland conjecture [58–61]of no global symmetry in quantum gravity.Without introducing any global symmetry,a plateau-like inflationary potential is always implied when the matter field is included in such a way to appropriately break the local conformal symmetry.

    The outline of this paper is as follows: In section 2,we review previous results on the emergence of metric Einstein gravity from Palatini quadratic gravity.In section 3,we show the emergence of non-plateau-like and plateau-like inflation models when adding the matter field differently in terms of the local conformal symmetry.We summarize our results and discuss possible future perspectives in section 4.The convention for metric gμνis(-,+,+,+),the Planck mass isMPl≡and quantities with an overbar symbol (like the Ricci scalarand covariant derivative) are always subjected to the Levi-Civita connectionThe Riemann tensor and its variation under the connection variationrespectively,where the torsion tensorTμρν=Γρμν-Γνρμwill beTμρν=Γρμν-Γνρμin teleparallel equivalent of general relativity simply set to zero hereafter for convenience due to the geometric trinity of gravity[62].We remind here that the geometric trinity of gravity is an equivalence among three different ways to describe gravity: the traditional way of using Riemann tensorRαβμνin general relativity describes a rotation of vector after transported in parallel along a closed curve,while the torsion tensor describes the non-closure of parallelograms formed by two vectors transported along each other,and the non-metricity tensorQλμν=?λ gμνin symmetric teleparallel equivalent of general relativity describes the dilation of the length of a vector when transported along a curve.This geometric trinity of gravity might be jeopardized when the matter field is added.We,therefore,leave the case with the presence of the torsion field for future work.

    2.Palatini quadratic gravity

    In this section,we review the Palatini quadratic gravity with a local conformal symmetry,which reduces to the metric Einstein gravity with a positive cosmological constant when fixing the gauge of the local conformal symmetry.Although most of the derivations in this section have been presented before in [43],we re-derive these results to set up our notations and conventions to be used later on.

    2.1.Palatini R2 gravity

    We start with the Palatini R2gravity with an action of a form

    whose field equation for metric reads

    Despite the trivial solution R=0,the non-trivial part of the field equation for metric is (differ from the usual GR case with an extra factor of 1/2 in front of the Ricci scalar)

    whose trace is identically satisfied (unlike the usual GR case that the trace part of the Einstein field equation gives rise to the vacuum solution R=0).Therefore,despite the trivial solution R=0,the trace part of the field equation for metric puts no constraint on Ricci scalar R,and the only constraint on R comes from the equation of motion (EoM) for the symmetric connection,

    which,after substituted with its trace in λ=ν by=0,becomes

    Expanding the above equation as

    by the non-metricity te nsorQλμν=?λ gμνand non-metricity vector Qλ=gμν?λgμνfollowed by contracted with gμν,one has

    Note that the action(1)is actually a redundant description due to the local conformal symmetry,S[g,Γ]=under the local conformal transformations,

    since the Ricci scalar-squareR(g,Γ)2=(gμν Rμν(Γ))2=compensates the contribution fromTo fix this gauge symmetry,one should fix one of the scalar degree of freedom,for example,gaugefixing R to some constant C ≠0.Then,the equation (7)reduces to the vanishing non-metricity with the metric compatible Levi-Civita connection,and the equation (3) reduces to the usual GR case of the Einstein field equation with a nonvanishing cosmological constant Λ=C/4.Note that the vacuum solution R=0 automatically satisfies the connection EOM(7),therefore,only in this case,it does not reduce to the metric Einstein gravity with a cosmological constant.In what follows,we will not consider the case with R=0.

    We can also introduce an auxiliary fieldφ22=F′(φ)=αφin the expansion ofF(R)=F(φ)+F′ (φ)(R-φ)for F(R)=(α/2)R2,and then arrive at an equivalent Jordan frame action

    which reduces to(1)when putting φ-field on-shell by its EoM φ2/2=αR.This Jordan-frame action enjoys a local gauged conformal symmetry,S[g,Γ;φ]=under the local gauged conformal transformations

    where φ is actually a gauge degree of freedom of the shift symmetry ln=lnφ-ln Ωcompensating the local conformal transformation (8).However,unlike in the metric formalism,the auxiliary field φ is not a dynamical degree of freedom.This could be seen after conformally transforming(9) into the Einstein-frame action as

    with a specific conformal factor Ω(x)2=φ(x)2MP2l.Note that φ remains unchanged during the local conformal transformations (8) and it only transforms as=Ω-1φwhen testing for the local gauged conformal symmetry.It is easy to see that this Einstein-frame actionis equivalent to the Jordan-frame action S[g,Γ;φ]by directly gauge-fixing φ to MPlthanks to the local gauged conformal symmetry of φ.Now that the Einstein-frame action is minimally coupled,putting the connection on-shell reproduces the Levi-Civita connection,and the metric-affine geometry reduces to the Riemannian geometry.Hence the metric Einstein gravity is recovered in a gauge-fixing form but with an additional positive cosmological constant.

    Equivalently [43],provides alternative treatment on the action (9) by first putting the connections on-shell before making either local conformal transformations (8) or gaugefixing φ to MPl.Note that the torsionless version of Stokes’theorem in Palatini formalism renders ∫ d4x?μ=0,one obtains the EoM of the connection,

    which,after contracting ν=λ,gives rise to an equation=0that could be rewritten as=0 in terms of a metric-compatible auxiliary metric fμν≡φ2gμν.Therefore,the connection could be solved as the Levi-Civita connectionin terms of fμν,which,after expressed in terms of gμνexplicitly,becomes

    with abbreviatingGμ≡?μlnφ2=lnφ2=?μlnφ2.Note that with on-shell connection,the Weyl gauge feildAμ≡=Gμis fxied and determined by Gμfeild alone,which is in fact related to the fact that the action (9) is invariant under the projective transformation=Γρμν+δρμξν(x)for an arbitrary vector feild ξμ(x)used for gauge-fxiing Aμ.Putting the connectionΓμρνon-shell(OS)with solution(13),the Ricci scalar readsR(g,ΓOS)=and the action (9) becomes

    which is exactly the Lagrangian form with a wrong-sign kinetic term desired by the α-attractor approach in the first place.The on-shell action (14) also enjoys a local gauged conformal symmetry,S[g;φ]=under the local gauged conformal transformations

    thanks to the plus sign of+3 (φ)2(namely conformon)that is crucial for exact cancellations with respect to the Ω-dependent terms inNow that φ is a gauge degree of freedom,one can either directly gaugefxi φ to MPlor choose a specifci conformal factorΩ2=φ2MP2lto conformally transform(14) viaS[gμν=Ω-2;φ]as

    which is exactly the action (11) with on-shell connection.

    In a short summary,the R2term in the Palatini formalism contributes an extra non-dynamical gauge degree of freedom φ of shift symmetry ln=lnφ2-ln Ω2under the local gauged conformal transformations (10) or (15).Therefore,lnφ2andGμ=?μlnφ2behave like the dilaton field and the would-be Goldstone field,respectively.After gauge-fixing φ to MPl,the metric Einstein gravity with a positive cosmological constant is recovered.

    2.2.Palatini R2+ gravity

    which also enjoys a local gauged conformal symmetry,S[g,Γ;φ]=under the local gauged conformal transformations (10).Note that=Aμ-?μln Ω2does not transform independently from the local conformal transformations (8) but inherited from(g)=-2?μln Ω2under the local conformal transformations(8).It is easy to see that both(18)and(19)admit additional gauge shift symmetry under=Aμ-?μω2for an arbitrary gauge function ω(x),and hence Aμis actually a gauge degree of freedom.It is worth noting that this gauge shift symmetry of Aμis different from the gauge shift symmetry of φ since ω does not need to coincide with the local conformal transformation factor Ω.

    Alternatively [43],provides another intriguing view on the action (19) by first putting the connection on-shell before making either local conformal transformations (8) or gaugefixing φ to MPl.The EoM of the connection is obtained as

    Note that at this point Aμdoes not enjoy the arbitrary gauge shift symmetry underA?μ=Aμ-?μω2anymore.It seems that putting the connection on shell picks out a particular gauge choice ω=Ω for Aμwhen transformed coherently with the local gauged conformal transformations (15).Note also that,putting the connection on-shell does not fix all its components but leaves Aμundetermined since contracting ρ=ν in(21)simply reduces to a trivial identity.This is caused by the explicitly broken projective symmetry of (19) and (23) under the projective transformation=Γρμν+δρμξν(x)for an arbitrary vector field ξμ(x),which would otherwise fix the Weyl gauge field Aμ.This is different from the case in section 2.1 where Aμis fully determined byAμ=Gμ≡?μlnφ2since the projective symmetry is not broken there.

    Finally,the on-shell action(23)still enjoys the local gauged conformal symmetry,S[g,A;φ]=under the local Ω2=to conformally transform (23) into the Einsteingauged conformal transformations (15),one can either directly gauge-fix φ to MPlor choose a specific conformal factor frame action byS[gμν=as

    which is the Palatini Einstein gravity with a positive cosmological constant plus a Proca gauge field action.Fixing the gauge of φ breaks the local gauge conformal symmetry of (23),and the would-be Goldstone field Gμis therefore absorbed by Aμto render a massive gauge feild with a massmA2=6β2MP2l.When Aμis decoupled below mA,the metricity is deduced and the metric Einstein gravity with a positive cosmological constant is therefore recovered at this decoupling limit.

    One can also arrive at the same result as(24)from(19)by putting the connection on-shell after making either local conformal transformations(8)or gauge-fixing φ to MPl.In specific,since the action (19) is locally gauged conformal invariant,we can fix the gauge of φ to some constant scale MPl,

    which,after putting Γ on-shell,reduces to the same form as(24)(but without over-tilde symbols).We can also choose a specific conformal factorΩ2=φ2MP2lto conformally transform (19)into the Einstein-frame action byS[gμν=,Γρμν=;φ]as

    3.Inclusion of matter field

    Now that the Palatini quadratic gravity simply reproduces the metric Einstein gravity with a positive cosmological constant in a gauge-fixing form,we need to add matter field to the Palatini quadratic gravity in order to account for the inflaton field responsible for the cosmic inflation.There are two ways to add the matter field:either preserving or breaking the local gauged conformal symmetry.

    3.1.Preserving the local conformal symmetry

    3.1.1.Palatini R2gravity.We start with the Palatini R2gravity with the inclusion of a matter field h as

    Note that at this point Aμis not an independent degree of freedom from the connectionΓμρν,thus one cannot separately vary the actions (27) or (29) with respect to AμfromΓμρν.In fact,Aμonly becomes an independent residual degree of freedom after putting the connection on-shell due to the explicit presence of Aμin the Dμterm that breaks the projective symmetry,

    which would otherwise fix the Weyl gauge field Aμfrom gaugefixing the arbitrary vector field ξμ(x).To put the connection onshell,one first varies the action(29)with respect to theΓμρν,and then obtain the EoM for the connection as

    This gauge symmetry allows us to fix one of the scalar degrees of freedom,for example,gauge-fixing ρ to the Planck scale MPl,and then the action (32) reduces to

    Due to the absence of kinetic term for Aμ,it can be integrated out by putting it on-shell via its EoM(a constraint equation),

    and then the action further reduces to

    which,after normalizing the kinetic term by redefining

    becomes

    with the potential U(h(φ),MPl) abbreviated as W(φ) of form

    If all effective potential terms of the matter field are absent(namely ξ=0 and λ=0),the final reduced theory is the metric Einstein gravity with a cosmological constant.Otherwise,the potential W(φ) does not admit an asymptotically flat potential since W(φ)is divergent at φ→∞limit.In fact,W(φ)supports a small-field tachyonic inflation at small φ limit for hierarchical couplings αλ ?ξ2?1 with the approximated potential

    from which the slow-roll parameters can be expanded as

    Therefore,the consistency relation r=-8ntis unchanged but the scalar spectral index ns=1+2η*-6∈* and the tensor-toscalar ratio r=16∈*evaluated at the horizon crossing of some pivot scale k*=a(t*)H(t*) is related by

    3.1.2.Palatini R2+gravity.Parallel discussions also apply for PalatiniR2+R[2μν]gravity with an action of form

    which,after replacing α2R2=φ2R-φ4/(4α),becomes

    with ρ2≡φ2+ξh2and U(h,ρ)≡(λ/4)h4+(ρ2-ξh2)/(8α)as defined before.To put connection on-shell,solving the EoM of the connection from the action (45),

    admits the same solution as(21),and the action(45)with onshell connection becomes

    which still enjoys a local gauged conformal symmetry,S[g,A;h,ρ]=under the local gauged conformal transformation (33).Again,this allows us to gauge-fix ρ to MPl,and the reduced action reads

    This is the same action proposed in [43]for the Palatini R2inflation with the same small-field tachyonic inflationary feature as (38).In a short summary,when the matter field is added in a way to preserve the local conformal symmetry(usually also break the projective symmetry at the same time),the asymptotically flat inflationary potential is not implied.

    3.2.Breaking the local conformal symmetry

    3.2.1.Palatini R2gravity.To break the local gauged conformal symmetry,we propose to replace the gauge covariant derivative Dμin (44) with a normal covariant derivative ?μ,namely.

    As we will see shortly below that the cosmic inflation with an asymptotically flat potential is always obtained if one further breaks the local gauged conformal symmetry in the non-minimal coupling or matter potential by adding lower-than-quadratic terms beyond G(h)=ξh2or higher-than-quartic terms beyond V(h)=(λ/4)h4so that the ratioV(h) G(h)2is an increasing function of h at a large h limit.

    Similar to the previous sections,we first extract the scalar degree of freedom in the R2term by replacing α2R2=φ2R-φ4/(4α),then we obtain the Jordan-frame action

    If both the non-minimal coupling G=ξh2and the matter potential V=(λ/4)h4include no extra dimensional scales,then the effective potential W is merely a cosmological constant,

    However,if G(h) or V(h) is amended with additional dimensional scales to break the local gauged conformal symmetry in such a way that G contains lower-than-quadratic terms,or V contains higher-than-quartic terms,

    Note that the inflationary potential W is even more flattened when the potential V becomes very steep.Therefore,this k-inflation [63,68]but with an asymptotically flat potential largely emerges as a result of the broken local gauged conformal symmetry in both matter kinetic and potential terms(regarding the non-minimal coupling term as some kind of effective potential term induced by the background gravity).

    respectively,from which the scalar/tensor spectral indexes and tensor-to-scalar ratio evaluated at the horizon crossing moment of some pivot scale k*=a(t*)H(t*)/cs(t*) are obtained as

    It can be numerically checked that this approximation is sufficiently stable for model predictions,which are the functions of N* with input parameters λ,ξ,and α.In order to identify the parameter regions of observational interest,we can use the measured values of nsand Asto fix λ,ξ,

    and then the tensor-to-scalar ratio reads

    Requiring r to be smaller than the current upper bound r0.05<0.036 [70],α should satisfy

    Using the best-fit values ns=0.9649 and ln (1 010As)=3.045 from Planck 2018 TT,TE,EE+lowE constraints [18],we finally identify the parameter space of α as

    The remaining freedom on N* can be traced back to different reheating histories.In general,as long as the above condition on α is satisfied,one can always find the parameter regions for λ and ξ to simultaneously meet the observational constraints ns=0.9649,ln (1010As)=3.045and r0.05<0.036.

    3.2.2.Palatini R2+gravity.Parallel discussions also apply for PalatiniR2+R[2μν]gravity with an action of form

    which,after replacing α2R2=φ2R-φ4/(4α),becomes

    Putting the connection on-shell with the same solution (21)gives rise to an action of a form

    which,after conformally transformed into Einstein frame viawith a specific conformal factorΩ2=,is reduced into

    When Aμis decoupled below the scale 6βMPl,we return back to (52) that immediately leads to the K-essence theory(54) and hence an asymptotically flat inflationary potential is similarly obtained.In a short summary,the asymptotically flat potential emerges as a result of breaking the local conformal symmetry appropriately for both scalar kinetic and effective potential terms,and is independent of the presence or absence of the projective symmetry as shown for (49) or (91),respectively.

    4.Conclusions and discussions

    Cosmic inflation is the standard pillar for the standard model of modern cosmology,describing a period of nearly exponential expansion of spacetime in the very early Universe to solve several fine-tuning problems of the standard hot big bang scenario and generate nearly scale-invariant primordial perturbations observed in the cosmic microwave background and large scale structures.The current observational data prefers a single-field slow-roll plateau-like inflationary potential,which could be theoretically motivated from the cosmological attractor approach.A conformon field with a wrong-sign kinetic term is introduced to respect the local conformal symmetry and a second scalar field is added in such a way to impose an additional global symmetry jointed with the conformon field,which is broken by the potential term but with the local conformal symmetry intact.After fixing the gauge of conformon field,the potential term with broken global symmetry gives rise to the exponentially flattened inflationary potential.

    However,this approach introduces the wrong-sign conformon field at the price of introducing an additional global symmetry for inflationary model buildings.Nevertheless,the wrong-sign conformon field could naturally arise in the Palatini quadratic gravity,though an additional global symmetry is also adopted for inflationary model buildings.In this paper,we point out that,in Palatini quadratic gravity,such an encumbrance of an additional global symmetry is needless.Appropriately breaking the local conformal symmetry alone for both kinetic and potential terms of a matter field is sufficient to produce an asymptotically flat inflationary potential regardless of the high steepness of original matter potential.

    For future perspectives,it is still mysterious what position should we find for the Palatini quadratic gravity in approaching the underlying quantum gravity.A related question is that,for Palatini quadratic gravity without matter field or with conformally invariant matter field,since the local conformal symmetry is a gauge symmetry,then what causes this redundancy or what is the origin for this local conformal symmetry?This is a profound question[71,72]on how gauge symmetry emerges from more physical symmetry [73,74].

    The next question concerns the transition from the local conformally symmetric matter phase to the locally conformalsymmetry broken matter phase.Breaking the local conformal symmetry in matter potential is easy by quantum corrections or renormalization group flow.However,the reduction of a gauge covariant derivative term into a normal covariant derivative term is unclear.A dynamical mechanism for triggering such a broken conformal symmetry in the kinetic term is desirable.

    The last question runs into the initial conditions for the cosmic inflation,which is usually the realm of the quantum cosmology [75]for the no-boundary [76,77]and tunneling[78–82]proposals.As far as we know,there is currently no study on quantum cosmology starting from the Palatini quadratic gravity,which might be related to the recent new result [83]in presence of non-minimal coupling compared to the case of absence [84,85].

    Acknowledgments

    We thank Li Li,Run-Qiu Yang,Shan-Ming Ruan for helpful discussions.This work is supported by the National Key Research and Development Program of China Grant No.2020YFC2201501,the National Natural Science Foundation of China Grants No.12105344,No.11 647 601,No.11821505,No.11851302,No.12047503,No.11991052,No.12075297 and No.12 047 558,the Key Research Program of the CAS Grant No.XDPB15,the Key Research Program of Frontier Sciences of CAS,and the Science Research Grants from the China Manned Space Project with NO.CMS-CSST-2021-B01.

    午夜精品一区二区三区免费看| 国产爱豆传媒在线观看| 日韩国内少妇激情av| 丁香六月欧美| 亚洲精品456在线播放app | www日本黄色视频网| 午夜福利在线在线| 我的老师免费观看完整版| 国语自产精品视频在线第100页| 婷婷亚洲欧美| 91狼人影院| 伦理电影大哥的女人| 久久久久国产精品人妻aⅴ院| 国产亚洲精品av在线| 欧美日本视频| 赤兔流量卡办理| 国产亚洲精品综合一区在线观看| 亚洲中文日韩欧美视频| 如何舔出高潮| 很黄的视频免费| 久久久久性生活片| 51国产日韩欧美| 男人和女人高潮做爰伦理| 欧美乱妇无乱码| 欧美成狂野欧美在线观看| 一本一本综合久久| 国产精品久久久久久人妻精品电影| av视频在线观看入口| 一夜夜www| 我要搜黄色片| 51午夜福利影视在线观看| 极品教师在线免费播放| 少妇裸体淫交视频免费看高清| 性色av乱码一区二区三区2| 亚洲五月天丁香| 别揉我奶头~嗯~啊~动态视频| 亚洲人成伊人成综合网2020| 久久久国产成人精品二区| aaaaa片日本免费| 亚洲人与动物交配视频| 欧美成狂野欧美在线观看| 97热精品久久久久久| 一区二区三区免费毛片| 中亚洲国语对白在线视频| 性插视频无遮挡在线免费观看| 男女视频在线观看网站免费| 69av精品久久久久久| 免费搜索国产男女视频| 国产精品久久视频播放| 午夜免费激情av| 亚洲欧美清纯卡通| 麻豆成人午夜福利视频| 午夜激情欧美在线| 欧美色欧美亚洲另类二区| 麻豆av噜噜一区二区三区| 午夜激情福利司机影院| 成人鲁丝片一二三区免费| 又爽又黄a免费视频| 欧美潮喷喷水| 亚洲av五月六月丁香网| 看十八女毛片水多多多| 国产精华一区二区三区| 亚洲第一欧美日韩一区二区三区| 精品久久久久久久久久免费视频| 亚洲精品一卡2卡三卡4卡5卡| 亚洲专区中文字幕在线| 丰满人妻一区二区三区视频av| 午夜亚洲福利在线播放| 俺也久久电影网| 久久草成人影院| 亚洲男人的天堂狠狠| 搡老熟女国产l中国老女人| 欧美+亚洲+日韩+国产| 久久中文看片网| 国产不卡一卡二| 亚洲电影在线观看av| 91午夜精品亚洲一区二区三区 | 高潮久久久久久久久久久不卡| 成人精品一区二区免费| 免费av观看视频| 亚洲成av人片在线播放无| 久久精品国产亚洲av涩爱 | 免费在线观看影片大全网站| 精品人妻1区二区| 午夜a级毛片| 国产成年人精品一区二区| 国产真实乱freesex| 看免费av毛片| 欧美+日韩+精品| 99视频精品全部免费 在线| 身体一侧抽搐| 中文字幕人成人乱码亚洲影| 日本五十路高清| 嫩草影视91久久| 欧美在线黄色| 五月玫瑰六月丁香| 黄色视频,在线免费观看| av视频在线观看入口| 男女视频在线观看网站免费| 欧美绝顶高潮抽搐喷水| 91在线观看av| 男女床上黄色一级片免费看| av女优亚洲男人天堂| 老司机午夜福利在线观看视频| 久久精品夜夜夜夜夜久久蜜豆| 啦啦啦韩国在线观看视频| 丰满乱子伦码专区| 永久网站在线| 少妇人妻精品综合一区二区 | 亚洲无线在线观看| 高清毛片免费观看视频网站| 97超视频在线观看视频| 99久久九九国产精品国产免费| 99久久无色码亚洲精品果冻| 一区二区三区激情视频| 欧美不卡视频在线免费观看| 亚洲精品久久国产高清桃花| 在线观看免费视频日本深夜| 桃色一区二区三区在线观看| 丰满人妻一区二区三区视频av| 中国美女看黄片| 午夜激情福利司机影院| 欧美+亚洲+日韩+国产| 中文字幕精品亚洲无线码一区| 51国产日韩欧美| 色视频www国产| 欧洲精品卡2卡3卡4卡5卡区| 日本精品一区二区三区蜜桃| a级一级毛片免费在线观看| 床上黄色一级片| 高清在线国产一区| 国产91精品成人一区二区三区| 18禁黄网站禁片午夜丰满| 性色av乱码一区二区三区2| 又紧又爽又黄一区二区| www.www免费av| 一区二区三区激情视频| 伦理电影大哥的女人| 欧美极品一区二区三区四区| 一本一本综合久久| 亚洲av熟女| 性色av乱码一区二区三区2| a级毛片免费高清观看在线播放| 色5月婷婷丁香| 老师上课跳d突然被开到最大视频 久久午夜综合久久蜜桃 | 亚洲欧美日韩东京热| 黄片小视频在线播放| 亚洲人成网站在线播放欧美日韩| 日本熟妇午夜| 我的老师免费观看完整版| .国产精品久久| 亚洲精品一卡2卡三卡4卡5卡| 国产精品1区2区在线观看.| 在线天堂最新版资源| 欧美日韩综合久久久久久 | 搡老岳熟女国产| 国产午夜精品久久久久久一区二区三区 | 中文字幕免费在线视频6| 69av精品久久久久久| 偷拍熟女少妇极品色| 国产一区二区三区在线臀色熟女| 嫩草影院新地址| 99国产精品一区二区蜜桃av| 久久午夜亚洲精品久久| 婷婷丁香在线五月| 美女被艹到高潮喷水动态| 国产伦一二天堂av在线观看| 精品福利观看| 好男人电影高清在线观看| 久久人人精品亚洲av| 国产成年人精品一区二区| 久久精品国产亚洲av香蕉五月| 久久亚洲精品不卡| 九九久久精品国产亚洲av麻豆| 久久精品国产自在天天线| 男女下面进入的视频免费午夜| 国产精品久久久久久精品电影| 哪里可以看免费的av片| 色综合站精品国产| 午夜亚洲福利在线播放| 中国美女看黄片| 无人区码免费观看不卡| 国产精品伦人一区二区| 丰满人妻熟妇乱又伦精品不卡| 夜夜躁狠狠躁天天躁| 一个人看视频在线观看www免费| 欧美区成人在线视频| 日韩人妻高清精品专区| 日韩中字成人| 国产亚洲精品久久久com| 看片在线看免费视频| 国产av在哪里看| 精品久久国产蜜桃| 成人无遮挡网站| 高潮久久久久久久久久久不卡| 国产精品综合久久久久久久免费| av视频在线观看入口| 中文在线观看免费www的网站| 国产视频一区二区在线看| 长腿黑丝高跟| 色av中文字幕| 国产爱豆传媒在线观看| 亚洲aⅴ乱码一区二区在线播放| 精品久久久久久久久久久久久| 身体一侧抽搐| 69av精品久久久久久| 99热精品在线国产| 久久国产乱子免费精品| 麻豆国产av国片精品| 欧美绝顶高潮抽搐喷水| 国产一区二区激情短视频| 人妻久久中文字幕网| 国产老妇女一区| 国产一区二区三区在线臀色熟女| 极品教师在线视频| 99国产精品一区二区三区| 免费av毛片视频| 亚洲人成伊人成综合网2020| 亚洲 欧美 日韩 在线 免费| 欧美一区二区亚洲| 国产色婷婷99| 亚洲精品日韩av片在线观看| 能在线免费观看的黄片| 亚洲人成网站在线播放欧美日韩| 国产伦人伦偷精品视频| 欧美色欧美亚洲另类二区| 免费av观看视频| 日本免费一区二区三区高清不卡| 久久久成人免费电影| 欧美一区二区亚洲| bbb黄色大片| 淫妇啪啪啪对白视频| 一级黄色大片毛片| 久久精品国产自在天天线| 欧美激情在线99| 97超级碰碰碰精品色视频在线观看| 精品国内亚洲2022精品成人| 动漫黄色视频在线观看| 国产精品av视频在线免费观看| 亚洲七黄色美女视频| 男人狂女人下面高潮的视频| 国产精品不卡视频一区二区 | 给我免费播放毛片高清在线观看| av在线老鸭窝| 久久久久久九九精品二区国产| 88av欧美| 如何舔出高潮| av在线观看视频网站免费| 日韩欧美精品免费久久 | 一边摸一边抽搐一进一小说| 免费av观看视频| 久久中文看片网| 女人被狂操c到高潮| 亚洲电影在线观看av| 最近中文字幕高清免费大全6 | 91狼人影院| 黄片小视频在线播放| 97超级碰碰碰精品色视频在线观看| 特级一级黄色大片| 美女免费视频网站| 欧美zozozo另类| 亚洲国产精品久久男人天堂| 国产毛片a区久久久久| 亚洲精品日韩av片在线观看| 久久久成人免费电影| 18美女黄网站色大片免费观看| 99在线视频只有这里精品首页| 亚洲不卡免费看| 国产精品98久久久久久宅男小说| 亚洲美女黄片视频| 国产精品免费一区二区三区在线| 91在线精品国自产拍蜜月| 亚洲第一电影网av| 波野结衣二区三区在线| 色综合亚洲欧美另类图片| av视频在线观看入口| 成年女人毛片免费观看观看9| 欧美日韩国产亚洲二区| 村上凉子中文字幕在线| 欧美黑人巨大hd| 日本撒尿小便嘘嘘汇集6| 国产亚洲精品综合一区在线观看| 精华霜和精华液先用哪个| 男女之事视频高清在线观看| 桃色一区二区三区在线观看| 99精品在免费线老司机午夜| 全区人妻精品视频| av欧美777| 亚洲黑人精品在线| 国产成人啪精品午夜网站| 少妇熟女aⅴ在线视频| 人人妻,人人澡人人爽秒播| 九色成人免费人妻av| 美女高潮的动态| 亚洲va日本ⅴa欧美va伊人久久| 久久精品国产亚洲av香蕉五月| or卡值多少钱| 午夜福利视频1000在线观看| 99热这里只有是精品50| 成人特级黄色片久久久久久久| 午夜福利欧美成人| 最近最新免费中文字幕在线| 亚洲人成网站高清观看| 国产高清视频在线播放一区| 欧美一区二区国产精品久久精品| 国产中年淑女户外野战色| netflix在线观看网站| av中文乱码字幕在线| 欧美精品国产亚洲| 国产视频内射| 亚洲无线观看免费| 亚洲精品一区av在线观看| av视频在线观看入口| 午夜激情福利司机影院| 国产亚洲精品综合一区在线观看| 久久久久久九九精品二区国产| 久久久精品欧美日韩精品| 亚洲成人久久爱视频| 亚洲久久久久久中文字幕| 久久久久久久久久成人| 久久国产乱子免费精品| 日本免费a在线| 国产精品久久久久久久久免 | 一区二区三区激情视频| 国产三级黄色录像| 色av中文字幕| 国产亚洲精品久久久久久毛片| 亚洲精品粉嫩美女一区| 国产麻豆成人av免费视频| 亚洲,欧美,日韩| 日韩欧美一区二区三区在线观看| 99精品久久久久人妻精品| 搞女人的毛片| 久久精品夜夜夜夜夜久久蜜豆| 亚洲成av人片免费观看| 成人永久免费在线观看视频| 日韩欧美一区二区三区在线观看| 国产淫片久久久久久久久 | 午夜福利18| 嫩草影院入口| 啦啦啦韩国在线观看视频| 午夜福利18| 嫁个100分男人电影在线观看| 9191精品国产免费久久| 久久精品国产亚洲av香蕉五月| 狂野欧美白嫩少妇大欣赏| 欧美不卡视频在线免费观看| 国产成人福利小说| 精品午夜福利视频在线观看一区| 亚洲国产高清在线一区二区三| 免费观看人在逋| 亚洲人成网站高清观看| 成人三级黄色视频| 一本久久中文字幕| 欧美乱色亚洲激情| 免费av毛片视频| 国产视频内射| 精品一区二区三区视频在线观看免费| 九九热线精品视视频播放| 蜜桃久久精品国产亚洲av| 国内精品美女久久久久久| 淫秽高清视频在线观看| 中出人妻视频一区二区| 全区人妻精品视频| 亚洲熟妇熟女久久| 能在线免费观看的黄片| 在线观看舔阴道视频| 91午夜精品亚洲一区二区三区 | 91av网一区二区| 日韩欧美免费精品| 日本黄色片子视频| 国产精品亚洲美女久久久| 久久欧美精品欧美久久欧美| 听说在线观看完整版免费高清| 欧美丝袜亚洲另类 | 日本黄色片子视频| 少妇高潮的动态图| 99久久精品热视频| x7x7x7水蜜桃| 欧美区成人在线视频| 深爱激情五月婷婷| 国产综合懂色| 神马国产精品三级电影在线观看| 18禁在线播放成人免费| 别揉我奶头~嗯~啊~动态视频| 啦啦啦韩国在线观看视频| 国产免费一级a男人的天堂| 久久精品影院6| 又爽又黄无遮挡网站| 永久网站在线| 欧美成人性av电影在线观看| 精品99又大又爽又粗少妇毛片 | 精品福利观看| 久久久久久国产a免费观看| 色综合欧美亚洲国产小说| 一进一出抽搐gif免费好疼| 久久午夜福利片| 日韩欧美在线乱码| 久久精品国产清高在天天线| 中出人妻视频一区二区| 久久欧美精品欧美久久欧美| 亚洲最大成人手机在线| 欧美+日韩+精品| www.999成人在线观看| 性欧美人与动物交配| 精品国产亚洲在线| 免费人成视频x8x8入口观看| 人人妻人人看人人澡| 黄片小视频在线播放| 91麻豆av在线| 国产亚洲精品久久久久久毛片| 国产黄色小视频在线观看| 麻豆一二三区av精品| 久久这里只有精品中国| 亚洲成a人片在线一区二区| 我的老师免费观看完整版| 中国美女看黄片| 国产免费男女视频| 有码 亚洲区| 亚洲avbb在线观看| 成年女人看的毛片在线观看| 一区二区三区四区激情视频 | 亚洲色图av天堂| 国产精品av视频在线免费观看| 国产中年淑女户外野战色| 在线天堂最新版资源| 搡老妇女老女人老熟妇| 精品久久久久久久人妻蜜臀av| 欧美午夜高清在线| 欧美日韩福利视频一区二区| 国产伦在线观看视频一区| 久久精品国产自在天天线| 国产成人影院久久av| 中文字幕高清在线视频| 丁香欧美五月| 级片在线观看| 中文资源天堂在线| 97超视频在线观看视频| 欧美黄色淫秽网站| 色哟哟哟哟哟哟| 亚洲性夜色夜夜综合| 蜜桃久久精品国产亚洲av| 全区人妻精品视频| 国产精品日韩av在线免费观看| 久久精品国产99精品国产亚洲性色| av福利片在线观看| 国产av不卡久久| 熟女人妻精品中文字幕| 国产伦在线观看视频一区| 黄片小视频在线播放| 欧美3d第一页| 国产午夜福利久久久久久| 国产高清有码在线观看视频| 99久久精品一区二区三区| 热99在线观看视频| 很黄的视频免费| 精品一区二区三区人妻视频| 女人十人毛片免费观看3o分钟| 国产在线男女| 国产私拍福利视频在线观看| 国产精品伦人一区二区| 97人妻精品一区二区三区麻豆| 久9热在线精品视频| 亚洲中文字幕日韩| 亚洲黑人精品在线| 色综合婷婷激情| 亚洲精品色激情综合| 久久人妻av系列| 日韩欧美三级三区| 午夜视频国产福利| 一区二区三区四区激情视频 | 90打野战视频偷拍视频| 一个人看视频在线观看www免费| 嫩草影院入口| 一区二区三区高清视频在线| 很黄的视频免费| 午夜福利欧美成人| 亚洲人成网站高清观看| or卡值多少钱| 亚洲av二区三区四区| 久久午夜亚洲精品久久| 日本与韩国留学比较| 国产精品久久电影中文字幕| 欧美黑人欧美精品刺激| 波多野结衣巨乳人妻| 日本a在线网址| 免费av不卡在线播放| 一级作爱视频免费观看| 村上凉子中文字幕在线| 亚洲av不卡在线观看| 神马国产精品三级电影在线观看| 久久久国产成人免费| 欧美区成人在线视频| 观看美女的网站| 亚洲午夜理论影院| 嫩草影院精品99| 老女人水多毛片| 欧美在线黄色| 久久久国产成人精品二区| av天堂在线播放| 欧美xxxx性猛交bbbb| 在线观看av片永久免费下载| 男人和女人高潮做爰伦理| 成年女人看的毛片在线观看| 一本久久中文字幕| 日本成人三级电影网站| 欧美成人a在线观看| 欧美精品啪啪一区二区三区| 欧美性猛交╳xxx乱大交人| 国产亚洲精品综合一区在线观看| 丰满乱子伦码专区| 精品久久久久久久人妻蜜臀av| 国产黄a三级三级三级人| 亚洲三级黄色毛片| 国产高清视频在线观看网站| 又黄又爽又刺激的免费视频.| 国产私拍福利视频在线观看| 级片在线观看| 国产精品免费一区二区三区在线| 国产aⅴ精品一区二区三区波| 国产私拍福利视频在线观看| 亚洲午夜理论影院| 在线观看午夜福利视频| 欧美又色又爽又黄视频| 精品人妻一区二区三区麻豆 | 一进一出抽搐gif免费好疼| 国产精品久久久久久久久免 | 又爽又黄无遮挡网站| 97人妻精品一区二区三区麻豆| 色综合欧美亚洲国产小说| 亚洲精品色激情综合| 91狼人影院| 18禁裸乳无遮挡免费网站照片| 午夜福利在线在线| av黄色大香蕉| 极品教师在线免费播放| 亚洲人成网站在线播放欧美日韩| 国产日本99.免费观看| 亚洲综合色惰| 18+在线观看网站| 欧美黑人巨大hd| 精品人妻偷拍中文字幕| 夜夜夜夜夜久久久久| 宅男免费午夜| 亚洲无线观看免费| 国产精华一区二区三区| 自拍偷自拍亚洲精品老妇| 亚洲天堂国产精品一区在线| 乱人视频在线观看| 中文亚洲av片在线观看爽| 日本黄色片子视频| 亚洲av免费在线观看| 国产伦一二天堂av在线观看| 欧美成狂野欧美在线观看| 日韩成人在线观看一区二区三区| 99热这里只有是精品50| 搡老妇女老女人老熟妇| 国产高潮美女av| 中文字幕免费在线视频6| 国产欧美日韩精品亚洲av| 欧美日韩瑟瑟在线播放| 亚洲av免费高清在线观看| 91av网一区二区| 一级毛片久久久久久久久女| 看十八女毛片水多多多| 可以在线观看的亚洲视频| 久久亚洲精品不卡| 免费av观看视频| a在线观看视频网站| 日本与韩国留学比较| 精品久久久久久久久久免费视频| 免费观看人在逋| 三级国产精品欧美在线观看| 亚洲人成网站在线播| 亚洲av日韩精品久久久久久密| 婷婷精品国产亚洲av| 欧美色欧美亚洲另类二区| 99热只有精品国产| 特级一级黄色大片| av女优亚洲男人天堂| 搡女人真爽免费视频火全软件 | 成人av在线播放网站| 精品国产三级普通话版| 午夜日韩欧美国产| 男人的好看免费观看在线视频| 色在线成人网| 免费在线观看日本一区| 丝袜美腿在线中文| 国产精品久久久久久亚洲av鲁大| 乱码一卡2卡4卡精品| 国产伦人伦偷精品视频| av在线蜜桃| 欧美高清性xxxxhd video| 一个人免费在线观看的高清视频| 日韩中文字幕欧美一区二区| 国产精品伦人一区二区| 精品久久国产蜜桃| 国产视频一区二区在线看| 又爽又黄无遮挡网站| 九色成人免费人妻av| 又紧又爽又黄一区二区| 又爽又黄无遮挡网站| 麻豆国产97在线/欧美| 国产老妇女一区| 男人狂女人下面高潮的视频| 成年女人永久免费观看视频| 女同久久另类99精品国产91| 亚洲精品456在线播放app | 精品熟女少妇八av免费久了| 丰满的人妻完整版| 人人妻人人看人人澡| 国产亚洲精品久久久com| 男人舔女人下体高潮全视频| 国产亚洲精品av在线| 禁无遮挡网站|