• <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 ?

    Inflationary Cosmology with Quantum Gravitational Effects and Swampland Conjectures?

    2019-10-16 08:45:34QiangWu武強(qiáng)andTaoZhu朱濤
    Communications in Theoretical Physics 2019年9期
    關(guān)鍵詞:武強(qiáng)

    Qiang Wu(武強(qiáng))and Tao Zhu(朱濤)

    Institute for Theoretical Physics and Cosmology,Zhejiang University of Technology,Hangzhou 310032,China

    (Received April 4,2019;revised manuscript received April 21,2019)

    AbstractRecently proposed two swampland criteria that arising from string theory landscape leads to the important challenge of the realization of single-field inflationary models.Especially one of swampland criteria which implies a large tensor-to-scalar ratio is strongly in tension with recent observational results.In this paper,we explore the possibility the swampland conjectures could be compatible with single-field inflationary scenarios if the effects due to the quantum theory of gravity are considered.We show that the quantum gravitational effects due to the nonlinear dispersion relation provides significant modifications on the amplitude of both the scalar and tensor perturbation spectra.Such modifications could be either raise or reduce the perturbation spectra depending on the values of the parameters in the nonlinear terms of the dispersion relations.Therefore,these effects can reduce the tensor-to-scalar ratio to a smaller value,which helps to relax the tension between the swampland conjecture and observational data.

    Key words:inflation,quantum gravitational effects,swampland conjectures,uniform asymptotic approximation

    1 Introduction

    As one of the most promising candidates for an ultraviolet completed description of the quantum gravity that combines gauge and gravitational interactions,string/M theory is expected to provide possibilities for an explicit realization of the cosmological inflationary paradigm.Indeed,at effective level,there are a lot of phenomenological single scalar field inflation models that can arise from the String/M theory.However,in order to consistently embed such single scalar field inflation models into a quantum theory of gravity,it was proposed recently that they have to pass the two criteria of the swampland conjectures.[1?2]Specifically,the swampland conjectures includes two criteria,which state that the scalar inflaton field ? being consistent with a reasonable quantum description of gravity has to fulfill the following two conditions.

    ?The Swampland Criterion I(SCI):The excursion of the scalar field in the field space is bounded by[3]

    ?The Swampland Criterion II(SCII):The gradient of the scalar potential V(?)with V(?)>0 is limited by[4]

    where MPlis the reduced Planck mass and V?=dV(?)/d?.Here c1and c2are two positive constants of order unity.

    The first criterion is not surprise since it reflects the condition for the validity of the effective field theory of inflation and can be fulfilled by a lot of single scalar field inflation models.For the second criterion,it obviously violates the slow-roll condition,thus leads to a strong tension with the standard slow-roll inflation of the single scalar field inflationary models,[5?6]in which the slow-roll parameter ?Vis defined as

    ?The refined Swampland Criterion(rSCII):the derivatives of the scalar potential V(?)are limited by

    where V??=d2V/d?2and c3is a third positive constant with order one.This refined version of the swampland criterion is weaker than SCII and its implications on inflation and cosmology have been discussed extensively,see Refs.[33–40]for examples.For rSCI,it is observed that the original second swampland condition SCII now is included in rSCII as only one of possible conditions.It is because of rSCII,some of the single scalar field inflation models could be compatible with the swampland conjectures.However,SCII is still one of possible conditions and in the current research,we will concentrate on it and provide a proposal that could be used to relax its tension with observational data.

    In general,CMB temperature anisotropy derived from the inflation models are sensitive to the vacuum state of the perturbation modes.Since the energy scale of inflation at the earlier stage of the inflation is not far from the Planck energy,[41?42]one naturally expects that the effects of the quantum gravity can leave some effects on the perturbation modes,which could produce excited initial conditions for the inflationary perturbations.For instance,in loop quantum cosmology,an excited state on the primordial perturbation modes can be generated during the quantum bounce phase prior to the inflation.[43?47]A similar dynamics for quantum bounce can also be achieved in the framework of the effective field theory description of nonsingular bounce.[48]It is worth noting that the nonsingular bounces from the phenomenological considerations of the effective field theory analysis provides an alternative way to address the initial state issues of the primordial perturbations,see Refs.[48–51]for examples.In Hoava-Lifshitz theory of quantum gravity,such excited states can be produced by the contribution of high-order spatial derivative terms in the action of the theory,which also supply a nonlinear dispersion relation for the inflationary perturbations.[52?54]We note that such nonlinear dispersion relation can also arise from high-order extension of the effective field theory of inflation[55?59]and phenomenological consideration of achieving a nearly scaleinvariant power spectrum,[60]for examples.

    For the nonlinear dispersion relations,normally it arises from the theory that violates the Lorentz symmetry at the high energy regime.For example,in Hoava-Lifshitz theory of quantum gravity,the Lorentz symmetry has to be violated when the high-order spatial derivative terms dominated at high energy regime,and restores in the low energy limit.[61?62]Since the swampland conjectures are based on the analysis that only restricts to the effective theory with Lorentz symmetry,it is important to see if the effects of the Lorentz violation can make the single scalar field inflation models compatible with the swampland conjectures.In fact,it is proposed very recently that the strong tension between the swampland conjecture SCII and the single field inflationary modes can be relaxed by the excited initial conditions on the perturbation modes.[12,21]As we mentioned,the nonlinear dispersion relation can provide a natural mechanism for generating excited initial states.

    In this paper,we consider concrete nonlinear dispersion relations for both the scalar and tensor perturbations and discuss their implications on the swampland conjectures.The nonlinear dispersion relations considered here can be concretely realized in the Hoava-Lifshitz theory of quantum gravity.We show that the nonlinear dispersion relation can modify both the scalar and tensor perturbation spectra but still keep the scale invariance.By using the analytical expressions of perturbation spectra derived from the uniform asymptotic approximation,it is shown that the modification of spectra by the nonlinear dispersion relation can significantly relax the strong tension between the swampland conjectures and the single field inflation.

    2 Effects of Nonlinear Dispersion Relations

    Inflationary theory of the early universe provides a natural mechanism for the generation of the formation of the large scale structure and anaistropies in the cosmic microwave background(CMB).However,it is still suffering from the trans-Planckian issue considering its energy scale at the earlier stage of the inflation is close to the Planck scale.[41?42]To address the trans-Planckian issue,one approach is to consider the nonlinear dispersion relations for both the inflationary scalar and tensor perturbations.[42,45,63?64]It is interesting to mention here that the nonlinear dispersion relation can arise naturally from the Hoava-Lifshitz theory of quantum gravity.[52?54,61?62]Recently it is also shown that such relations can arise from high-order extension of the effective field theory of inflation.[55]In this section,we show that the nonlinear dispersion relation can modify both the inflationary scalar and tensor spectra significantly,which could provide a mechanism to relax the tension between the SCII and Planck data.

    To proceed,let us start with the equations of motion for the scalar and tensor perturbations.With the nonlinear dispersion relation(η),the inflationary mode function uk(η)for perturbations(scalar or tensor)obeys the modified Mukhanov-Sasaki equation

    Here η represents the conformal time,′denotes derivatives of η,and z(η)is related to the slow-roll evolution of the background.We parametrize the nonlinear dispersion relation in the form of

    where M?is the relevant energy scale of trans-Planckian physics,k is the comoving wavenumber of the mode,b1and b2are dimensionless constants.In the Hoava-Lifshitz theory of quantum gravity,the coefficients b1and b2can be related to the coupling constants of the theory,[52?54,62]in whichis related to the sixth order spatial derivative terms andis related to the fourth order.In order to get a healthy ultraviolet limit,we require>0.

    For scalar or tensor modes the equation of motion described by Eq.(5)can be solved analytically by the uni-form asymptotic approximation developed in Refs.[65–66].We would like to mention that this mathematical method has been applied to the calculations of the primordial spectra in a lot of inflation modes with quantum gravitational effects,[65?72]calculations of quantum gravitational effects of loop quantum cosmology,[73?76]studying parametric resonance during inflation and reheating,[77]and derivation of quantization condition in quantum mechanics.[78]In the uniform asymptotic approximation,we use the dimensionless variable y= ?kη.Then the equation of motion Eq.(5)can be rewritten as[79?80]

    This is a second-order ordinary differential equation.Normally it’s solution is sensitive to the poles and turning points of g(y)and q(x).In the uniform asymptotic approximation,the functions g(y)and q(y)are determined by the behaviors of the corresponding error control function around the poles or turning points.[65,79?80]For the second-order ordinary differential equation(7),we find that g(y)and q(y)contain a second-order pole at the origin,i.e.,y=0.In order to ensure the corresponding error control function of the uniform asymptotic approximate solutions,[65,79?80]the functions g(y)and q(y)have to be chosen as,[65,79?80]

    We observe that the function g(y)defined in the above could also have turning points.According to the nature of these turning points,as depicted in Fig.1,g(y)can be normally divided into four physical cases.[79]We label the corresponding turning points of g(y)=0 by y0,y1and y2with y0

    With the analysis about the turning points of g(y)in the above,we can employ the uniform asymptotic approximation to construct the corresponding approximate solutions associated about each turning points,which have been presented in details in Ref.[65]).By imposing the Bunch-Davies vacuum as the initial state,[65]using the approximate solutions of mode function for both scalar and tensor perturbations,the corresponding power spectra can be casted formally in the form,[65]

    Fig.1 (Color online)The schematic plots of function g(y)in Eq.(9)for four representative cases.The number and nature of the turning points for each case are different.Case(a):three single real turning points(y0?y10.

    where A represents the modification of the power spectra due to the presence of the nonlinear dispersion relation(6),which could be amplified by the non-adiabatic evolution of inflationary perturbations,and is given by

    with

    where ?(x) ≡ x/2? (x/4)lnx2+phΓ(ix+1/2)/2 with phΓ(ix+1/2)being the phase of the Gamma function Γ(ix+1/2),which is zero when x=0,and is determined by continuity otherwise.[65,79]Here αkand βkdenote the Bogoliubov coefficients of the excited state generated by the nonlinear dispersion relation.We see thatis related to the integral ofbetween y1and y2.When y1and y2are two real and single turning points of g(y),is positive,while it becomes negative if the two turning points are complex conjugated.Obviously,the perturbation spectra is amplified by the non-adiabatic evolution of the primordial perturbation since for this case the two turning points are both real and single.When the two turning points are complex conjugated,sinceis negatively large,the modified factor A is order of 1 and the violation of the adiabatic evolution of the primordial perturbation is strongly suppressed.

    Obviously the perturbation spectra can be modified due to nonlinear dispersion relation,which could arise from Hoava-Lifshitz theory of gravity.The effects can be described by two terms.One is determined by the modified factor A,which measures the non-adiabatic effects.Another is due to the exponential integration offrom y0to 0.To compare different effects,it is convenient to introduce the integral M0without the presence of the nonlinear terms in the dispersion relation(by setting b1=0=b2),

    When b1and b2terms are included,this integral now becomes

    With the help of M0and M,the primordial power spectra(10)can be expressed as

    To estimate the primordial power spectrum(16)with the presence of the nonlinear terms in the dispersion relation,let us study the integral in Eq.(15)in details.For primordial perturbation modes,the inflationary mode function uk(η)for the cosmological scalar perturbation can be related to the comoving curvature fluctuation aswhile for tensor perturbation we have.In these expression,the Hubble slow-roll parameter ? defined as ?=Then the ratio between the amplitudes of the tensor and scalar perturbation spectra can be calculated via

    where rGR=16? denotes the ratio between the amplitudes of the tensor and scalar perturbation spectra predicted in slow-roll inflation models when the nonlinear terms in the dispersion relation are set to zero.The quantity σkis expressed as

    where the superscript “s” and “t” denote the quantities for the scalar and tensor perturbations respectively.We note that we have usedIn the above expression,we observe that the effects due to the nonlinear terms in the dispersion relation is measured by the factor

    With SCII,we write the ratio between the amplitudes of the tensor and scalar perturbation spectra as

    The main purpose of the current paper is to justify that the above criterion can be fulfilled with the presence of the nonlinear terms in the modified dispersion relations.

    From Eq.(20),for the condition to be satisfied,one can either reduce the modified factor A or reduce σk.The former possibility is related to the non-adiabatic effects of the primordial perturbations due to the presence of the nonlinear terms in the modified dispersion relations.It is worth mentioning that when we consider the nonadiabatic effects,one assumes σk? 1 for simplicity,which can be easily achieved if? 1.

    However,once the non-adiabatic evolutions of the primordial perturbations are involved,as we mentioned,the corresponding perturbation modes are non longer at the Bunch-Davies vacuum states and can grow exponentially during the process.In this case,one has to be at caution about the question that whether the amplification of the non-adiabatic modes could be large enough to destroy the background evolution due to their back-reactions.This important issue has been discussed in details in Refs.[81–82],which shows that to avoid large back-reactions,the Bogoliubov coefficient βkhas to be constrained by

    where Hinfis the energy scale of the inflation which is constrained by Hinf/MPl≤ 2.7×10?5due to the most recent Planck 2018 results.[7?8]Thus,if we take Hinf/MPl2×10?3,one can infer that

    Then one has

    which leads to the constraint on|αk+ βk|2as,

    Using this constraint,it is obvious that the ratio between the modified factors Atfor the scalar perturbation and Asfor the tensor perturbation is restricted to be

    This condition provides a strong constraint on the nonadiabatic effects on the primordial perturbation spectrum.Clearly,from this condition,it is obvious that we have a large space for adjusting parameters b1and b2such that

    Another way to fulfill the condition(20)is to reduce the factor σk,which is related to two direct integrals of√from the turning point y0until the end of the slowroll inflation.Therefore,in order to achieve the condition(20),one has to properly adjust the parameters in the expression of the integrand.As we mentioned,when ??? 1,therefore the only way for this to be possible is to relax ??? 1 by requiring1.In order to show the effect of σkexplicitly,we considerIt is worth noting that this implies that the adiabatic condition is satisfied during inflation for the scalar and tensor perturbation modes.To estimate the integrals in the expression of σk,one observes that due to the nonlinear terms in the modified dispersion relation,the calculation becomes very much mathematics involved.However,for the purpose to show that the condition(20)can be fulfilled by reducing the value of σk,we plot the gs(y)and gt(y)in Fig.2 by specifying a set of values for the parameters in the dispersion relation.For scalar perturbation we choose>0,which leads to a shift of y0from ν for linear dispersion relation to a larger value,while for tensor perturbation we consider<0,which leads to y0<ν.With these reasons,one sees that the curve of g(y)for tensor perturbation is always beneath the scalar one,which implies that.Note that for the purpose to make the SCII to be consistent with observational data,one has to require thatand for the parameters chosen in Fig.2 we find σk~ 0.1.

    Here we would like to make some remarks about the modification on the scalar and tensor power spectra.First,as shown in Refs.[65,71–72],the effects due to the nonlinear terms in the dispersion relation in the form of Eq.(6)can only make modifications on the amplitudes of the primordial scalar and tensor spectrum.This implies that the non-adiabatic evolution of the primordial perturbations due to the nonlinear dispersion relation does not break the nearly scale invariance of the spectrum.Considering the observational data favors a nearly scale invariant scalar spectrum,therefore,the modifications on the power spectrum due to the nonlinear dispersion relation is consistent with the recent observational data.Second,the parameters b1and b2involved in the nonlinear terms of the dispersion relation(6)are related to the fourth and sixth order spatial derivative terms in Hoava-Lifshitz theory respectively.While the most of the consistency analysis are related to the parameter b2,the parameter b1is less constraint.As a result,we have a large parameter space for the parameter b1that does not lead any inconsistent issues.

    Fig.2 (Color online)Comparison of g(y)for primordial scalar perturbation and the tensor perturbation in the interval y∈(0,y0)for a set of values for the parameters in the dispersion relation(6).

    3 Conclusions

    In the current research,we discuss the implications of the quantum gravitational effects due to the nonlinear dispersion relations on relaxing the strong tension between the recent proposed swampland conjectures and the single field inflationary models.The nonlinear dispersion relations for both the scalar and tensor perturbations considered in this paper can arise naturally in the Hoava-Lifshitz theory of quantum gravity.We show that the quantum gravitational effects due to the nonlinear dispersion relation provide significant modifications on the amplitude of both the scalar and tensor power spectra.Such modifications could be either raise or reduce the power spectra depending on the parameters of the nonlinear dispersion relations.Therefore,these effects can reduce the tensor-to-scalar ratio to a smaller value,which helps to relax the tension between the swampland conjecture and Planck data.

    猜你喜歡
    武強(qiáng)
    吃老本
    吃老本
    小讀者(2023年12期)2023-07-01 00:12:40
    武強(qiáng)木板年畫的傳承、圖新與藝術(shù)生機(jī)
    論武強(qiáng)年畫急需再生性研究的緊迫性
    西部皮革(2021年8期)2021-05-13 03:00:46
    武強(qiáng)
    移動(dòng)電商助力“9+5”武強(qiáng)年畫發(fā)展探討
    俯視黃河
    詩潮(2019年8期)2019-08-23 05:39:48
    一帆風(fēng)雨
    鴨綠江(2016年8期)2016-11-14 23:25:49
    全國音樂教育服務(wù)項(xiàng)目交流暨聯(lián)盟示范基地評(píng)審活動(dòng)在武強(qiáng)舉辦
    衡水非物質(zhì)文化遺產(chǎn)保護(hù)與傳承探略:武強(qiáng)年畫
    欧美成人a在线观看| 国产伦人伦偷精品视频| 亚洲,欧美精品.| 亚洲成人中文字幕在线播放| 亚洲精品亚洲一区二区| 成年女人看的毛片在线观看| 一进一出抽搐gif免费好疼| 亚洲av二区三区四区| 色综合婷婷激情| 18+在线观看网站| 又黄又爽又刺激的免费视频.| 好男人在线观看高清免费视频| 性插视频无遮挡在线免费观看| 国产欧美日韩精品亚洲av| 国产高潮美女av| 天堂av国产一区二区熟女人妻| 亚洲人成网站在线播| 如何舔出高潮| 一级av片app| 日本撒尿小便嘘嘘汇集6| 国产中年淑女户外野战色| 午夜精品在线福利| 中国美女看黄片| 狠狠狠狠99中文字幕| 美女xxoo啪啪120秒动态图 | 90打野战视频偷拍视频| 久久中文看片网| av天堂在线播放| 亚洲专区中文字幕在线| 精品人妻偷拍中文字幕| 欧美日韩黄片免| 每晚都被弄得嗷嗷叫到高潮| 小说图片视频综合网站| 国产黄片美女视频| av福利片在线观看| 亚洲精品一卡2卡三卡4卡5卡| 一本综合久久免费| 在线观看舔阴道视频| 久久久久久久久久成人| 亚洲,欧美,日韩| 看片在线看免费视频| 欧美潮喷喷水| 国产精品电影一区二区三区| 蜜桃亚洲精品一区二区三区| 国产淫片久久久久久久久 | 亚洲狠狠婷婷综合久久图片| 热99在线观看视频| 亚洲美女黄片视频| 国产一级毛片七仙女欲春2| 757午夜福利合集在线观看| 国产亚洲精品综合一区在线观看| 波多野结衣巨乳人妻| 国产色爽女视频免费观看| 99久国产av精品| 97超级碰碰碰精品色视频在线观看| 可以在线观看的亚洲视频| 亚洲欧美清纯卡通| 99国产精品一区二区蜜桃av| 国产黄色小视频在线观看| 国产精品爽爽va在线观看网站| 亚洲最大成人av| 女生性感内裤真人,穿戴方法视频| 国产黄a三级三级三级人| 精品乱码久久久久久99久播| 高清日韩中文字幕在线| 亚洲国产精品999在线| 亚洲精品在线观看二区| 亚洲专区中文字幕在线| 国产高潮美女av| 亚洲 欧美 日韩 在线 免费| 夜夜看夜夜爽夜夜摸| 成人国产综合亚洲| 黄色配什么色好看| 国产精品野战在线观看| 99热这里只有是精品50| 国产aⅴ精品一区二区三区波| 国产探花在线观看一区二区| 久久草成人影院| 麻豆av噜噜一区二区三区| 色视频www国产| 老司机福利观看| av在线老鸭窝| 波多野结衣巨乳人妻| 久久久久免费精品人妻一区二区| 麻豆一二三区av精品| 韩国av一区二区三区四区| 成人精品一区二区免费| 小蜜桃在线观看免费完整版高清| 成人一区二区视频在线观看| 在线播放无遮挡| 欧美不卡视频在线免费观看| 99久久九九国产精品国产免费| 伊人久久精品亚洲午夜| 天天一区二区日本电影三级| 亚洲经典国产精华液单 | 乱人视频在线观看| or卡值多少钱| 男女之事视频高清在线观看| 亚洲精品久久国产高清桃花| 男女视频在线观看网站免费| 毛片一级片免费看久久久久 | 色吧在线观看| 欧美黄色片欧美黄色片| 变态另类丝袜制服| 乱人视频在线观看| 日本a在线网址| av视频在线观看入口| 男人的好看免费观看在线视频| 精品欧美国产一区二区三| 国产成人av教育| 首页视频小说图片口味搜索| 国产aⅴ精品一区二区三区波| 麻豆一二三区av精品| 黄色一级大片看看| 精品不卡国产一区二区三区| 身体一侧抽搐| 好男人电影高清在线观看| 久久人人精品亚洲av| eeuss影院久久| 亚洲av美国av| 亚洲无线在线观看| 欧美性猛交黑人性爽| 免费大片18禁| 亚洲精品影视一区二区三区av| 亚洲欧美日韩高清专用| 99热6这里只有精品| 亚洲不卡免费看| 99热精品在线国产| 亚洲欧美日韩东京热| 99视频精品全部免费 在线| 日本免费一区二区三区高清不卡| 亚洲中文字幕一区二区三区有码在线看| ponron亚洲| 精品久久久久久,| 黄片小视频在线播放| 久久久久久大精品| 丝袜美腿在线中文| 午夜福利视频1000在线观看| 精品熟女少妇八av免费久了| 色综合欧美亚洲国产小说| 日韩欧美在线二视频| 免费观看精品视频网站| 激情在线观看视频在线高清| 好男人电影高清在线观看| 免费av毛片视频| 国产精品三级大全| 俄罗斯特黄特色一大片| 久久九九热精品免费| 国产成人av教育| 99热这里只有是精品在线观看 | 99国产精品一区二区三区| 天堂网av新在线| 内地一区二区视频在线| 一进一出抽搐动态| 欧美成人性av电影在线观看| 亚洲精品色激情综合| 国产午夜精品久久久久久一区二区三区 | 老司机深夜福利视频在线观看| 又黄又爽又刺激的免费视频.| 欧美色欧美亚洲另类二区| 十八禁人妻一区二区| 亚洲欧美日韩卡通动漫| 天堂√8在线中文| 中文字幕人成人乱码亚洲影| 又粗又爽又猛毛片免费看| 三级国产精品欧美在线观看| 亚洲精品一区av在线观看| 亚州av有码| 亚洲av第一区精品v没综合| 午夜精品久久久久久毛片777| 婷婷丁香在线五月| 国产探花在线观看一区二区| 久久精品国产亚洲av涩爱 | 亚洲 国产 在线| 人妻夜夜爽99麻豆av| 亚洲精品成人久久久久久| 免费电影在线观看免费观看| 久久精品人妻少妇| 国产精品亚洲av一区麻豆| 超碰av人人做人人爽久久| 首页视频小说图片口味搜索| 亚洲av中文字字幕乱码综合| 国产爱豆传媒在线观看| 国产在线精品亚洲第一网站| 精品国内亚洲2022精品成人| 成人特级黄色片久久久久久久| 久久亚洲精品不卡| 天美传媒精品一区二区| 亚洲国产色片| 色尼玛亚洲综合影院| 欧美激情国产日韩精品一区| 老熟妇仑乱视频hdxx| 国产精品久久久久久精品电影| 18禁在线播放成人免费| 亚洲五月婷婷丁香| 精品久久久久久成人av| 日日摸夜夜添夜夜添av毛片 | 成人特级黄色片久久久久久久| 日韩中字成人| or卡值多少钱| av女优亚洲男人天堂| 亚洲一区高清亚洲精品| 看黄色毛片网站| 色哟哟哟哟哟哟| 91麻豆精品激情在线观看国产| 女人十人毛片免费观看3o分钟| 狂野欧美白嫩少妇大欣赏| 高清在线国产一区| 日韩精品中文字幕看吧| 亚洲美女黄片视频| 欧美日韩中文字幕国产精品一区二区三区| 亚洲最大成人手机在线| 18禁黄网站禁片午夜丰满| 午夜精品久久久久久毛片777| 亚洲美女搞黄在线观看 | 亚洲精品成人久久久久久| 久久亚洲精品不卡| 99热只有精品国产| 亚洲精华国产精华精| 成人亚洲精品av一区二区| 亚洲成av人片在线播放无| 91午夜精品亚洲一区二区三区 | 国产精品自产拍在线观看55亚洲| 欧美日韩福利视频一区二区| 精品人妻一区二区三区麻豆 | 一二三四社区在线视频社区8| 午夜福利视频1000在线观看| 亚洲不卡免费看| 亚洲av五月六月丁香网| 成人三级黄色视频| 嫩草影院精品99| 18禁黄网站禁片午夜丰满| 久久久精品大字幕| 日韩中文字幕欧美一区二区| av欧美777| 69av精品久久久久久| 中文字幕免费在线视频6| 欧美乱色亚洲激情| 2021天堂中文幕一二区在线观| 国产一区二区三区在线臀色熟女| 亚洲精华国产精华精| 精品99又大又爽又粗少妇毛片 | 激情在线观看视频在线高清| 久久国产乱子免费精品| 国产一区二区三区在线臀色熟女| 日本一二三区视频观看| 午夜久久久久精精品| 亚洲 欧美 日韩 在线 免费| 我的女老师完整版在线观看| 在线观看午夜福利视频| 又爽又黄a免费视频| 国产精品98久久久久久宅男小说| 精品久久久久久久久亚洲 | 欧美性猛交╳xxx乱大交人| 日韩 亚洲 欧美在线| a级一级毛片免费在线观看| 午夜福利高清视频| 国产欧美日韩一区二区三| 精品免费久久久久久久清纯| 国产精品伦人一区二区| 日本熟妇午夜| av国产免费在线观看| 51午夜福利影视在线观看| 老司机午夜福利在线观看视频| 国产精品亚洲美女久久久| 日本黄大片高清| 深夜精品福利| 免费观看的影片在线观看| 日韩欧美国产在线观看| 全区人妻精品视频| 亚洲av免费在线观看| 国产亚洲av嫩草精品影院| 国产精品一区二区免费欧美| 永久网站在线| 亚洲熟妇中文字幕五十中出| 久久久色成人| 亚洲在线观看片| 三级国产精品欧美在线观看| 十八禁网站免费在线| 欧美乱妇无乱码| 亚洲天堂国产精品一区在线| 久久精品91蜜桃| 最近最新中文字幕大全电影3| 中文字幕高清在线视频| 国产乱人视频| a级毛片免费高清观看在线播放| 精品欧美国产一区二区三| 夜夜躁狠狠躁天天躁| 日韩人妻高清精品专区| 国产欧美日韩一区二区三| 久久天躁狠狠躁夜夜2o2o| 亚洲av电影不卡..在线观看| 国产精品98久久久久久宅男小说| 国产精品av视频在线免费观看| 亚洲国产精品成人综合色| 99热这里只有精品一区| 三级男女做爰猛烈吃奶摸视频| 久久久久久久久大av| 亚洲五月婷婷丁香| 最近最新中文字幕大全电影3| 国内精品美女久久久久久| 免费高清视频大片| 亚洲成人久久爱视频| 18+在线观看网站| 嫩草影视91久久| 免费大片18禁| 亚洲人与动物交配视频| 国产精品久久久久久久久免 | 丁香欧美五月| 丝袜美腿在线中文| 99热这里只有是精品50| 伦理电影大哥的女人| 我的女老师完整版在线观看| 国产欧美日韩一区二区精品| 亚洲中文日韩欧美视频| 2021天堂中文幕一二区在线观| 一区二区三区四区激情视频 | 看片在线看免费视频| 99国产极品粉嫩在线观看| 亚洲七黄色美女视频| 亚洲天堂国产精品一区在线| 三级国产精品欧美在线观看| 午夜福利免费观看在线| 国产视频内射| 国产白丝娇喘喷水9色精品| 男女做爰动态图高潮gif福利片| 午夜福利在线观看吧| 夜夜躁狠狠躁天天躁| 国产三级中文精品| 欧美成人性av电影在线观看| 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 | 亚洲精品亚洲一区二区| 观看美女的网站| 亚洲avbb在线观看| 成年女人看的毛片在线观看| 亚洲av日韩精品久久久久久密| 最新在线观看一区二区三区| 看十八女毛片水多多多| 欧美精品国产亚洲| 精品熟女少妇八av免费久了| 真人做人爱边吃奶动态| 成人三级黄色视频| 午夜福利在线观看吧| 美女被艹到高潮喷水动态| 99国产极品粉嫩在线观看| 男女之事视频高清在线观看| 高清在线国产一区| ponron亚洲| 精品免费久久久久久久清纯| 日韩欧美国产在线观看| 国产乱人视频| 69人妻影院| 欧美一级a爱片免费观看看| av在线观看视频网站免费| 亚洲欧美日韩卡通动漫| 国产精品一区二区免费欧美| 久久欧美精品欧美久久欧美| 欧美zozozo另类| 在线播放国产精品三级| 日韩人妻高清精品专区| 欧美在线一区亚洲| 乱码一卡2卡4卡精品| 神马国产精品三级电影在线观看| а√天堂www在线а√下载| 国产在线精品亚洲第一网站| 久久欧美精品欧美久久欧美| 丝袜美腿在线中文| 高潮久久久久久久久久久不卡| 国产精品影院久久| 一个人观看的视频www高清免费观看| 亚洲第一电影网av| 12—13女人毛片做爰片一| 欧美日韩乱码在线| av在线老鸭窝| 国产真实伦视频高清在线观看 | 男插女下体视频免费在线播放| 色综合婷婷激情| 热99在线观看视频| 久9热在线精品视频| 99国产精品一区二区三区| 在线免费观看的www视频| 国产日本99.免费观看| 麻豆成人av在线观看| 淫秽高清视频在线观看| 欧美成人免费av一区二区三区| 午夜福利在线观看免费完整高清在 | 国产高清视频在线播放一区| 免费大片18禁| 亚洲在线观看片| 亚洲国产精品sss在线观看| 免费观看的影片在线观看| 国产精品99久久久久久久久| 香蕉av资源在线| 亚洲成a人片在线一区二区| 亚洲第一区二区三区不卡| 搡老妇女老女人老熟妇| 午夜精品一区二区三区免费看| 美女大奶头视频| 精品欧美国产一区二区三| 欧美精品啪啪一区二区三区| 天堂动漫精品| 99久国产av精品| 国内精品美女久久久久久| 久久久久久久精品吃奶| 日日摸夜夜添夜夜添小说| 草草在线视频免费看| 国产中年淑女户外野战色| 精品不卡国产一区二区三区| 舔av片在线| 久久久久精品国产欧美久久久| 久久精品人妻少妇| 亚洲精品影视一区二区三区av| 国产亚洲精品av在线| 亚洲,欧美精品.| 色av中文字幕| 日韩人妻高清精品专区| 一区二区三区免费毛片| 搞女人的毛片| 亚洲精品色激情综合| 欧美日韩亚洲国产一区二区在线观看| 成年女人看的毛片在线观看| 成人特级av手机在线观看| 国产大屁股一区二区在线视频| 97碰自拍视频| 亚洲最大成人手机在线| 欧美不卡视频在线免费观看| 久久久久久大精品| 久久国产精品人妻蜜桃| 亚洲国产精品sss在线观看| 少妇人妻精品综合一区二区 | 欧美日韩亚洲国产一区二区在线观看| 成人av一区二区三区在线看| 中亚洲国语对白在线视频| 国产熟女xx| 亚洲自偷自拍三级| 欧美日韩亚洲国产一区二区在线观看| 欧美+亚洲+日韩+国产| 国产亚洲av嫩草精品影院| 欧美日韩瑟瑟在线播放| a级毛片免费高清观看在线播放| 真实男女啪啪啪动态图| 亚洲精品成人久久久久久| av女优亚洲男人天堂| 一级黄色大片毛片| 18禁在线播放成人免费| 日韩大尺度精品在线看网址| 久久国产乱子免费精品| 在线免费观看不下载黄p国产 | 久久国产精品影院| 俄罗斯特黄特色一大片| 又黄又爽又刺激的免费视频.| 在线观看一区二区三区| 国产日本99.免费观看| 一区二区三区高清视频在线| 成人无遮挡网站| 欧美激情国产日韩精品一区| 欧美一区二区国产精品久久精品| 欧洲精品卡2卡3卡4卡5卡区| 欧美日本亚洲视频在线播放| 成人av在线播放网站| 99视频精品全部免费 在线| 色播亚洲综合网| 在现免费观看毛片| 国内精品久久久久精免费| 久久精品国产亚洲av香蕉五月| 如何舔出高潮| 亚洲精品一区av在线观看| 精品熟女少妇八av免费久了| 亚洲人成网站在线播放欧美日韩| 免费观看人在逋| 真人做人爱边吃奶动态| 五月玫瑰六月丁香| 老女人水多毛片| 九九久久精品国产亚洲av麻豆| 一卡2卡三卡四卡精品乱码亚洲| 91午夜精品亚洲一区二区三区 | 一本一本综合久久| 国产视频一区二区在线看| 欧美成人性av电影在线观看| 国产精品不卡视频一区二区 | 免费在线观看日本一区| 久久99热这里只有精品18| 久久草成人影院| 大型黄色视频在线免费观看| 男插女下体视频免费在线播放| 国产黄片美女视频| 亚洲国产精品成人综合色| 国产成+人综合+亚洲专区| 国产亚洲欧美在线一区二区| 亚洲在线观看片| 国产91精品成人一区二区三区| 国产久久久一区二区三区| 人人妻人人澡欧美一区二区| 在线免费观看不下载黄p国产 | 久久久久亚洲av毛片大全| 国产淫片久久久久久久久 | 国产精品一区二区三区四区久久| 亚洲男人的天堂狠狠| 无遮挡黄片免费观看| 日韩有码中文字幕| 夜夜看夜夜爽夜夜摸| 欧美xxxx黑人xx丫x性爽| 天天一区二区日本电影三级| 俄罗斯特黄特色一大片| 国产亚洲精品综合一区在线观看| 少妇的逼好多水| 中文字幕久久专区| 国产高清激情床上av| 蜜桃久久精品国产亚洲av| 男女下面进入的视频免费午夜| 麻豆av噜噜一区二区三区| 99国产极品粉嫩在线观看| 国产成人aa在线观看| 成人av一区二区三区在线看| 青草久久国产| 又紧又爽又黄一区二区| 精品久久久久久久末码| 在线十欧美十亚洲十日本专区| 国产精品精品国产色婷婷| 亚洲av中文字字幕乱码综合| 亚洲内射少妇av| 亚洲在线观看片| 日本精品一区二区三区蜜桃| 十八禁国产超污无遮挡网站| 88av欧美| 丰满人妻熟妇乱又伦精品不卡| 草草在线视频免费看| 黄色丝袜av网址大全| 99久久精品热视频| 国产精品久久电影中文字幕| 热99在线观看视频| 校园春色视频在线观看| 亚洲国产精品999在线| 日本黄色片子视频| 日本五十路高清| 久久99热6这里只有精品| 国产野战对白在线观看| 桃色一区二区三区在线观看| 国产野战对白在线观看| 成年免费大片在线观看| 精品人妻1区二区| 夜夜夜夜夜久久久久| 欧美日本亚洲视频在线播放| 久久久国产成人精品二区| 美女大奶头视频| 特大巨黑吊av在线直播| 色噜噜av男人的天堂激情| 精品午夜福利视频在线观看一区| 自拍偷自拍亚洲精品老妇| 两人在一起打扑克的视频| 久久人人精品亚洲av| 国产成人欧美在线观看| 18禁黄网站禁片免费观看直播| 特大巨黑吊av在线直播| 五月伊人婷婷丁香| 如何舔出高潮| 午夜福利欧美成人| 中出人妻视频一区二区| 最新中文字幕久久久久| 一卡2卡三卡四卡精品乱码亚洲| 久久精品夜夜夜夜夜久久蜜豆| 亚洲男人的天堂狠狠| 一进一出好大好爽视频| 十八禁国产超污无遮挡网站| 亚洲熟妇中文字幕五十中出| av专区在线播放| 国产一区二区亚洲精品在线观看| 看免费av毛片| 九色成人免费人妻av| 色综合婷婷激情| 在线观看美女被高潮喷水网站 | 91午夜精品亚洲一区二区三区 | 国产v大片淫在线免费观看| 精品人妻视频免费看| 色av中文字幕| 久久精品夜夜夜夜夜久久蜜豆| 国产精品永久免费网站| 国产91精品成人一区二区三区| 精品一区二区三区av网在线观看| www.999成人在线观看| 国产欧美日韩精品一区二区| 国产一区二区激情短视频| 真人做人爱边吃奶动态| 国产精品自产拍在线观看55亚洲| netflix在线观看网站| 国产黄色小视频在线观看| 伦理电影大哥的女人| 国产精华一区二区三区| 12—13女人毛片做爰片一| 99热6这里只有精品| 日韩成人在线观看一区二区三区| 老司机福利观看| 香蕉av资源在线| 免费在线观看日本一区| 亚洲国产欧美人成| 欧美高清成人免费视频www| 国产黄色小视频在线观看| 国内精品一区二区在线观看| 午夜福利在线观看吧| 国产一区二区三区视频了| 能在线免费观看的黄片| av中文乱码字幕在线| 如何舔出高潮| 国产免费av片在线观看野外av| 天堂网av新在线| 国产一区二区激情短视频| 色综合婷婷激情| 狠狠狠狠99中文字幕| 久久香蕉精品热| 18禁黄网站禁片午夜丰满| 亚洲自拍偷在线| 久久精品国产亚洲av天美| 久久中文看片网| 午夜免费男女啪啪视频观看 | 中文亚洲av片在线观看爽|