Towards a robust estimate for gravitational leptogenesis...Courtesy H.Oide Towards a robust estimate...
Transcript of Towards a robust estimate for gravitational leptogenesis...Courtesy H.Oide Towards a robust estimate...
Courtesy H.Oide
Towards a robust estimate for gravitational leptogenesis
Zooming in on Axions in the Early Universe 24/06/2020 @ Virtual Institute at CERN
based on: K. Kamada, J. Kume, Y. Yamada, & J. Yokoyama, JCAP 01 (2020) 016, 1911.02657 [hep-ph]
Kohei Kamada (RESCEU, U Tokyo)
K. Kamada, J. Kume, & Y. Yamada, work in progress (2007.xxxxx?)
Jun’ya Kume (Ph,D student at Tokyo) Yusuke Yamada (PD at Tokyo)
Courtesy H.Oide
The message of this talk1. Gravitational Leptogenesis is yet another possibility to
produce baryon asymmetry through the chiral anomaly implemented in the SM and GR.
2. Appearance of apparent ghost-like degree of freedom as well as UV divergences are the theoretical issues in the scenario.
3. Here we clarify these issues and determine in which case the present BAU can be explained with the scenario.
Courtesy H.Oide
1. Introduction: Baryogenesis and Gravitational Leptogenesis
2. Issues in Gravitational Leptogenesis driven by Axion Inflation
3. Condition for the successful baryogenesis 4. Summary
Courtesy H.Oide
12 G. Steigman: Primordial Nucleosynthesis
Figure 6. The CBR temperature fluctuation anisotropy spectra for three choices of the baryondensity parameter ωB = 0.018, 0.023, 0.028, in order of increasing height of the first peak. Alsoshown are the WMAP data points.
Figure 7. The normalized likelihood distributions for the baryon density parameter η10 derivedfrom SBBN and the primordial abundance of deuterium (solid curve; see §4.1) and from the CBRusing WMAP data alone (dashed curve). The bottom horizontal axis is the baryon-to-photonratio parameter η10; the top axis is the baryon density parameter ωB = ΩBh2 .
- We live in a matter-antimatter asymmetric Universe. - BBN and CMB can evaluate it quantitatively.
’03 Steigman
23. Big-Bang nucleosynthesis 3
Figure 23.1: The abundances of 4He, D, 3He, and 7Li as predicted by the standardmodel of Big-Bang nucleosynthesis — the bands show the 95% CL range [5].Boxes indicate the observed light element abundances. The narrow vertical bandindicates the CMB measure of the cosmic baryon density, while the wider bandindicates the BBN concordance range (both at 95% CL).
February 8, 2016 19:55
CMBBBN
Particle Data Group 2015
nB
n= (6.09± 0.06) 1010
(Planck 2015) = (6.180± 0.195) 1010
BBN+D ; ’15 Cyburt+
bh2 = 0.018, 0.023, 0.028
Baryon Asymmetry of the Universe
Courtesy H.Oide
Inflation dilutes the preexisting asymmetry.
After inflation before BBN, asymmetry must be generated. matter : anti matter : photon :
~10000000000+1 ~10000000000 ~10000000000
matter : anti matter : photon :
~1 ~0 ~10000000000
annihilationT 100MeV
WMAP team
Courtesy H.Oide
In order to generate baryon asymmetry... Sakharov’s condition is required.
1. B-violation 2. C & CP-violation 3. Deviation from thermal equilibrium
(’67 Sakharov)
Courtesy H.Oide
In order to generate baryon asymmetry... Sakharov’s condition is required.
1. B-violation 2. C & CP-violation 3. Deviation from thermal equilibrium
(’67 Sakharov)
BSM is required!? - Leptogenesis : RH neutrinos - Affleck-Dine : SUSY with B and CP op.
- EW baryogenesis : 1st order EWPT + CP op.
(’85 Fukugita&Yanagida)
(’85 Affleck&Dine, ’95 Dine,Randall&Thomas)
(’85 Kuzmin, Rubakov&Shaposhnikov)
Courtesy H.Oide
Many of baryogenesis models add a new physics beyond the SM that breaks B and/or C&CP.
But the SM ingredients indeed can satisfy the Sakharov’s condition.
Courtesy H.Oide
Many of baryogenesis models add a new physics beyond the SM that breaks B and/or C&CP.
But the SM ingredients indeed can satisfy the Sakharov’s condition.
Chiral anomaly in the SM
µjµB = µjµ
L = Ng
g2
162tr
WµWµ
g2
322Yµ Y µ
(’76 ‘t Hooft)
Gravitational chiral anomaly in the lepton current
rµjµL =
NRL
24(4)2RR, rµj
µB = 0.
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QB = QL = Ng
NCS
g2
162HY
QL =NRL
24(4)2K0
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(’84 Alvarez-Gaume & Witten)
Courtesy H.Oide
If a mechanism that generates long-range helical hyper gauge fields or gravitational waves works in the early Universe non-thermally, it satisfies the Sakharov’s condition and can generate BAU.
1. B-violation => Chiral anomaly 2. C & CP-violation => Long-range helicity 3. Deviation from thermal equilibrium => non-thermal BG fields
Such a mechanism surely requires physics beyond the SM or GR, but it would open a new window to explore the physics for baryogenesis.
The dynamics of Axion-like particles is the most promising origin.
Courtesy H.Oide
If a mechanism that generates long-range helical hyper gauge fields or gravitational waves works in the early Universe non-thermally, it satisfies the Sakharov’s condition and can generate BAU.
1. B-violation => Chiral anomaly 2. C & CP-violation => Long-range helicity 3. Deviation from thermal equilibrium => non-thermal BG fields
Magnetic field case (’98 Giovannini&Shaposhnikov, ’15 Anber&Sabancilar, ’16 Fujita&KK, ’16 KK&Long)
…B-L conserved => late time dynamics w/ EW sphaleron is important.See Neil, Robert, & Benedict’s talks.
Such a mechanism surely requires physics beyond the SM or GR, but it would open a new window to explore the physics for baryogenesis.
The dynamics of Axion-like particles is the most promising origin.
Courtesy H.Oide
Gravitational Leptogenesis
Lint =N
642
MplRR
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(’06 Alexander, Peskin & Sheikh-Jabbari)
Simple way to generate helical gravitational waves … axion inflation with anomalous coupling to gravity
During inflation helical gravitational waves are generated and lepton asymmetry is generated simultaneously through gravitational chiral anomaly.
Courtesy H.Oide
Gravitational Leptogenesis
Lint =N
642
MplRR
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L = ()R2 4RµR
µ +RµRµ
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LW =
4fTr(WµW
µ)
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(’06 Alexander, Peskin & Sheikh-Jabbari)
Simple way to generate helical gravitational waves … axion inflation with anomalous coupling to gravity
During inflation helical gravitational waves are generated and lepton asymmetry is generated simultaneously through gravitational chiral anomaly.
cf. Several variants - w/ Gauss-Bonnet term
- Chromo-natural inflation
(’19 Kawai & Kim)
(’14 Maleknejad, ’18 Caldwell & Devulder, ’18 Adshead, Long & Sfakianakis)
See Ema & Tomohiro’s talks.
Courtesy H.Oide
Standard (?) estimate for baryon asymmetry(’06 Alexander, Peskin & Sheikh-Jabbari)
1. Parameterize inflation dynamics with and and take them as background.
Hinf ' Hend
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<latexit sha1_base64="nZ/A+jLhR/0gXR8MhFydW2F9oVg=">AAACF3icbVDLSgMxFL1TX7W+qi7dBIvgqsyIoO6KblxWsA9oh5LJZDqhSWZIMkIZ+hku3OinuBO3Lv0St6btLGzrgcDh3Hu4JydIOdPGdb+d0tr6xuZWebuys7u3f1A9PGrrJFOEtkjCE9UNsKacSdoyzHDaTRXFIuC0E4zupvPOE1WaJfLRjFPqCzyULGIEGyv18n6YGNRPYzYZVGtu3Z0BrRKvIDUo0BxUf6yZZIJKQzjWuue5qfFzrAwjnE4q/UzTFJMRHtKepRILqv18FnmCzqwSoihR9kmDZupfR46F1mMR2E2BTayXZ1Px31kgFi7n2kaLabgUx0TXfs5kmhkqyTxNlHFkEjQtCYVMUWL42BJMFLMfQiTGChNjq6zYprzlXlZJ+6LuXdZvHi5rjduiszKcwCmcgwdX0IB7aEILCCTwDK/w5rw4786H8zlfLTmF5xgW4Hz9AojJoMs=</latexit>
2. Write down the quadratic action for GWs,
NHinf
22M3pl
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A useful parameterization:
S(2)GW =
1
2
Zdd3k
X
A=L,R
z2A(, k)|(hA
k )0|2 k2|hA
k |2
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z2A(, k) a2()M2
pl
2
1 Ak
8
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R = +1, L = 1
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Courtesy H.Oide
Standard (?) estimate for baryon asymmetry(’06 Alexander, Peskin & Sheikh-Jabbari)
3. Solve mode equation
(µAk )
00 +
k2 z00A
zA
(µA
k ) = 0
<latexit sha1_base64="Ph2bG6ZM+F/OQY69d3yApTn8DVk=">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</latexit>
µAk () zA(, k)h
Ak ()
<latexit sha1_base64="0vVCCaD+w8qXY6XA8TfvGNnXhZ8=">AAACRnicbVDLSgMxFL1T3/VVdekmWAQLUmakYN352LisYFVw6pBJb21oMjMmmUId+it+jQs3uvcn3Em3po+Fth4IHM45l9x7wkRwbVz308nNzS8sLi2v5FfX1jc2C1vbNzpOFcM6i0Ws7kKqUfAI64YbgXeJQipDgbdh52Lo33ZRaR5H16aXYEPSx4i3OKPGSkGh6ss0yPxQkk7/4ezAR0NLxMenlHfJczAWDjsl0p4OBYWiW3ZHILPEm5AiTFALCgO/GbNUYmSYoFrfe25iGhlVhjOB/byfakwo69BHvLc0ohJ1Ixtd2Cf7VmmSVqzsiwwZqb8nMiq17snQJiU1bT3tDcV/vVD++TnTdrU2NqfWMa1qI+NRkhqM2HibViqIicmwU9LkCpkRPUsoU9weRFibKsqMbT5vm/Kme5klN0dlr1I+uaoUT88nnS3DLuzBAXhwDKdwCTWoA4MXeIV3+HDenC/n2xmMozlnMrMDf5CDH3JbsLE=</latexit>
with assuming and asymptotic plane wave at early epochs|k| 1
<latexit sha1_base64="Ll7106lZZ2bQgLUX0KlqHt+Bvfk=">AAACInicbVDLSgMxFM3UV62v8bFzEyyCqzIjBXVXdOOyQl/QGUomc6cNzTxIMkKd9l9cuNFPcSeuBP/DrWk7C9t6IOFwzr3k5HgJZ1JZ1pdRWFvf2Nwqbpd2dvf2D8zDo5aMU0GhSWMei45HJHAWQVMxxaGTCCChx6HtDe+mfvsRhGRx1FCjBNyQ9CMWMEqUlnrmyXjoNAagCHb0NcYO59jumWWrYs2AV4mdkzLKUe+ZP44f0zSESFFOpOzaVqLcjAjFKIdJyUklJIQOSR+6mkYkBOlms/QTfK4VHwex0CdSeKb+3chIKOUo9PRkSNRALntT8V/PCxdezqSONgB/KY4Krt2MRUmqIKLzNEHKsYrxtC/sMwFU8ZEmhAqmP4TpgAhClW61pJuyl3tZJa3Lil2t3DxUy7XbvLMiOkVn6ALZ6ArV0D2qoyai6Ak9o1f0ZrwY78aH8TkfLRj5zjFagPH9CwpipA4=</latexit>
µAk () =
1pkexpiki exp
A
32
W,3/2
i
r4 32
64k
!
<latexit sha1_base64="TzFtp4fQK2mEnGUL60JN1mx1xok=">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</latexit>
iA
p256/2 3
<latexit sha1_base64="wnpOWNJn41Og2dbjnUx0fNy3a5A=">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</latexit>
4. Calculate the 0th-component of the Chern-Simons current
K0(f) =1
2a4f
Z
k<af
d3k
(2)3kX
A=R,L
A
z2A
"|µA
k0|2
k2
z0AzA
2!|µA
k |2 z0AzA
(µAkµ
Ak
0+ h.c.)
#
<latexit sha1_base64="9ShPu3lMmY77LHHMN9avxiL4IGQ=">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</latexit>
:
<latexit sha1_base64="NbH9OHhD1hsdfs7FehAcxLYVNTI=">AAACFXicbVC7SgNBFJ2NrxhfUUubwSBYhV0J+KiCNhYWEcxDkiXMzt4kQ2Zml5lZISz5Cgsb/RQ7sbX2S2ydJFuYxAMDh3PP5Z45QcyZNq777eRWVtfWN/Kbha3tnd294v5BQ0eJolCnEY9UKyAaOJNQN8xwaMUKiAg4NIPhzWTefAKlWSQfzCgGX5C+ZD1GibHSY+fOWkNyhbvFklt2p8DLxMtICWWodYs/nTCiiQBpKCdatz03Nn5KlGGUw7jQSTTEhA5JH9qWSiJA++k08BifWCXEvUjZJw2eqn83UiK0HonAOgUxA704m4j/zgIxdznVNtoAwoU4pnfhp0zGiQFJZ2l6CccmwpOKcMgUUMNHlhCqmP0QpgOiCDW2yIJtylvsZZk0zspepXx5XylVr7PO8ugIHaNT5KFzVEW3qIbqiCKBntErenNenHfnw/mcWXNOtnOI5uB8/QLr5p9W</latexit>
cutoff scale for GW production'
162ainf
Hf
Mpl
2
Hinf
4
H3inf .
<latexit sha1_base64="SYQ2JBR897iwoVr8rbqOwTYDFqM=">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</latexit>
Courtesy H.Oide
Standard (?) estimate for baryon asymmetry(’06 Alexander, Peskin & Sheikh-Jabbari)
5. Through the gravitational chiral anomaly, lepton asymmetry is produced.
µ :
<latexit sha1_base64="97dZA+gBvIepvmWUX6saHAp2p88=">AAACEXicbVDLSgMxFL1TX7W+qi7dBIvgqsxIwceq6MZlBacttEPJZNI2NMkMSUYoQ7/BhRv9FHfi1i/wS9yatrOwrQcCh3Pu5Z6cMOFMG9f9dgpr6xubW8Xt0s7u3v5B+fCoqeNUEeqTmMeqHWJNOZPUN8xw2k4UxSLktBWO7qZ+64kqzWL5aMYJDQQeSNZnBBsr+V2R3qBeueJW3RnQKvFyUoEcjV75pxvFJBVUGsKx1h3PTUyQYWUY4XRS6qaaJpiM8IB2LJVYUB1ks7ATdGaVCPVjZZ80aKb+3ciw0HosQjspsBnqZW8q/uuFYuFypm20IY2W4pj+VZAxmaSGSjJP0085MjGa1oMipigxfGwJJorZDyEyxAoTY0ss2aa85V5WSfOi6tWq1w+1Sv0276wIJ3AK5+DBJdThHhrgAwEGz/AKb86L8+58OJ/z0YKT7xzDApyvXweRnc8=</latexit>
cutoff scale for chiral anomaly
6. After reheating EW sphaleron transfers lepton asymmetry to baryon asymmetry
nL(f) =NRL
24(4)2af K
0(f)k<µaf
'
20484
Hinf
Mpl
2 µ
Hinf
4
H3inf
<latexit sha1_base64="dNRaSAr7siHG1yB3TDYBuZta4kw=">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</latexit>
nB = 28
79nL
af
a
3=
7
404484
Hinf
Mpl
2 µ
Hinf
4
H3inf
af
a
3
<latexit sha1_base64="pv47c9hyqjY6bqDe0vU1mS3nMFA=">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</latexit>
Courtesy H.Oide
Standard (?) estimate for baryon asymmetry(’06 Alexander, Peskin & Sheikh-Jabbari)
5. Through the gravitational chiral anomaly, lepton asymmetry is produced.
µ :
<latexit sha1_base64="97dZA+gBvIepvmWUX6saHAp2p88=">AAACEXicbVDLSgMxFL1TX7W+qi7dBIvgqsxIwceq6MZlBacttEPJZNI2NMkMSUYoQ7/BhRv9FHfi1i/wS9yatrOwrQcCh3Pu5Z6cMOFMG9f9dgpr6xubW8Xt0s7u3v5B+fCoqeNUEeqTmMeqHWJNOZPUN8xw2k4UxSLktBWO7qZ+64kqzWL5aMYJDQQeSNZnBBsr+V2R3qBeueJW3RnQKvFyUoEcjV75pxvFJBVUGsKx1h3PTUyQYWUY4XRS6qaaJpiM8IB2LJVYUB1ks7ATdGaVCPVjZZ80aKb+3ciw0HosQjspsBnqZW8q/uuFYuFypm20IY2W4pj+VZAxmaSGSjJP0085MjGa1oMipigxfGwJJorZDyEyxAoTY0ss2aa85V5WSfOi6tWq1w+1Sv0276wIJ3AK5+DBJdThHhrgAwEGz/AKb86L8+58OJ/z0YKT7xzDApyvXweRnc8=</latexit>
cutoff scale for chiral anomaly
6. After reheating EW sphaleron transfers lepton asymmetry to baryon asymmetry
nL(f) =NRL
24(4)2af K
0(f)k<µaf
'
20484
Hinf
Mpl
2 µ
Hinf
4
H3inf
<latexit sha1_base64="dNRaSAr7siHG1yB3TDYBuZta4kw=">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</latexit>
nB = 28
79nL
af
a
3=
7
404484
Hinf
Mpl
2 µ
Hinf
4
H3inf
af
a
3
<latexit sha1_base64="pv47c9hyqjY6bqDe0vU1mS3nMFA=">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</latexit>
Present BAU can be explained for the instant reheating with ..?µ ' Mpl
<latexit sha1_base64="eFHm4/kEsje1BO+jw9wsR6cajUQ=">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</latexit>
Courtesy H.Oide
1. At early times , inevitably one of the helicity modes satisfies . => Appearance of ghost mode.
! 1
<latexit sha1_base64="bsiRk3ReebXYlELn+04GLEjgHzg=">AAACJnicbVBNS8NAFNz4WetX1IvgZbEIXiyJFNSb6MVjBatCU8pm+9Iu3WzC7osSgv4aD170p3gT8ea/8Oq25qDVgYVh5j123oSpFAY9792Zmp6ZnZuvLFQXl5ZXVt219UuTZJpDiycy0dchMyCFghYKlHCdamBxKOEqHJ6O/Ksb0EYk6gLzFDox6ysRCc7QSl13MwBkNNCiP0CmdXJL9wKhIsy7bs2re2PQv8QvSY2UaHbdz6CX8CwGhVwyY9q+l2KnYBoFl3BXDTIDKeND1oe2pYrFYDrF+II7umOVHo0SbZ9COlZ/bhQsNiaPQzsZMxyYSW8k/uuF8a+fC2OjDaA3EQejw04hVJohKP6dJsokxYSOOqM9oYGjzC1hXAt7EOUDphlH22zVNuVP9vKXXO7X/Ub96LxROz4pO6uQLbJNdolPDsgxOSNN0iKc3JMH8kSenUfnxXl13r5Hp5xyZ4P8gvPxBUOaplQ=</latexit>
z2A < 0
<latexit sha1_base64="0t0XYp4k8xyTPFAtkXyi4Wf87Oc=">AAACFXicbVC7TsMwFL3hWcqrwMhiUSExVUlVCZAYCiyMRaIP1IbKcZzWqp1EtoNUon4FAwt8ChtiZeZLWHHbDLTlSJaOzrlX9/h4MWdK2/a3tbS8srq2ntvIb25t7+wW9vYbKkokoXUS8Ui2PKwoZyGta6Y5bcWSYuFx2vQG12O/+UilYlF4p4cxdQXuhSxgBGsj3T91Lx/K6ALZ3ULRLtkToEXiZKQIGWrdwk/Hj0giaKgJx0q1HTvWboqlZoTTUb6TKBpjMsA92jY0xIIqN50EHqFjo/goiKR5oUYT9e9GioVSQ+GZSYF1X817Y/FfzxMzl1NlovWpPxdHB2duysI40TQk0zRBwpGO0Lgi5DNJieZDQzCRzHwIkT6WmGhTZN405cz3skga5ZJTKZ3fVorVq6yzHBzCEZyAA6dQhRuoQR0ICHiGV3izXqx368P6nI4uWdnOAczA+voF3wietQ==</latexit>
2. Baryon asymmetry/Gravitational waves UV divergent. Is it physical?
👻Remember Leila’s talk
Courtesy H.Oide
Is ghost dangerous? zA = 0
<latexit sha1_base64="D6jZeYdQ/HvPSkyLG5osVsh7xlw=">AAACEXicbVDLSsNAFJ3UV62vqks3g0VwVRIpqAuh6sZlBdMW2lAmk5t26GQSZiZCDf0GF270U9yJW7/AL3HrtM3Cth4YOJxzL/fM8RPOlLbtb6uwsrq2vlHcLG1t7+zulfcPmipOJQWXxjyWbZ8o4EyAq5nm0E4kkMjn0PKHtxO/9QhSsVg86FECXkT6goWMEm0k96l3fWX3yhW7ak+Bl4mTkwrK0eiVf7pBTNMIhKacKNVx7ER7GZGaUQ7jUjdVkBA6JH3oGCpIBMrLpmHH+MQoAQ5jaZ7QeKr+3chIpNQo8s1kRPRALXoT8V/Pj+YuZ8pEG0CwEEeHF17GRJJqEHSWJkw51jGe1IMDJoFqPjKEUMnMhzAdEEmoNiWWTFPOYi/LpHlWdWrVy/tapX6Td1ZER+gYnSIHnaM6ukMN5CKKGHpGr+jNerHerQ/rczZasPKdQzQH6+sX6zKdvg==</latexit>
= 8
k, kphys =
k
a=
8Hinf
<latexit sha1_base64="uCkkJnmOflKE9QYZ3ovXTAYBPHY=">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</latexit>
at
If the physical momentum at that time is larger than the cutoff scale of the theory, the ghost might not be physical.
(’05 Alexander & Martin)
It just gives the upper bound of : || < 8Hinf
Mpl
<latexit sha1_base64="CO//odVbko1gnEuAmRVvnsZ/AU8=">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</latexit>
<latexit sha1_base64="hylDeY8CUP0GQmPoeBNlm/3dqig=">AAACEnicbVDLSgMxFM3UV62vqks3wSK4KjNSUHdFNy4r9CG0Q8lk7rSxSWZIMkIZ+g8u3OinuBO3/oBf4ta0nYVtPRA4nHMv9+QECWfauO63U1hb39jcKm6Xdnb39g/Kh0dtHaeKQovGPFYPAdHAmYSWYYbDQ6KAiIBDJxjdTv3OEyjNYtk04wR8QQaSRYwSY6V2rzkEQ/rlilt1Z8CrxMtJBeVo9Ms/vTCmqQBpKCdadz03MX5GlGGUw6TUSzUkhI7IALqWSiJA+9ks7QSfWSXEUazskwbP1L8bGRFaj0VgJwUxQ73sTcV/vUAsXM60jTaEcCmOia78jMkkNSDpPE2UcmxiPO0Hh0wBNXxsCaGK2Q9hOiSKUGNbLNmmvOVeVkn7ourVqtf3tUr9Ju+siE7QKTpHHrpEdXSHGqiFKHpEz+gVvTkvzrvz4XzORwtOvnOMFuB8/QJjMp6T</latexit>
N < 1.1 1071/2
Hinf
105Mpl
1
<latexit sha1_base64="XmMix0EDrhEQbOtjqzmcUN8zjc0=">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</latexit>
For the slow-roll inflation:
👻Remember Leila’s talk
Courtesy H.Oide
UV divergence?1. An approach is to say ..
The divergence is physical, which comes from unknown UV physics. The cut-off scale of the chiral gravitational effect is taken to be the right-handed neutrino mass, , with type-I sea-saw being in mind.
µ = MR
<latexit sha1_base64="qGsGW4A7Gy4hjVuGfxoevKn/KCY=">AAACIHicbVDLSsNAFJ3UV62vWJduBovgqiRSUBdC0Y0boYp9QBPCZDJph84kYWYiltBfceFGP8WduNQfceukzcK2Hhg4nHMv98zxE0alsqwvo7Syura+Ud6sbG3v7O6Z+9WOjFOBSRvHLBY9H0nCaETaiipGeokgiPuMdP3Rde53H4mQNI4e1DghLkeDiIYUI6Ulz6w6PIWX8NZzOFJDwbP7iWfWrLo1BVwmdkFqoEDLM3+cIMYpJ5HCDEnZt61EuRkSimJGJhUnlSRBeIQGpK9phDiRbjbNPoHHWglgGAv9IgWn6t+NDHEpx9zXk3lCuejl4r+ez+cuZ1JHG5JgIY4Kz92MRkmqSIRnacKUQRXDvC0YUEGwYmNNEBZUfwjiIRIIK91pRTdlL/ayTDqndbtRv7hr1JpXRWdlcAiOwAmwwRloghvQAm2AwRN4Bq/gzXgx3o0P43M2WjKKnQMwB+P7F+CHo4A=</latexit>
2. The other approach is to say ..
We should renormalize it!!!
MR < 1016GeV
<latexit sha1_base64="uQvJLlre1fqK5h9fxPg7BkLOkRE=">AAACL3icbVDLSgMxFM3UV62vUZduokVwVWak+AAXRRe6EarYB7S1ZNLbNjSZGZKMUIZZ+zUu3OiniBtx6xe4NX0ItvVA4HDOveTc44WcKe0471Zqbn5hcSm9nFlZXVvfsDe3yiqIJIUSDXggqx5RwJkPJc00h2oogQiPQ8XrXQz8ygNIxQL/TvdDaAjS8VmbUaKN1LR3r5t1QXRXivg2OXOd+9g9SvCvdAnlpGlnnZwzBJ4l7phk0RjFpv1dbwU0EuBryolSNdcJdSMmUjPKIcnUIwUhoT3SgZqhPhGgGvHwlATvG6WF24E0z9d4qP7diIlQqi88MznIqKa9gfiv54mJn2NlonWhNRVHt08aMfPDSINPR2naEcc6wIPycItJoJr3DSFUMnMQpl0iCdWm4oxpyp3uZZaUD3NuPnd6k88WzsedpdEO2kMHyEXHqICuUBGVEEWP6Am9oFfr2XqzPqzP0WjKGu9sowlYXz/ymqm0</latexit>
=> constraint:
Courtesy H.Oide
How to renormalize the UV divergence
hRR()i = 1
2a4@
Z
k<af
d3k
(2)3kX
A=R,L
A
z2A
"|µA
k0|2
k2
z0AzA
2!|µA
k |2 z0AzA
(µAkµ
Ak
0+ h.c.)
#
<latexit sha1_base64="Gnb0/T51mTCk/f6ANblyAU7CP5o=">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</latexit>
with µAk () =
1pkexpiki exp
A
32
W,3/2
i
r4 32
64k
!
<latexit sha1_base64="TzFtp4fQK2mEnGUL60JN1mx1xok=">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</latexit>
hRR()i =3H6
inf
2M2pl
"
Hinf
4
+ 3
Hinf
2
10 log
2
Hinf
+
39
2 10
#+O
2
<latexit sha1_base64="phSow7PX49mqewypi/icUqibf80=">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</latexit>
# by using the Mellin-Barens representation
W,µ(z) =ez/2
2i
Z i1
i1dsdzs
(s )(s µ+ 1/2)(s+ µ+ 1/2)
( µ+ 1/2)(µ + 1/2)
<latexit sha1_base64="EYOcx8jXt0476b7ucNXvqR12QUE=">AAACzHicbZFNbxMxEIa9y1cJXykcuVgEpFQl6W5UqfRQqYIDiAMqomkqdZOV1+ttrNhey/YiJZav/Cz+B7+EK07iVm3KSJbefWZe73imkIxqkyR/ovje/QcPH209bj15+uz5i/b2yzNdNwqTIa5Zrc4LpAmjggwNNYycS0UQLxgZFbNPy/zoJ1Ga1uLUzCUZc3QpaEUxMh7l7d+j3GYzJCV6n/HGdRc78AhmlULYkontLfYGztkBzCSF1MGMCpPbHl2KyszdxF5LWGpYLiY6mLPPiHPU1b315TswgJ4nvNlN9wY30O4Vcle+YLuuDdh/hsy6HObtTtJPVgHvijSIDghxkrf/ZmWNG06EwQxpfZEm0owtUoZiRlwrazSRCM/QJbnwUiBO9Niu5uzgO09KWNXKH2Hgit50WMS1nvPCV3Jkpnozt4T/zRX81p+t9q1NSbnRjqk+jC0VsjFE4HU3VcOgqeFys7CkimDD5l4grKh/EMRT5Jdh/P5bflLp5lzuirNBP93vH37f7xx/DDPbAq/BG9AFKTgAx+ALOAFDgKO30dfoR3Qaf4tNbGO3Lo2j4HkFbkX86x8I6trS</latexit>
1p256/2 3
'
16
<latexit sha1_base64="cjNHlJLtY6G4vEDUI2uu05Ft1Uc=">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</latexit>
(cf. ’18 Adshead+, ’19 Ballardini+ )
Courtesy H.Oide
How to renormalize the UV divergence
hRR()i = 1
2a4@
Z
k<af
d3k
(2)3kX
A=R,L
A
z2A
"|µA
k0|2
k2
z0AzA
2!|µA
k |2 z0AzA
(µAkµ
Ak
0+ h.c.)
#
<latexit sha1_base64="Gnb0/T51mTCk/f6ANblyAU7CP5o=">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</latexit>
with µAk () =
1pkexpiki exp
A
32
W,3/2
i
r4 32
64k
!
<latexit sha1_base64="TzFtp4fQK2mEnGUL60JN1mx1xok=">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</latexit>
hRR()i =3H6
inf
2M2pl
"
Hinf
4
+ 3
Hinf
2
10 log
2
Hinf
+
39
2 10
#+O
2
<latexit sha1_base64="phSow7PX49mqewypi/icUqibf80=">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</latexit>
# by using the Mellin-Barens representation
W,µ(z) =ez/2
2i
Z i1
i1dsdzs
(s )(s µ+ 1/2)(s+ µ+ 1/2)
( µ+ 1/2)(µ + 1/2)
<latexit sha1_base64="EYOcx8jXt0476b7ucNXvqR12QUE=">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</latexit>
(cf. ’18 Adshead+, ’19 Ballardini+ )
“Minimal subtraction” 1p256/2 3
'
16
<latexit sha1_base64="cjNHlJLtY6G4vEDUI2uu05Ft1Uc=">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</latexit>
Courtesy H.Oide
UV divergence can be removed by the following center terms,
EOM for inflaton :
N642Mpl
hRRiren
<latexit sha1_base64="0HI++S/x7g1huUij3wYBkLW7OAo=">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</latexit>
(cf. ’07 Fischler & Paban, ’19 Ballardini+ )
+ · · ·
<latexit sha1_base64="s1zRjbD13127Xa7M4yFy6pGJ2WM=">AAACE3icbVDLSgMxFL1TX7W+qi7dBIsgCGVGCuqu6MZlBfuAdiiZTKYNTSZDkhHK0I9w4UY/xZ249QP8Erem7Sxs64HA4Zx7uScnSDjTxnW/ncLa+sbmVnG7tLO7t39QPjxqaZkqQptEcqk6AdaUs5g2DTOcdhJFsQg4bQeju6nffqJKMxk/mnFCfYEHMYsYwcZK7YseCaXR/XLFrbozoFXi5aQCORr98k8vlCQVNDaEY627npsYP8PKMMLppNRLNU0wGeEB7VoaY0G1n83iTtCZVUIUSWVfbNBM/buRYaH1WAR2UmAz1MveVPzXC8TC5UzbaEMaLsUx0bWfsThJDY3JPE2UcmQkmhaEQqYoMXxsCSaK2Q8hMsQKE2NrLNmmvOVeVknrsurVqjcPtUr9Nu+sCCdwCufgwRXU4R4a0AQCI3iGV3hzXpx358P5nI8WnHznGBbgfP0CEbye7w==</latexit>
=@2+ V 0 =
N642Mpl
hRRi Lct
<latexit sha1_base64="n6nDrfmImmqLRXYSEujICZbdl/U=">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</latexit>
Lct =(a1R3gµ + a2R(RR)g
µ + a3(RR)R
µ)@µ@
+ (a4R2 + a5R
µRµ)(@µ@) + (a6Rgµ + a7Rµ)(@µ@)
<latexit sha1_base64="MC/QX0YKeCbmvUdudorM423UmT4=">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</latexit>
Courtesy H.Oide
If we take the minimal subtraction, the resultant BAU is
nB =7
404484
39
2 10
Hinf
Mpl
2
H3inf
af
a
3
<latexit sha1_base64="iHC8ZtfB6h0RzOepndIbsI4VFY8=">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</latexit>
For the instant reheating, we obtainnB
s' 8.3 1028
8Hinf/Mpl
Hinf
105Mpl
9/2
<latexit sha1_base64="fL7yq2j1EHOJifcmxVTWgTOqRMY=">AAACq3icbVHLThsxFPUMfdD0QVqW3ViNKsGCMBOoGnaIbthUoioBVBxGHudOxsLzqH2nUmT5U/phfEm3dSYBNaFXsnR87j328XFaK2kwiu6CcOPJ02fPN190Xr56/War+/bdhakaLWAkKlXpq5QbULKEEUpUcFVr4EWq4DK9/TLvX/4CbWRVnuOshnHBp6XMpODoqaT7m2WaC1smJ84aR5mRBfykw/4BZeihoXF0Y/cGQ99qB9l5DsidHdLThBUcc11YWWZu/+vDtlbO3auZggx3FtJVgbPtyZ8cXVUyLac57t7Yo/2BS7q9qB+1RR+DeAl6ZFlnSfcPm1SiKaBEobgx13FU49hyjVIocB3WGKi5uOVTuPaw5N7k2LYxOvrRMxOaVdqvEmnL/quwvDBmVqR+cm7YrPfm5H97abFyszXeWg6TNTuYDcc+mrpBKMXCTdYoihWdfxydSA0C1cwDLrT0D6Ii5z5Y9N/b8UnF67k8BheDfnzYP/p22Ds+WWa2Sd6TD2SHxOQzOSan5IyMiAg2gt1gEByEe+H38EfIFqNhsNRsk5UK4S/wRdP5</latexit>
It is hard to explain the present BAU ...
😢
Courtesy H.Oide
If we take the minimal subtraction, the resultant BAU is
nB =7
404484
39
2 10
Hinf
Mpl
2
H3inf
af
a
3
<latexit sha1_base64="iHC8ZtfB6h0RzOepndIbsI4VFY8=">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</latexit>
For the instant reheating, we obtainnB
s' 8.3 1028
8Hinf/Mpl
Hinf
105Mpl
9/2
<latexit sha1_base64="fL7yq2j1EHOJifcmxVTWgTOqRMY=">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</latexit>
It is hard to explain the present BAU ...But is there any reason we shall employ the minimal subtraction? The renormalization condition that fixes the finite term that remains after renormalization cannot be determined.
Without the knowledge of the UV completion, we cannot exclude the possibility that we can keep the large finite term.
😢
Courtesy H.Oide
Adopt the lepton asymmetry just after inflation:
nL(f) '
20484
Hinf
Mpl
2 µ
Hinf
4
H3inf
<latexit sha1_base64="Opp53K12iCH0k8pYxeB6zcodR6I=">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</latexit>
The cosmic history:
End of inflation Reheating Mat-Rad
equality Present
Hf ' Hinf
<latexit sha1_base64="ATV4v6eZvVh8EXmlAS1av3re0Dc=">AAACMHicbVDLSgMxFM3UV62vUZduQovgqsxIQd0V3XRZwT6gLSWT3mlDk5kxyQhl6N6vceFGP0VX4tYfcGumHdC2Hggczr2XnHO8iDOlHefdyq2tb2xu5bcLO7t7+wf24VFThbGk0KAhD2XbIwo4C6ChmebQjiQQ4XFoeeObdN56AKlYGNzpSQQ9QYYB8xkl2kh9u1jrdwXRIykSf4q7igm4x78aC/xp3y45ZWcGvErcjJRQhnrf/u4OQhoLCDTlRKmO60S6lxCpGeUwLXRjBRGhYzKEjqEBEaB6ySzLFJ8aZYD9UJoXaDxT/14kRCg1EZ7ZTD2q5Vkq/jvzxMLPiTLWRjBYsqP9y55JHcUaAjp348cc6xCn7eEBk0A1nxhCqGQmEKYjIgnVpuOCacpd7mWVNM/LbqV8dVspVa+zzvLoBBXRGXLRBaqiGqqjBqLoET2hF/RqPVtv1of1OV/NWdnNMVqA9fUDKzGq8A==</latexit>
T = TR
<latexit sha1_base64="6anX4vLinp2i2UXkif+dCyX0CJo=">AAACEXicbVDLSsNAFJ3UV62vqks3g0VwVRIpqAuh6MZllaYttKFMJjft0MkkzEyEEvoNLtzop7gTt36BX+LWaZuFbT0wcDjnXu6Z4yecKW3b31ZhbX1jc6u4XdrZ3ds/KB8etVScSgoujXksOz5RwJkAVzPNoZNIIJHPoe2P7qZ++wmkYrFo6nECXkQGgoWMEm0kt3nT7D/2yxW7as+AV4mTkwrK0eiXf3pBTNMIhKacKNV17ER7GZGaUQ6TUi9VkBA6IgPoGipIBMrLZmEn+MwoAQ5jaZ7QeKb+3chIpNQ48s1kRPRQLXtT8V/PjxYuZ8pEG0KwFEeHV17GRJJqEHSeJkw51jGe1oMDJoFqPjaEUMnMhzAdEkmoNiWWTFPOci+rpHVRdWrV64dapX6bd1ZEJ+gUnSMHXaI6ukcN5CKKGHpGr+jNerHerQ/rcz5asPKdY7QA6+sXA3KdzQ==</latexit>
EOSw
<latexit sha1_base64="oTxWFQduV47F1iZIeUu187mprZc=">AAACDXicbVDLSgMxFM3UV62vqks3wSK4KjMiqLuiG5ct2Ae0Q8lk7rShSWZIMkoZ+gUu3OinuBO3foNf4ta0nYVtPRA4nHMv9+QECWfauO63U1hb39jcKm6Xdnb39g/Kh0ctHaeKQpPGPFadgGjgTELTMMOhkyggIuDQDkZ3U7/9CEqzWD6YcQK+IAPJIkaJsVLjqV+uuFV3BrxKvJxUUI56v/zTC2OaCpCGcqJ113MT42dEGUY5TEq9VENC6IgMoGupJAK0n82CTvCZVUIcxco+afBM/buREaH1WAR2UhAz1MveVPzXC8TC5UzbaEMIl+KY6NrPmExSA5LO00QpxybG02pwyBRQw8eWEKqY/RCmQ6IINbbAkm3KW+5llbQuqt5l9aZxWand5p0V0Qk6RefIQ1eohu5RHTURRYCe0St6c16cd+fD+ZyPFpx85xgtwPn6BY+QnIY=</latexit>
No late-time entropy production
Baryon-to-entropy ratio is fixed here
Courtesy H.Oide
Adopt the lepton asymmetry just after inflation:
nL(f) '
20484
Hinf
Mpl
2 µ
Hinf
4
H3inf
<latexit sha1_base64="Opp53K12iCH0k8pYxeB6zcodR6I=">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</latexit>
The cosmic history:
End of inflation Reheating Mat-Rad
equality Present
Hf ' Hinf
<latexit sha1_base64="ATV4v6eZvVh8EXmlAS1av3re0Dc=">AAACMHicbVDLSgMxFM3UV62vUZduQovgqsxIQd0V3XRZwT6gLSWT3mlDk5kxyQhl6N6vceFGP0VX4tYfcGumHdC2Hggczr2XnHO8iDOlHefdyq2tb2xu5bcLO7t7+wf24VFThbGk0KAhD2XbIwo4C6ChmebQjiQQ4XFoeeObdN56AKlYGNzpSQQ9QYYB8xkl2kh9u1jrdwXRIykSf4q7igm4x78aC/xp3y45ZWcGvErcjJRQhnrf/u4OQhoLCDTlRKmO60S6lxCpGeUwLXRjBRGhYzKEjqEBEaB6ySzLFJ8aZYD9UJoXaDxT/14kRCg1EZ7ZTD2q5Vkq/jvzxMLPiTLWRjBYsqP9y55JHcUaAjp348cc6xCn7eEBk0A1nxhCqGQmEKYjIgnVpuOCacpd7mWVNM/LbqV8dVspVa+zzvLoBBXRGXLRBaqiGqqjBqLoET2hF/RqPVtv1of1OV/NWdnNMVqA9fUDKzGq8A==</latexit>
T = TR
<latexit sha1_base64="6anX4vLinp2i2UXkif+dCyX0CJo=">AAACEXicbVDLSsNAFJ3UV62vqks3g0VwVRIpqAuh6MZllaYttKFMJjft0MkkzEyEEvoNLtzop7gTt36BX+LWaZuFbT0wcDjnXu6Z4yecKW3b31ZhbX1jc6u4XdrZ3ds/KB8etVScSgoujXksOz5RwJkAVzPNoZNIIJHPoe2P7qZ++wmkYrFo6nECXkQGgoWMEm0kt3nT7D/2yxW7as+AV4mTkwrK0eiXf3pBTNMIhKacKNV17ER7GZGaUQ6TUi9VkBA6IgPoGipIBMrLZmEn+MwoAQ5jaZ7QeKb+3chIpNQ48s1kRPRQLXtT8V/PjxYuZ8pEG0KwFEeHV17GRJJqEHSeJkw51jGe1oMDJoFqPjaEUMnMhzAdEkmoNiWWTFPOci+rpHVRdWrV64dapX6bd1ZEJ+gUnSMHXaI6ukcN5CKKGHpGr+jNerHerQ/rcz5asPKdY7QA6+sXA3KdzQ==</latexit>
EOSw
<latexit sha1_base64="oTxWFQduV47F1iZIeUu187mprZc=">AAACDXicbVDLSgMxFM3UV62vqks3wSK4KjMiqLuiG5ct2Ae0Q8lk7rShSWZIMkoZ+gUu3OinuBO3foNf4ta0nYVtPRA4nHMv9+QECWfauO63U1hb39jcKm6Xdnb39g/Kh0ctHaeKQpPGPFadgGjgTELTMMOhkyggIuDQDkZ3U7/9CEqzWD6YcQK+IAPJIkaJsVLjqV+uuFV3BrxKvJxUUI56v/zTC2OaCpCGcqJ113MT42dEGUY5TEq9VENC6IgMoGupJAK0n82CTvCZVUIcxco+afBM/buREaH1WAR2UhAz1MveVPzXC8TC5UzbaEMIl+KY6NrPmExSA5LO00QpxybG02pwyBRQw8eWEKqY/RCmQ6IINbbAkm3KW+5llbQuqt5l9aZxWand5p0V0Qk6RefIQ1eohu5RHTURRYCe0St6c16cd+fD+ZyPFpx85xgtwPn6BY+QnIY=</latexit>
No late-time entropy production
Baryon-to-entropy ratio is fixed here
Usual reheating withnB
s< 1.2 1018
Hf
1013GeV
1/2 µ
1016GeV
4
8Hf/Mpl
<latexit sha1_base64="MCrm/wyujAAV5Cz2I/wDqKqT/qw=">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</latexit>
😢w 1/3
<latexit sha1_base64="2qe8tKo6CcL2oELnNiq3ISl5wFA=">AAACFHicbVC7TsMwFHXKq5RXgZHFokJiKglUArYKFsYi0YfURpXj3LZWbSfYDqiK+hMMLPApbIiVnS9hxW0z0MKRLB2dc6/u8QlizrRx3S8nt7S8srqWXy9sbG5t7xR39xo6ShSFOo14pFoB0cCZhLphhkMrVkBEwKEZDK8nfvMBlGaRvDOjGHxB+pL1GCXGSq3HDod77+SsWyy5ZXcK/Jd4GSmhDLVu8bsTRjQRIA3lROu258bGT4kyjHIYFzqJhpjQIelD21JJBGg/neYd4yOrhLgXKfukwVP190ZKhNYjEdhJQcxAL3oT8V8vEHOXU22jDSBciGN6F37KZJwYkHSWppdwbCI8aQiHTAE1fGQJoYrZD2E6IIpQY3ss2Ka8xV7+ksZp2auUL28rpepV1lkeHaBDdIw8dI6q6AbVUB1RxNETekGvzrPz5rw7H7PRnJPt7KM5OJ8/QZqe/Q==</latexit>
Courtesy H.Oide
It’s too early to give up!
If , effective entropy “reduction” can occur. w > 1/3
<latexit sha1_base64="tPvOlJ2ykBZxnLlY2YOQUdK001M=">AAACEXicbVDLSsNAFJ3UV62vqks3g0VwVRMtqBspunFZwbSFNpTJ5KYdOpOEmYlSQr/BhRv9FHfi1i/wS9w6bbOw1QMDh3Pu5Z45fsKZ0rb9ZRWWlldW14rrpY3Nre2d8u5eU8WppODSmMey7RMFnEXgaqY5tBMJRPgcWv7wZuK3HkAqFkf3epSAJ0g/YiGjRBvJfbxyTs565YpdtafAf4mTkwrK0eiVv7tBTFMBkaacKNVx7ER7GZGaUQ7jUjdVkBA6JH3oGBoRAcrLpmHH+MgoAQ5jaV6k8VT9vZERodRI+GZSED1Qi95E/NfzxdzlTJloAwgW4ujwwstYlKQaIjpLE6Yc6xhP6sEBk0A1HxlCqGTmQ5gOiCRUmxJLpilnsZe/pHladWrVy7tapX6dd1ZEB+gQHSMHnaM6ukUN5CKKGHpCL+jVerberHfrYzZasPKdfTQH6/MHgf6dfw==</latexit>
Courtesy H.Oide
Axion-like particle: shift-symmetric pseudo scalar
It is rather strange to assume the potential-driven inflation with matter-like reheating epoch.
?-1.0 -0.5 0.5 1.0
0.5
1.0
1.5
2.0
Courtesy H.Oide
Axion-like particle: shift-symmetric pseudo scalar
It is rather strange to assume the potential-driven inflation with matter-like reheating epoch.
It is not strange to consider the k-inflation with kination reheating epoch and gravitational reheating.
L(X,) =K()X
M2pl
+X2
M4pl
, X = 1
2(@)2
<latexit sha1_base64="PH2q4DlbRS/+U7UXmPr+irLuVr8=">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</latexit>
X ' M
2pl
2K(), 3H2
plM2pl '
1
4K
2()
<latexit sha1_base64="XsiR/o4gc9brMaVVimhreAn5URk=">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</latexit>
(’99 Armendariz-Picon, Damour & Mukhanov)
(’93 Spokoiny, ’96 Joyce)
Courtesy H.Oide
Axion-like particle: shift-symmetric pseudo scalar
It is rather strange to assume the potential-driven inflation with matter-like reheating epoch.
It is not strange to consider the k-inflation with kination reheating epoch and gravitational reheating.
L(X,) =K()X
M2pl
+X2
M4pl
, X = 1
2(@)2
<latexit sha1_base64="PH2q4DlbRS/+U7UXmPr+irLuVr8=">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</latexit>
X ' M
2pl
2K(), 3H2
plM2pl '
1
4K
2()
<latexit sha1_base64="XsiR/o4gc9brMaVVimhreAn5URk=">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</latexit>
Benefit: ' N22
Hinf
Mpl
3/2
<latexit sha1_base64="4eybBk5GJf5jUeMF9E62lqokhHE=">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</latexit>
<8Hinf
Mpl) N < 104
Hinf
105Mpl
1/2
<latexit sha1_base64="UNTyvBgERkOIgxL4DxWcDbZ9uaY=">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</latexit>
(’99 Armendariz-Picon, Damour & Mukhanov)
(’93 Spokoiny, ’96 Joyce)
Courtesy H.Oide
Reheating after k-inflation: K() ! const.
<latexit sha1_base64="5m2hug8T7Umip9lW4v3lMVT6R7Q=">AAACMnicbVC7SgNBFJ31bXxFLW0Go6BN2JWA2ok2gk0EowF3CbOTSXZwHsvMXSUs+QG/xsJG/0Q7sbW3dTZJYaIHBg7n3Muce+JUcAu+/+ZNTc/Mzs0vLJaWlldW18rrG9dWZ4ayBtVCm2ZMLBNcsQZwEKyZGkZkLNhNfHdW+Df3zFiu1RX0UhZJ0lW8wykBJ7XKOxd7YZrwfRwa3k2AGKMfcCgJJEbmVCsL/SpulSt+1R8A/yXBiFTQCPVW+Ttsa5pJpoAKYu1t4KcQ5cQAp4L1S2FmWUroHemyW0cVkcxG+eCaPt51Sht3tHFPAR6ovzdyIq3tydhNFjntpFeI/3qxHPs5ty5awtoTcaBzFOVcpRkwRYdpOpnAoHHRH25zwyiIniOEGu4OwjQhhlBwLZdcU8FkL3/J9UE1qFWPL2uVk9NRZwtoC22jPRSgQ3SCzlEdNRBFj+gJvaBX79l79z68z+HolDfa2URj8L5+AJJHqw4=</latexit>
= p =K
M2pl
X
<latexit sha1_base64="176sfJ37JwrtJlIFxeLUtY4g83E=">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</latexit>
w = 1
<latexit sha1_base64="vzakCqlvu9lEy69JGpEGf8x1QZo=">AAACD3icbVDLSgMxFL1TX7W+qi7dBIvgqsxIQV0IRTcuK9oHtEPJZNI2NMkMSUYpQz/BhRv9FHfi1k/wS9yatrOwrQcCh3Pu5Z6cIOZMG9f9dnIrq2vrG/nNwtb2zu5ecf+goaNEEVonEY9UK8CaciZp3TDDaStWFIuA02YwvJn4zUeqNIvkgxnF1Be4L1mPEWysdP905XWLJbfsToGWiZeREmSodYs/nTAiiaDSEI61bntubPwUK8MIp+NCJ9E0xmSI+7RtqcSCaj+dRh2jE6uEqBcp+6RBU/XvRoqF1iMR2EmBzUAvehPxXy8Qc5dTbaMNaLgQx/Qu/JTJODFUklmaXsKRidCkHBQyRYnhI0swUcx+CJEBVpgYW2HBNuUt9rJMGmdlr1K+vKuUqtdZZ3k4gmM4BQ/OoQq3UIM6EOjDM7zCm/PivDsfzudsNOdkO4cwB+frF5F8nQg=</latexit>
EOS / a6
<latexit sha1_base64="u9EJbK6Svv5iejCaZ+AwTNrs9dY=">AAACIXicbVC7TsMwFHV4lvIKdGSxqJBYqBJU8dgqWBiLRB9SEyrHcRqrdhzZDlIU9VsYWOBT2BAb4kNYcR8DbTmSpaNz7tU9PkHKqNKO82WtrK6tb2yWtsrbO7t7+/bBYVuJTGLSwoIJ2Q2QIowmpKWpZqSbSoJ4wEgnGN6O/c4TkYqK5EHnKfE5GiQ0ohhpI/XtiidjAb1UilQLiB6Ls4tR3646NWcCuEzcGamCGZp9+8cLBc44STRmSKme66TaL5DUFDMyKnuZIinCQzQgPUMTxInyi0n4ETwxSggjIc1LNJyofzcKxJXKeWAmOdKxWvTG4r9ewOcuF8pEi0m4EEdHV35BkzTTJMHTNFHGoCljXBcMqSRYs9wQhCU1H4I4RhJhbUotm6bcxV6WSfu85tZr1/f1auNm1lkJHIFjcApccAka4A40QQtgkINn8ArerBfr3fqwPqejK9ZspwLmYH3/AsFUo/M=</latexit>
(’93 Spokoiny, ’96 Joyce)
Courtesy H.Oide
Reheating after k-inflation: K() ! const.
<latexit sha1_base64="5m2hug8T7Umip9lW4v3lMVT6R7Q=">AAACMnicbVC7SgNBFJ31bXxFLW0Go6BN2JWA2ok2gk0EowF3CbOTSXZwHsvMXSUs+QG/xsJG/0Q7sbW3dTZJYaIHBg7n3Muce+JUcAu+/+ZNTc/Mzs0vLJaWlldW18rrG9dWZ4ayBtVCm2ZMLBNcsQZwEKyZGkZkLNhNfHdW+Df3zFiu1RX0UhZJ0lW8wykBJ7XKOxd7YZrwfRwa3k2AGKMfcCgJJEbmVCsL/SpulSt+1R8A/yXBiFTQCPVW+Ttsa5pJpoAKYu1t4KcQ5cQAp4L1S2FmWUroHemyW0cVkcxG+eCaPt51Sht3tHFPAR6ovzdyIq3tydhNFjntpFeI/3qxHPs5ty5awtoTcaBzFOVcpRkwRYdpOpnAoHHRH25zwyiIniOEGu4OwjQhhlBwLZdcU8FkL3/J9UE1qFWPL2uVk9NRZwtoC22jPRSgQ3SCzlEdNRBFj+gJvaBX79l79z68z+HolDfa2URj8L5+AJJHqw4=</latexit>
= p =K
M2pl
X
<latexit sha1_base64="176sfJ37JwrtJlIFxeLUtY4g83E=">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</latexit>
w = 1
<latexit sha1_base64="vzakCqlvu9lEy69JGpEGf8x1QZo=">AAACD3icbVDLSgMxFL1TX7W+qi7dBIvgqsxIQV0IRTcuK9oHtEPJZNI2NMkMSUYpQz/BhRv9FHfi1k/wS9yatrOwrQcCh3Pu5Z6cIOZMG9f9dnIrq2vrG/nNwtb2zu5ecf+goaNEEVonEY9UK8CaciZp3TDDaStWFIuA02YwvJn4zUeqNIvkgxnF1Be4L1mPEWysdP905XWLJbfsToGWiZeREmSodYs/nTAiiaDSEI61bntubPwUK8MIp+NCJ9E0xmSI+7RtqcSCaj+dRh2jE6uEqBcp+6RBU/XvRoqF1iMR2EmBzUAvehPxXy8Qc5dTbaMNaLgQx/Qu/JTJODFUklmaXsKRidCkHBQyRYnhI0swUcx+CJEBVpgYW2HBNuUt9rJMGmdlr1K+vKuUqtdZZ3k4gmM4BQ/OoQq3UIM6EOjDM7zCm/PivDsfzudsNOdkO4cwB+frF5F8nQg=</latexit>
EOS / a6
<latexit sha1_base64="u9EJbK6Svv5iejCaZ+AwTNrs9dY=">AAACIXicbVC7TsMwFHV4lvIKdGSxqJBYqBJU8dgqWBiLRB9SEyrHcRqrdhzZDlIU9VsYWOBT2BAb4kNYcR8DbTmSpaNz7tU9PkHKqNKO82WtrK6tb2yWtsrbO7t7+/bBYVuJTGLSwoIJ2Q2QIowmpKWpZqSbSoJ4wEgnGN6O/c4TkYqK5EHnKfE5GiQ0ohhpI/XtiidjAb1UilQLiB6Ls4tR3646NWcCuEzcGamCGZp9+8cLBc44STRmSKme66TaL5DUFDMyKnuZIinCQzQgPUMTxInyi0n4ETwxSggjIc1LNJyofzcKxJXKeWAmOdKxWvTG4r9ewOcuF8pEi0m4EEdHV35BkzTTJMHTNFHGoCljXBcMqSRYs9wQhCU1H4I4RhJhbUotm6bcxV6WSfu85tZr1/f1auNm1lkJHIFjcApccAka4A40QQtgkINn8ArerBfr3fqwPqejK9ZspwLmYH3/AsFUo/M=</latexit>
a
<latexit sha1_base64="IpQ8ZiwT1PrnQDiNHD0vL26aw+0=">AAACDXicbVDLSgMxFM3UV62vqks3wSK4KjNSUHdFNy5bsA9oh5LJ3GlDk8yQZIQy9AtcuNFPcSdu/Qa/xK1pOwvbeiBwOOde7skJEs60cd1vp7CxubW9U9wt7e0fHB6Vj0/aOk4VhRaNeay6AdHAmYSWYYZDN1FARMChE4zvZ37nCZRmsXw0kwR8QYaSRYwSY6UmGZQrbtWdA68TLycVlKMxKP/0w5imAqShnGjd89zE+BlRhlEO01I/1ZAQOiZD6FkqiQDtZ/OgU3xhlRBHsbJPGjxX/25kRGg9EYGdFMSM9Ko3E//1ArF0OdM22gjClTgmuvEzJpPUgKSLNFHKsYnxrBocMgXU8IklhCpmP4TpiChCjS2wZJvyVntZJ+2rqler3jZrlfpd3lkRnaFzdIk8dI3q6AE1UAtRBOgZvaI358V5dz6cz8Vowcl3TtESnK9fawqccA==</latexit>
<latexit sha1_base64="jtPJmHSllVEx/luT4L+lH27/CBc=">AAACEHicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoO6KblxWsA9oh5LJpJ3QJDMkGaEM/QUXbvRT3Ilb/8AvcWumnYVtPRA4nHMv9+QECWfauO63U1pb39jcKm9Xdnb39g+qh0dtHaeK0BaJeay6AdaUM0lbhhlOu4miWAScdoLxXe53nqjSLJaPZpJQX+CRZENGsMmlvoriQbXm1t0Z0CrxClKDAs1B9acfxiQVVBrCsdY9z02Mn2FlGOF0WumnmiaYjPGI9iyVWFDtZ7OsU3RmlRANY2WfNGim/t3IsNB6IgI7KbCJ9LKXi/96gVi4nGkbLaLhUhwzvPYzJpPUUEnmaYYpRyZGeTsoZIoSwyeWYKKY/RAiEVaYGNthxTblLfeyStoXde+yfvNwWWvcFp2V4QRO4Rw8uIIG3EMTWkAggmd4hTfnxXl3PpzP+WjJKXaOYQHO1y/2jZ3S</latexit>
inf = 3H2infM
2inf
<latexit sha1_base64="Wq/dADyooORCKxZsX0Iv3MJEnEU=">AAACRHicbVDLSsNAFJ34rPUVdelmsAiuSlKLj4VQdNONUME+oKlhMpm0Q2eSMDMRSuif+DUu3OgP+A/uRNyJkzYL23pg4HDuvcw5x4sZlcqy3o2l5ZXVtfXCRnFza3tn19zbb8koEZg0ccQi0fGQJIyGpKmoYqQTC4K4x0jbG95k8/YjEZJG4b0axaTHUT+kAcVIack1zxwxiFyHIzUQPKVhML6Cp7A+ozxU4O2c4Jolq2xNABeJnZMSyNFwzW/Hj3DCSagwQ1J2bStWvRQJRTEj46KTSBIjPER90tU0RJzIXjrJN4bHWvFhEAn9QgUn6t+LFHEpR9zTm5lLOT/LxH9nHp/5OZXa2oD4c3ZUcNHTueNEkRBP3QQJgyqCWaPQp4JgxUaaICyoDgTxAAmEle69qJuy53tZJK1K2a6WL++qpdp13lkBHIIjcAJscA5qoA4aoAkweALP4BW8GS/Gh/FpfE1Xl4z85gDMwPj5BVFssuc=</latexit>
inflation end
/ a6
<latexit sha1_base64="u9EJbK6Svv5iejCaZ+AwTNrs9dY=">AAACIXicbVC7TsMwFHV4lvIKdGSxqJBYqBJU8dgqWBiLRB9SEyrHcRqrdhzZDlIU9VsYWOBT2BAb4kNYcR8DbTmSpaNz7tU9PkHKqNKO82WtrK6tb2yWtsrbO7t7+/bBYVuJTGLSwoIJ2Q2QIowmpKWpZqSbSoJ4wEgnGN6O/c4TkYqK5EHnKfE5GiQ0ohhpI/XtiidjAb1UilQLiB6Ls4tR3646NWcCuEzcGamCGZp9+8cLBc44STRmSKme66TaL5DUFDMyKnuZIinCQzQgPUMTxInyi0n4ETwxSggjIc1LNJyofzcKxJXKeWAmOdKxWvTG4r9ewOcuF8pEi0m4EEdHV35BkzTTJMHTNFHGoCljXBcMqSRYs9wQhCU1H4I4RhJhbUotm6bcxV6WSfu85tZr1/f1auNm1lkJHIFjcApccAka4A40QQtgkINn8ArerBfr3fqwPqejK9ZspwLmYH3/AsFUo/M=</latexit>
reheating
/ a4
<latexit sha1_base64="MdiAANpQKcVV+l8PzlTCgIcg5tk=">AAACIXicbVDLSgMxFM3UV62v0S7dBIvgxjIjBXVXdOOygn1AZyyZTKYNzSRDkhGGod/iwo1+ijtxJ36IW9N2Frb1QOBwzr3ckxMkjCrtOF9WaW19Y3OrvF3Z2d3bP7APjzpKpBKTNhZMyF6AFGGUk7ammpFeIgmKA0a6wfh26nefiFRU8AedJcSP0ZDTiGKkjTSwq54cCeglUiRaQPSYnzcmA7vm1J0Z4CpxC1IDBVoD+8cLBU5jwjVmSKm+6yTaz5HUFDMyqXipIgnCYzQkfUM5iony81n4CTw1SggjIc3jGs7Uvxs5ipXK4sBMxkiP1LI3Ff/1gnjhcq5MtBEJl+Lo6MrPKU9STTiep4lSBk0Z07pgSCXBmmWGICyp+RDEIyQR1qbUimnKXe5llXQu6m6jfn3fqDVvis7K4BicgDPggkvQBHegBdoAgww8g1fwZr1Y79aH9TkfLVnFThUswPr+Bb4Ao/E=</latexit>
(’93 Spokoiny, ’96 Joyce)
Courtesy H.Oide
Reheating after k-inflation: K() ! const.
<latexit sha1_base64="5m2hug8T7Umip9lW4v3lMVT6R7Q=">AAACMnicbVC7SgNBFJ31bXxFLW0Go6BN2JWA2ok2gk0EowF3CbOTSXZwHsvMXSUs+QG/xsJG/0Q7sbW3dTZJYaIHBg7n3Muce+JUcAu+/+ZNTc/Mzs0vLJaWlldW18rrG9dWZ4ayBtVCm2ZMLBNcsQZwEKyZGkZkLNhNfHdW+Df3zFiu1RX0UhZJ0lW8wykBJ7XKOxd7YZrwfRwa3k2AGKMfcCgJJEbmVCsL/SpulSt+1R8A/yXBiFTQCPVW+Ttsa5pJpoAKYu1t4KcQ5cQAp4L1S2FmWUroHemyW0cVkcxG+eCaPt51Sht3tHFPAR6ovzdyIq3tydhNFjntpFeI/3qxHPs5ty5awtoTcaBzFOVcpRkwRYdpOpnAoHHRH25zwyiIniOEGu4OwjQhhlBwLZdcU8FkL3/J9UE1qFWPL2uVk9NRZwtoC22jPRSgQ3SCzlEdNRBFj+gJvaBX79l79z68z+HolDfa2URj8L5+AJJHqw4=</latexit>
= p =K
M2pl
X
<latexit sha1_base64="176sfJ37JwrtJlIFxeLUtY4g83E=">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</latexit>
w = 1
<latexit sha1_base64="vzakCqlvu9lEy69JGpEGf8x1QZo=">AAACD3icbVDLSgMxFL1TX7W+qi7dBIvgqsxIQV0IRTcuK9oHtEPJZNI2NMkMSUYpQz/BhRv9FHfi1k/wS9yatrOwrQcCh3Pu5Z6cIOZMG9f9dnIrq2vrG/nNwtb2zu5ecf+goaNEEVonEY9UK8CaciZp3TDDaStWFIuA02YwvJn4zUeqNIvkgxnF1Be4L1mPEWysdP905XWLJbfsToGWiZeREmSodYs/nTAiiaDSEI61bntubPwUK8MIp+NCJ9E0xmSI+7RtqcSCaj+dRh2jE6uEqBcp+6RBU/XvRoqF1iMR2EmBzUAvehPxXy8Qc5dTbaMNaLgQx/Qu/JTJODFUklmaXsKRidCkHBQyRYnhI0swUcx+CJEBVpgYW2HBNuUt9rJMGmdlr1K+vKuUqtdZZ3k4gmM4BQ/OoQq3UIM6EOjDM7zCm/PivDsfzudsNOdkO4cwB+frF5F8nQg=</latexit>
EOS / a6
<latexit sha1_base64="u9EJbK6Svv5iejCaZ+AwTNrs9dY=">AAACIXicbVC7TsMwFHV4lvIKdGSxqJBYqBJU8dgqWBiLRB9SEyrHcRqrdhzZDlIU9VsYWOBT2BAb4kNYcR8DbTmSpaNz7tU9PkHKqNKO82WtrK6tb2yWtsrbO7t7+/bBYVuJTGLSwoIJ2Q2QIowmpKWpZqSbSoJ4wEgnGN6O/c4TkYqK5EHnKfE5GiQ0ohhpI/XtiidjAb1UilQLiB6Ls4tR3646NWcCuEzcGamCGZp9+8cLBc44STRmSKme66TaL5DUFDMyKnuZIinCQzQgPUMTxInyi0n4ETwxSggjIc1LNJyofzcKxJXKeWAmOdKxWvTG4r9ewOcuF8pEi0m4EEdHV35BkzTTJMHTNFHGoCljXBcMqSRYs9wQhCU1H4I4RhJhbUotm6bcxV6WSfu85tZr1/f1auNm1lkJHIFjcApccAka4A40QQtgkINn8ArerBfr3fqwPqejK9ZspwLmYH3/AsFUo/M=</latexit>
a
<latexit sha1_base64="IpQ8ZiwT1PrnQDiNHD0vL26aw+0=">AAACDXicbVDLSgMxFM3UV62vqks3wSK4KjNSUHdFNy5bsA9oh5LJ3GlDk8yQZIQy9AtcuNFPcSdu/Qa/xK1pOwvbeiBwOOde7skJEs60cd1vp7CxubW9U9wt7e0fHB6Vj0/aOk4VhRaNeay6AdHAmYSWYYZDN1FARMChE4zvZ37nCZRmsXw0kwR8QYaSRYwSY6UmGZQrbtWdA68TLycVlKMxKP/0w5imAqShnGjd89zE+BlRhlEO01I/1ZAQOiZD6FkqiQDtZ/OgU3xhlRBHsbJPGjxX/25kRGg9EYGdFMSM9Ko3E//1ArF0OdM22gjClTgmuvEzJpPUgKSLNFHKsYnxrBocMgXU8IklhCpmP4TpiChCjS2wZJvyVntZJ+2rqler3jZrlfpd3lkRnaFzdIk8dI3q6AE1UAtRBOgZvaI358V5dz6cz8Vowcl3TtESnK9fawqccA==</latexit>
<latexit sha1_base64="jtPJmHSllVEx/luT4L+lH27/CBc=">AAACEHicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoO6KblxWsA9oh5LJpJ3QJDMkGaEM/QUXbvRT3Ilb/8AvcWumnYVtPRA4nHMv9+QECWfauO63U1pb39jcKm9Xdnb39g+qh0dtHaeK0BaJeay6AdaUM0lbhhlOu4miWAScdoLxXe53nqjSLJaPZpJQX+CRZENGsMmlvoriQbXm1t0Z0CrxClKDAs1B9acfxiQVVBrCsdY9z02Mn2FlGOF0WumnmiaYjPGI9iyVWFDtZ7OsU3RmlRANY2WfNGim/t3IsNB6IgI7KbCJ9LKXi/96gVi4nGkbLaLhUhwzvPYzJpPUUEnmaYYpRyZGeTsoZIoSwyeWYKKY/RAiEVaYGNthxTblLfeyStoXde+yfvNwWWvcFp2V4QRO4Rw8uIIG3EMTWkAggmd4hTfnxXl3PpzP+WjJKXaOYQHO1y/2jZ3S</latexit>
inf = 3H2infM
2inf
<latexit sha1_base64="Wq/dADyooORCKxZsX0Iv3MJEnEU=">AAACRHicbVDLSsNAFJ34rPUVdelmsAiuSlKLj4VQdNONUME+oKlhMpm0Q2eSMDMRSuif+DUu3OgP+A/uRNyJkzYL23pg4HDuvcw5x4sZlcqy3o2l5ZXVtfXCRnFza3tn19zbb8koEZg0ccQi0fGQJIyGpKmoYqQTC4K4x0jbG95k8/YjEZJG4b0axaTHUT+kAcVIack1zxwxiFyHIzUQPKVhML6Cp7A+ozxU4O2c4Jolq2xNABeJnZMSyNFwzW/Hj3DCSagwQ1J2bStWvRQJRTEj46KTSBIjPER90tU0RJzIXjrJN4bHWvFhEAn9QgUn6t+LFHEpR9zTm5lLOT/LxH9nHp/5OZXa2oD4c3ZUcNHTueNEkRBP3QQJgyqCWaPQp4JgxUaaICyoDgTxAAmEle69qJuy53tZJK1K2a6WL++qpdp13lkBHIIjcAJscA5qoA4aoAkweALP4BW8GS/Gh/FpfE1Xl4z85gDMwPj5BVFssuc=</latexit>
inflation end
/ a6
<latexit sha1_base64="u9EJbK6Svv5iejCaZ+AwTNrs9dY=">AAACIXicbVC7TsMwFHV4lvIKdGSxqJBYqBJU8dgqWBiLRB9SEyrHcRqrdhzZDlIU9VsYWOBT2BAb4kNYcR8DbTmSpaNz7tU9PkHKqNKO82WtrK6tb2yWtsrbO7t7+/bBYVuJTGLSwoIJ2Q2QIowmpKWpZqSbSoJ4wEgnGN6O/c4TkYqK5EHnKfE5GiQ0ohhpI/XtiidjAb1UilQLiB6Ls4tR3646NWcCuEzcGamCGZp9+8cLBc44STRmSKme66TaL5DUFDMyKnuZIinCQzQgPUMTxInyi0n4ETwxSggjIc1LNJyofzcKxJXKeWAmOdKxWvTG4r9ewOcuF8pEi0m4EEdHV35BkzTTJMHTNFHGoCljXBcMqSRYs9wQhCU1H4I4RhJhbUotm6bcxV6WSfu85tZr1/f1auNm1lkJHIFjcApccAka4A40QQtgkINn8ArerBfr3fqwPqejK9ZspwLmYH3/AsFUo/M=</latexit>
reheating
/ a4
<latexit sha1_base64="MdiAANpQKcVV+l8PzlTCgIcg5tk=">AAACIXicbVDLSgMxFM3UV62v0S7dBIvgxjIjBXVXdOOygn1AZyyZTKYNzSRDkhGGod/iwo1+ijtxJ36IW9N2Frb1QOBwzr3ckxMkjCrtOF9WaW19Y3OrvF3Z2d3bP7APjzpKpBKTNhZMyF6AFGGUk7ammpFeIgmKA0a6wfh26nefiFRU8AedJcSP0ZDTiGKkjTSwq54cCeglUiRaQPSYnzcmA7vm1J0Z4CpxC1IDBVoD+8cLBU5jwjVmSKm+6yTaz5HUFDMyqXipIgnCYzQkfUM5iony81n4CTw1SggjIc3jGs7Uvxs5ipXK4sBMxkiP1LI3Ff/1gnjhcq5MtBEJl+Lo6MrPKU9STTiep4lSBk0Z07pgSCXBmmWGICyp+RDEIyQR1qbUimnKXe5llXQu6m6jfn3fqDVvis7K4BicgDPggkvQBHegBdoAgww8g1fwZr1Y79aH9TkfLVnFThUswPr+Bb4Ao/E=</latexit>
nB
s= 9.7 1011
µ
1016GeV
4
105
Treh
107GeV
1
<latexit sha1_base64="bf7cms68jTMNdhEHp/e2/mln3u4=">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</latexit>
(’93 Spokoiny, ’96 Joyce)
Courtesy H.Oide
Proof of concept for successful reheating
a
<latexit sha1_base64="IpQ8ZiwT1PrnQDiNHD0vL26aw+0=">AAACDXicbVDLSgMxFM3UV62vqks3wSK4KjNSUHdFNy5bsA9oh5LJ3GlDk8yQZIQy9AtcuNFPcSdu/Qa/xK1pOwvbeiBwOOde7skJEs60cd1vp7CxubW9U9wt7e0fHB6Vj0/aOk4VhRaNeay6AdHAmYSWYYZDN1FARMChE4zvZ37nCZRmsXw0kwR8QYaSRYwSY6UmGZQrbtWdA68TLycVlKMxKP/0w5imAqShnGjd89zE+BlRhlEO01I/1ZAQOiZD6FkqiQDtZ/OgU3xhlRBHsbJPGjxX/25kRGg9EYGdFMSM9Ko3E//1ArF0OdM22gjClTgmuvEzJpPUgKSLNFHKsYnxrBocMgXU8IklhCpmP4TpiChCjS2wZJvyVntZJ+2rqler3jZrlfpd3lkRnaFzdIk8dI3q6AE1UAtRBOgZvaI358V5dz6cz8Vowcl3TtESnK9fawqccA==</latexit>
<latexit sha1_base64="jtPJmHSllVEx/luT4L+lH27/CBc=">AAACEHicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoO6KblxWsA9oh5LJpJ3QJDMkGaEM/QUXbvRT3Ilb/8AvcWumnYVtPRA4nHMv9+QECWfauO63U1pb39jcKm9Xdnb39g+qh0dtHaeK0BaJeay6AdaUM0lbhhlOu4miWAScdoLxXe53nqjSLJaPZpJQX+CRZENGsMmlvoriQbXm1t0Z0CrxClKDAs1B9acfxiQVVBrCsdY9z02Mn2FlGOF0WumnmiaYjPGI9iyVWFDtZ7OsU3RmlRANY2WfNGim/t3IsNB6IgI7KbCJ9LKXi/96gVi4nGkbLaLhUhwzvPYzJpPUUEnmaYYpRyZGeTsoZIoSwyeWYKKY/RAiEVaYGNthxTblLfeyStoXde+yfvNwWWvcFp2V4QRO4Rw8uIIG3EMTWkAggmd4hTfnxXl3PpzP+WjJKXaOYQHO1y/2jZ3S</latexit>
inf = 3H2infM
2inf
<latexit sha1_base64="Wq/dADyooORCKxZsX0Iv3MJEnEU=">AAACRHicbVDLSsNAFJ34rPUVdelmsAiuSlKLj4VQdNONUME+oKlhMpm0Q2eSMDMRSuif+DUu3OgP+A/uRNyJkzYL23pg4HDuvcw5x4sZlcqy3o2l5ZXVtfXCRnFza3tn19zbb8koEZg0ccQi0fGQJIyGpKmoYqQTC4K4x0jbG95k8/YjEZJG4b0axaTHUT+kAcVIack1zxwxiFyHIzUQPKVhML6Cp7A+ozxU4O2c4Jolq2xNABeJnZMSyNFwzW/Hj3DCSagwQ1J2bStWvRQJRTEj46KTSBIjPER90tU0RJzIXjrJN4bHWvFhEAn9QgUn6t+LFHEpR9zTm5lLOT/LxH9nHp/5OZXa2oD4c3ZUcNHTueNEkRBP3QQJgyqCWaPQp4JgxUaaICyoDgTxAAmEle69qJuy53tZJK1K2a6WL++qpdp13lkBHIIjcAJscA5qoA4aoAkweALP4BW8GS/Gh/FpfE1Xl4z85gDMwPj5BVFssuc=</latexit>
inflation end
/ a6
<latexit sha1_base64="u9EJbK6Svv5iejCaZ+AwTNrs9dY=">AAACIXicbVC7TsMwFHV4lvIKdGSxqJBYqBJU8dgqWBiLRB9SEyrHcRqrdhzZDlIU9VsYWOBT2BAb4kNYcR8DbTmSpaNz7tU9PkHKqNKO82WtrK6tb2yWtsrbO7t7+/bBYVuJTGLSwoIJ2Q2QIowmpKWpZqSbSoJ4wEgnGN6O/c4TkYqK5EHnKfE5GiQ0ohhpI/XtiidjAb1UilQLiB6Ls4tR3646NWcCuEzcGamCGZp9+8cLBc44STRmSKme66TaL5DUFDMyKnuZIinCQzQgPUMTxInyi0n4ETwxSggjIc1LNJyofzcKxJXKeWAmOdKxWvTG4r9ewOcuF8pEi0m4EEdHV35BkzTTJMHTNFHGoCljXBcMqSRYs9wQhCU1H4I4RhJhbUotm6bcxV6WSfu85tZr1/f1auNm1lkJHIFjcApccAka4A40QQtgkINn8ArerBfr3fqwPqejK9ZspwLmYH3/AsFUo/M=</latexit>
reheating
/ a4
<latexit sha1_base64="MdiAANpQKcVV+l8PzlTCgIcg5tk=">AAACIXicbVDLSgMxFM3UV62v0S7dBIvgxjIjBXVXdOOygn1AZyyZTKYNzSRDkhGGod/iwo1+ijtxJ36IW9N2Frb1QOBwzr3ckxMkjCrtOF9WaW19Y3OrvF3Z2d3bP7APjzpKpBKTNhZMyF6AFGGUk7ammpFeIgmKA0a6wfh26nefiFRU8AedJcSP0ZDTiGKkjTSwq54cCeglUiRaQPSYnzcmA7vm1J0Z4CpxC1IDBVoD+8cLBU5jwjVmSKm+6yTaz5HUFDMyqXipIgnCYzQkfUM5iony81n4CTw1SggjIc3jGs7Uvxs5ipXK4sBMxkiP1LI3Ff/1gnjhcq5MtBEJl+Lo6MrPKU9STTiep4lSBk0Z07pgSCXBmmWGICyp+RDEIyQR1qbUimnKXe5llXQu6m6jfn3fqDVvis7K4BicgDPggkvQBHegBdoAgww8g1fwZr1Y79aH9TkfLVnFThUswPr+Bb4Ao/E=</latexit>
104m
2H
2inf
<latexit sha1_base64="r1MuElbt1MwaPiuJoL/fQ5GlOzs=">AAACP3icbVDNSsNAGNzUv1r/oh69LBbBiyUpBfVW9NJjBdsKTRs2m02zdDcJuxuhhDyHT+PBiz6DT+BNvIk3N20PtnVgYZjv+9iZ8RJGpbKsd6O0tr6xuVXeruzs7u0fmIdHXRmnApMOjlksHjwkCaMR6SiqGHlIBEHcY6TnjW+Lee+RCEnj6F5NEjLgaBTRgGKktOSatiPC2HVwSKEjKYfQtobZRSOHfFifyS3X4UiFgmc0CnKtmlWrZk0BV4k9J1UwR9s1vx0/xiknkcIMSdm3rUQNMiQUxYzkFSeVJEF4jEakr2mEOJGDbBoth2da8WEQC/0iBafq34sMcSkn3NObhUu5PCvEf2ceX/g5k9paSPwlOyq4GujcSapIhGdugpRBFcOiTOhTQbBiE00QFlQHgjhEAmGlK6/opuzlXlZJt16zG7Xru0a1eTPvrAxOwCk4Bza4BE3QAm3QARg8gWfwCt6MF+PD+DS+ZqslY35zDBZg/PwCXvqvTg==</latexit>
(cf. ’19 Hashiba & Yokoyama)
/ a3
<latexit sha1_base64="jds5/8oLN96TzvOFTTdWeCiah/0=">AAACIXicbVC7TsMwFHV4lvIKdGSxqJBYqBKoBGwVLIxFog+pCZXjOI1VO45sBymK+i0MLPApbIgN8SGsuI+BthzJ0tE59+oenyBlVGnH+bJWVtfWNzZLW+Xtnd29ffvgsK1EJjFpYcGE7AZIEUYT0tJUM9JNJUE8YKQTDG/HfueJSEVF8qDzlPgcDRIaUYy0kfp2xZOxgF4qRaoFRI/F2cWob1edmjMBXCbujFTBDM2+/eOFAmecJBozpFTPdVLtF0hqihkZlb1MkRThIRqQnqEJ4kT5xST8CJ4YJYSRkOYlGk7UvxsF4krlPDCTHOlYLXpj8V8v4HOXC2WixSRciKOjK7+gSZppkuBpmihj0JQxrguGVBKsWW4IwpKaD0EcI4mwNqWWTVPuYi/LpH1ec+u16/t6tXEz66wEjsAxOAUuuAQNcAeaoAUwyMEzeAVv1ov1bn1Yn9PRFWu2UwFzsL5/AbxWo/A=</latexit>
m Hinf ' 1013GeV
<latexit sha1_base64="UZGoy2/RjbRLN5HaEu1o2BvxbYk=">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</latexit>
) Treh ' 107GeV
<latexit sha1_base64="E5WMtkghAOa2tb9a16PzgSiaaTg=">AAACQXicbVDLSgMxFM3UV62vqks3wSK4KjNaqO6KLnRZpS/o1JJJbzuhycyYZJQy9EP8Ghdu9BP8BHfixoUb04dgqwcCh3PuJeceL+JMadt+tVILi0vLK+nVzNr6xuZWdnunpsJYUqjSkIey4REFnAVQ1UxzaEQSiPA41L3++civ34FULAwqehBBS5BewLqMEm2kdvbYvWY9XxMpw3tcabuCaF+KRII/xK5iAm6xY98U8Y9xAbVhO5uz8/YY+C9xpiSHpii3s59uJ6SxgEBTTpRqOnakWwmRmlEOw4wbK4gI7ZMeNA0NiADVSsbHDfGBUTq4G0rzAo3H6u+NhAilBsIzk6OMat4bif96npj5OVEmmg+duTi6e9JKWBDFGgI6SdONOdYhHtWJO0wC1XxgCKGSmYMw9YkkVJvSM6YpZ76Xv6R2lHcK+dOrQq50Nu0sjfbQPjpEDiqiErpEZVRFFD2gR/SMXqwn6816tz4moylrurOLZmB9fQM/W7FY</latexit>
nB
s= 9.7 1011
µ
1016GeV
4
105
Treh
107GeV
1
<latexit sha1_base64="bf7cms68jTMNdhEHp/e2/mln3u4=">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</latexit>
Courtesy H.Oide
1. Gravitational Leptogenesis is a baryogenesis mechanism that takes advantage of the gravitational chiral anomaly.
2. The ghost mode can be pushed above the cutoff scale of the theory so that it is not catastrophe of the scenario.
3. The UV divergence can be renormalized but renormalization condition cannot be fixed without the knowledge of the UV physics.
4. Nevertheless resultant baryon asymmetry is small in general. With somehow exotic assumtions, i) the UV cutoff-dependent baryon asymmetry, and ii) kination with gravitational reheating, it can finally make it to explain the present BAU.