Inflationary model building, reconstructing parameters and observational limits
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1 Inflationary model building, reconstructing parameters and observational limits Sayantan Choudhury Physics and Applied Mathematics Unit Indian Statistical Institute, Kolkata Date: 30/09/2014 Contact: Webpage:
2 Inflationary paradigm and allied issues. Observational limits. Modeling inflation and parameter estimation. Reconstruction of inflationary potential. Bottom lines. Open issues and future prospects. 2
3 DB,arXiv:
4 DB,arXiv:
5 DB,arXiv:
6 Homogeneous and isotropic universe: FRW metric (for spatially flat k=0): 6
7 Homogeneous and isotropic universe: FRW metric (for spatially flat k=0): Friedman Equations in GR: Equation of continuity in GR: Equation of state: 7
8 Homogeneous and isotropic universe: FRW metric (for spatially flat k=0): Friedman Equations in GR: Equation of continuity in GR: Equation of state: FRW Solutions: 8
9 Big Bang Puzzles: 1. Horizon problem 2. Flatness problem 3. Monopole problem 9
10 Big Bang Puzzles: 1. Horizon problem 2. Flatness problem 3. Monopole problem 10
11 Big Bang Puzzles: 1. Horizon problem 2. Flatness problem 3. Monopole problem 11
12 Inflationary paradigm and allied issues Condition for inflation: 12
13 Inflationary paradigm and allied issues Condition for inflation: No. of e-foldings: 13
14 Inflationary paradigm and allied issues Condition for inflation: No. of e-foldings: Inflationary dynamics: Assume inflaton = scalar 14
15 Inflationary paradigm and allied issues Condition for inflation: No. of e-foldings: Inflationary dynamics: Assume inflaton = scalar 15
16 Inflationary paradigm and allied issues Condition for inflation: No. of e-foldings: Inflationary dynamics: Assume inflaton = scalar Scalar Field Eqn.: 16
17 Inflation via Slow-roll: 21
18 Inflation via Slow-roll: Flatness/ Slow-Roll parameter 22
19 Inflation via Slow-roll: Flatness/ Slow-Roll parameter End of inflation Necessarily required to solve horizon problem 23
20 Inflationary Model Building 24
21 ALGORITHM 25
22 Construct a potential ALGORITHM Determine the various cosmological parameters Put cosmic variances from observation Apply Slow-Roll technique Determine the field value at the CMB scale from N Determine various CMB inflationary observables Confront with latest observational probes Determine the CMB power spectrum from model 26
23 Inflationary observables: 27
24 Inflationary observables: Metric perturbation = Curvature (Scalar)+ (SVT decomposition) Gauge(Vector)+ Primordial Gravity Waves (Tensor) 28
25 Inflationary observables: Metric perturbation = Curvature (Scalar)+ (SVT decomposition) Gauge(Vector)+ Primordial Gravity Waves (Tensor) 29
26 Inflationary observables: Metric perturbation = Curvature (Scalar)+ (SVT decomposition) Gauge(Vector)+ Primordial Gravity Waves (Tensor) 30
27 Inflationary observables: arxiv: Metric perturbation = Curvature (Scalar)+ (SVT decomposition) Gauge(Vector)+ Primordial Gravity Waves (Tensor) Power spectrum 31
28 Inflationary observables: Metric perturbation = Curvature (Scalar)+ (SVT decomposition) DB,LM,arXiv: Gauge(Vector)+ Primordial Gravity Waves (Tensor) Power spectrum 32
29 Inflationary observables via flow eqn within slow-roll 33
30 34
31 35
32 36
33 37
34 CMB TT Power spectrum 38
35 CMB TT Power spectrum 39
36 WMAP (Upto z=3300) Early Universe Planck Early Universe (PGW etc.) ACT CMB Lensing, SZ effect etc. SDSS LSS,Galaxy evolution and cluster, DM, Lensing Various probes COrE Inflation, CMB EPIC Inflation, CMB SNLS (High z) DE LiteBIRD Inflation,CMB B -mode HST (Upto z=2100) BICEP(1&2) PGW LIGO (INDIGO) GW SPT CMB SZ effect LHC DM PRISM Early Universe, 40 CMB
37 WMAP (Upto z=3300) Early Universe Planck Early Universe (PGW etc.) ACT CMB Lensing, SZ effect etc. SDSS LSS,Galaxy evolution and cluster, DM, Lensing Various probes COrE Inflation, CMB EPIC Inflation, CMB SNLS (High z) DE LiteBIRD Inflation,CMB B -mode HST (Upto z=2100) BICEP(1&2) PGW LIGO (INDIGO) GW SPT CMB SZ effect LHC DM PRISM Early Universe, 41 CMB
38 42
39 7 3 r= Tensor to scalar ratio 43
40 Cosmological Parameter Dependences 44
41 Observational limits 45
42 Observational limits Origin??? 46
43 Primordial Gravity Waves: If blue???? 47
44 Primordial Gravity Waves: If blue???? Deviation from inflationary consistency relation 48
45 Present status of joint constraints 49
46 Present status of joint constraints Red tilted Blue tilted 50
47 Present status of joint constraints Red tilted Red tilted This region is ruled out by the constraint on spectral index/tilt 51
48 But why value of r is important?? 52
49 But why value of r is important?? If r is fixed 53
50 But why value of r is important?? If r is fixed Scale of inflation P.A.R.Ade et. al, arxiv:
51 But why value of r is important?? If r is fixed Scale of inflation P.A.R.Ade et. al, arxiv: Reheating temperature SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, 55
52 But why value of r is important?? If r is fixed Scale of inflation Reheating temperature But if r is fixed via detection of tensor modes at present then scale of inflation lie around the GUT (O( )) scale. SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, 56
53 CMB B-modes???? 58
54 CMB B-modes???? Peak at l=80 59
55 SC,PLB 735 (2014)
56 Modeling inflation & parameter estimation Hilltop Inflection point Chaotic Natural 61
57 Modeling inflation & parameter estimation Hilltop Inflection point Chaotic Natural 62
58 Small Field Model: MSSM inflation 63
59 Small Field Model: MSSM inflation 64
60 Small Field Model: MSSM inflation 65
61 Small Field Model: MSSM inflation 66
62 Small Field Model: MSSM inflation 67
63 Small Field Model: MSSM inflation 68
64 Small Field Model: MSSM inflation Example of Low scale visible sector model of inflation 69
65 Small Field Model: MSSM inflation SC,JHEP 04 (2014) 105, SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, 70
66 Small Field Model: MSSM inflation Example of High scale model of inflation SC,JHEP 04 (2014) 105, SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, Origin??? Hidden Sector : Heavy fields from String sector 71
67 Small Field Model: MSSM inflation Example of High scale model of inflation Cosmological Constant Hubble induced terms SC,JHEP 04 (2014) 105, SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, Origin??? Hidden Sector : Heavy fields from String sector 72
68 73
69 74
70 MSSM INFLATON CANDIDATE n=4 flat directions: QQQL,uude,QuQd, QuLe 75
71 MSSM INFLATON CANDIDATE n=4 flat directions: QQQL,uude,QuQd, QuLe Gauge invariant superpotential: 76
72 MSSM INFLATON CANDIDATE n=6 flat directions: udd, LLe 77
73 MSSM INFLATON CANDIDATE n=6 flat directions: udd, LLe Gauge invariant Superpotential: 78
74 Saddle point condition: 79
75 Saddle point condition: Sub-Planckian 80
76 SC,JHEP 04 (2014) 105, SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, 81
77 SC,JHEP 04 (2014) 105, SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, 82
78 Validity of slow-roll approximation SC,AM,SP, JCAP 07 (2013) 041 Slow-Roll Solution of Mukhanov-Sasaki Eqn 83
79 Validity of slow-roll approximation SC,AM,SP, JCAP 07 (2013) 041 l=2 Slow-Roll Solution of Mukhanov-Sasaki Eqn l=2500 Observed region by Planck 84
80 For n=4 flat directions SC,SP, JCAP 04 (2012) 018 Inflationary observables 86
81 For n=4 flat directions SC,SP, JCAP 04 (2012) 018 Saddle point condition: Inflationary observables 87
82 For n=4 flat directions SC,SP, JCAP 04 (2012) 018 Saddle point condition: Inflationary observables 88
83 For n=6 flat directions SC,AM,SP, JCAP 07 (2013) HOSL Inflationary observables 89
84 For n=6 flat directions SC,AM,SP, JCAP 07 (2013) HOSL Inflationary observables 90
85 SC,AM,SP, JCAP 07 (2013)
86 SC,AM,SP, JCAP 07 (2013)
87 SC,AM,SP, JCAP 07 (2013)
88 94
89 Reconstruction of inflationary potential 95
90 Reconstruction of inflationary potential ALGORITHM 96
91 Reconstruction of inflationary potential Inflationary observables at CMB scale ALGORITHM 97
92 Reconstruction of inflationary potential Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM 98
93 Reconstruction of inflationary potential Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM Construct potential and its derivatives at CMB scale 99
94 Reconstruction of inflationary potential Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM Construct potential and its derivatives at CMB scale Using matrix inversion technique further construct the co-efficient of Taylor 100 expansion
95 Reconstruction of inflationary potential Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM Construct potential and its derivatives at CMB scale Reconstructed potential Using matrix inversion technique further construct the co-efficient of Taylor 101 expansion
96 Reconstruction of inflationary potential Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM Construct potential and its derivatives at CMB scale SC,AM,arXiv: , , SC,arXiv: Reconstructed potential Using matrix inversion technique further construct the co-efficient of Taylor 102 expansion
97 Reconstruction of inflationary potential SC,AM,arXiv: , , SC,arXiv: Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM Construct potential and its derivatives at CMB scale Reconstructed potential Using matrix inversion technique further construct the co-efficient of Taylor 103 expansion
98 Reconstruction of inflationary potential and parameter estimation Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM Construct potential and its derivatives at CMB scale Reconstructed potential Using matrix inversion technique further construct the co-efficient of Taylor 104 expansion
99 Reconstruction of inflationary potential and parameter estimation Inflationary observables at CMB scale Assume Slow-Roll INVERSION PROCEDURE ALGORITHM Construct potential and its derivatives at CMB scale Reconstructed potential Using matrix inversion technique further construct the co-efficient of Taylor 105 expansion
100 Let us take Planck+WP+High L +BICEP2: 106
101 Let us take Planck+WP+High L +BICEP2: 107
102 Let us take Planck+WP+High L +BICEP2: New consistency relations SC,AM,arXiv:
103 Let us take Planck+WP+High L +BICEP2: SC,AM,arXiv: New consistency relations 109
104 TT 110
105 TE 111
106 EE EE 112
107 BB 113
108 Ifs and Buts in the formalism. Let us take Planck+WP+High L +BICEP2: 1. Need to further determine the values of the cosmological parameters. 2. Need to check the proper thermal history can be explained. SC,AM,arXiv: Need to check which class of models are New consistency relations favoured.. 4. To rule out models need to increase the statistical accuracy level by upgrading the tool.. 5. Need to break the degeneracy between the cosmological parameters. 114
109 115
110 Field excursion is super-planckian or Sub-Planckian??? 116
111 Field excursion is super-planckian or Sub-Planckian??? Effective field theory prescription Valid??? 117
112 EFT with Large r????? 118
113 Tensor-to scalar ratio: 119
114 Tensor-to scalar ratio: SC,AM,NPB 882 (2014) 386 SC,AM,arXiv: , , SC,arXiv:
115 Tensor-to scalar ratio: SC,AM,NPB 882 (2014) 386 SC,AM,arXiv: , , SC,arXiv:
116 In RS Model: 122
117 In RS Model: SC,arXiv:
118 In RS Model: SC,arXiv:
119 Bottom lines High scale models of inflations are favoured after BICEP2. 125
120 Bottom lines High scale models of inflations are favoured after BICEP2. Validity of EFT prescription requires: running +HOSL,Mutifield, RS or more sophisticated parametrization for powspec to get large r. 126
121 Bottom lines High scale models of inflations are favoured after BICEP2. Validity of EFT prescription requires: running +HOSL,Mutifield, RS or more sophisticated parametrization for powspec to get large r. Proposed semi-analytical reconstruction technique is valid for any preferred choice of input observational data. 127
122 Bottom lines High scale models of inflations are favoured after BICEP2. Validity of EFT prescription requires: running +HOSL,Mutifield, RS or more sophisticated parametrization for powspec to get large r. Proposed semi-analytical reconstruction technique is valid for any preferred choice of input observational data. High scale MSSM model fits well with CMB TT spectra within 2<l<2500 (Planck). 128
123 Bottom lines High scale models of inflations are favoured after BICEP2. Validity of EFT prescription requires: running +HOSL,Mutifield, RS or more sophisticated parametrization for powspec to get large r. Proposed semi-analytical reconstruction technique is valid for any preferred choice of input observational data. High scale MSSM model fits well with CMB TT spectra within 2<l<2500 (Planck). New sets of infla consistency relations and values of 129 the tensor mode parameters are proposed.
124 Open issues and future prospects To comment on the correct value of r from any observation requires new tools for separating various components of CMB B-modes (=Infla+PMF+NG+Lensing etc.). 130
125 Open issues and future prospects To comment on the correct value of r from any observation requires new tools for separating various components of CMB B-modes (=Infla+PMF+NG+Lensing etc.). Fitting any model at a pivot scale is not enough. Need to check whether the models thoroughly fits well CMB spectra. (For Planck 2<l<2500). 131
126 Open issues and future prospects To comment on the correct value of r from any observation requires new tools for separating various components of CMB B-modes (=Infla+PMF+NG+Lensing etc.). Fitting any model at a pivot scale is not enough. Need to check whether the models thoroughly fits well CMB spectra. (For Planck 2<l<2500). If BICEP results are correct then need to clarify the issue of getting blue tilted gravity waves. 132
127 Open issues and future prospects The primordial non-gaussianity is not yet been detected with high statistical accuracy ( & ). But if it is detected in near future experiments then using this tool it is possible to rule out various inflationary models. 133
128 Open issues and future prospects The primordial non-gaussianity is not yet been detected with high statistical accuracy ( & ). But if it is detected in near future experiments then using this tool it is possible to rule out various inflationary models. To increase the numerical convergence of the proposed reconstruction technique need to incorporate the numerically integrated powspec by solving MS eqn using various numerical methods. 134
129 Open issues and future prospects Need to check which class of potentials are more favoured by the proposed reconstruction technique. 135
130 Open issues and future prospects Need to check which class of potentials are more favoured by the proposed reconstruction technique. Need to work on thermal features. Ex: Reheating, Dark matter etc. 136
131 Open issues and future prospects Need to check which class of potentials are more favoured by the proposed reconstruction technique. Need to work on thermal features. Ex: Reheating, Dark matter etc. Need to propose an unified approach through which it is possible to unify inflation, dark matter & dark energy. Need also to check how Reconstruction business works here. 137
132 Thanks for your time time. 138
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