Inflationary model building, reconstructing parameters and observational limits

Inflationary model building, reconstructing parameters and observational limits Sayantan Choudhury Physics and Applied Mathematics Unit Indian Statistical Institute, Kolkata Date: 30/09/2014 Contact: sayanphysicsisi@gmail.com Webpage: http://isical.academia.edu/sayantanchoudhury

Inflationary paradigm and allied issues. Observational limits. Modeling inflation and parameter estimation. Reconstruction of inflationary potential. Bottom lines. Open issues and future prospects. 2

DB,arXiv:0907.5424 3

DB,arXiv:0907.5424 4

DB,arXiv:0907.5424 5

Homogeneous and isotropic universe: FRW metric (for spatially flat k=0): 6

Homogeneous and isotropic universe: FRW metric (for spatially flat k=0): Friedman Equations in GR: Equation of continuity in GR: Equation of state: 7

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

Big Bang Puzzles: 1. Horizon problem 2. Flatness problem 3. Monopole problem 9

Big Bang Puzzles: 1. Horizon problem 2. Flatness problem 3. Monopole problem 10

Big Bang Puzzles: 1. Horizon problem 2. Flatness problem 3. Monopole problem 11

Inflationary paradigm and allied issues Condition for inflation: 12

Inflationary paradigm and allied issues Condition for inflation: No. of e-foldings: 13

Inflationary paradigm and allied issues Condition for inflation: No. of e-foldings: Inflationary dynamics: Assume inflaton = scalar 14

Inflationary paradigm and allied issues Condition for inflation: No. of e-foldings: Inflationary dynamics: Assume inflaton = scalar 15

Inflationary paradigm and allied issues Condition for inflation: No. of e-foldings: Inflationary dynamics: Assume inflaton = scalar Scalar Field Eqn.: 16

Inflation via Slow-roll: 21

Inflation via Slow-roll: Flatness/ Slow-Roll parameter 22

Inflation via Slow-roll: Flatness/ Slow-Roll parameter End of inflation Necessarily required to solve horizon problem 23

Inflationary Model Building 24

ALGORITHM 25

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

Inflationary observables: 27

Inflationary observables: Metric perturbation = Curvature (Scalar)+ (SVT decomposition) Gauge(Vector)+ Primordial Gravity Waves (Tensor) 28

Inflationary observables: Metric perturbation = Curvature (Scalar)+ (SVT decomposition) Gauge(Vector)+ Primordial Gravity Waves (Tensor) 29

Inflationary observables: Metric perturbation = Curvature (Scalar)+ (SVT decomposition) Gauge(Vector)+ Primordial Gravity Waves (Tensor) 30

Inflationary observables: arxiv:1404.2601 Metric perturbation = Curvature (Scalar)+ (SVT decomposition) Gauge(Vector)+ Primordial Gravity Waves (Tensor) Power spectrum 31

Inflationary observables: Metric perturbation = Curvature (Scalar)+ (SVT decomposition) DB,LM,arXiv:1404.2601 Gauge(Vector)+ Primordial Gravity Waves (Tensor) Power spectrum 32

Inflationary observables via flow eqn within slow-roll 33

CMB TT Power spectrum 38

CMB TT Power spectrum 39

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

7 3 r= Tensor to scalar ratio 43

Cosmological Parameter Dependences 44

Observational limits 45

Observational limits Origin??? 46

Primordial Gravity Waves: If blue???? 47

Primordial Gravity Waves: If blue???? Deviation from inflationary consistency relation 48

Present status of joint constraints 49

Present status of joint constraints Red tilted Blue tilted 50

Present status of joint constraints Red tilted Red tilted This region is ruled out by the constraint on spectral index/tilt 51

But why value of r is important?? 52

But why value of r is important?? If r is fixed 53

But why value of r is important?? If r is fixed Scale of inflation P.A.R.Ade et. al, arxiv:1303.5082 54

But why value of r is important?? If r is fixed Scale of inflation P.A.R.Ade et. al, arxiv:1303.5082 Reheating temperature SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, 55

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

CMB B-modes???? 58

CMB B-modes???? Peak at l=80 59

SC,PLB 735 (2014) 138 60

Modeling inflation & parameter estimation Hilltop Inflection point Chaotic Natural 61

Modeling inflation & parameter estimation Hilltop Inflection point Chaotic Natural 62

Small Field Model: MSSM inflation 63

Small Field Model: MSSM inflation 64

Small Field Model: MSSM inflation 65

Small Field Model: MSSM inflation 66

Small Field Model: MSSM inflation 67

Small Field Model: MSSM inflation 68

Small Field Model: MSSM inflation Example of Low scale visible sector model of inflation 69

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

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

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

MSSM INFLATON CANDIDATE n=4 flat directions: QQQL,uude,QuQd, QuLe 75

MSSM INFLATON CANDIDATE n=4 flat directions: QQQL,uude,QuQd, QuLe Gauge invariant superpotential: 76

MSSM INFLATON CANDIDATE n=6 flat directions: udd, LLe 77

MSSM INFLATON CANDIDATE n=6 flat directions: udd, LLe Gauge invariant Superpotential: 78

Saddle point condition: 79

Saddle point condition: Sub-Planckian 80

SC,JHEP 04 (2014) 105, SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, 81

SC,JHEP 04 (2014) 105, SC,AM,EP, JHEP 04 (2014) 077, SC,AM,SP, JCAP 07 (2013) 041, 82

Validity of slow-roll approximation SC,AM,SP, JCAP 07 (2013) 041 Slow-Roll Solution of Mukhanov-Sasaki Eqn 83

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

For n=4 flat directions SC,SP, JCAP 04 (2012) 018 Inflationary observables 86

For n=4 flat directions SC,SP, JCAP 04 (2012) 018 Saddle point condition: Inflationary observables 87

For n=4 flat directions SC,SP, JCAP 04 (2012) 018 Saddle point condition: Inflationary observables 88

For n=6 flat directions SC,AM,SP, JCAP 07 (2013) 041 + HOSL Inflationary observables 89

For n=6 flat directions SC,AM,SP, JCAP 07 (2013) 041 + HOSL Inflationary observables 90

SC,AM,SP, JCAP 07 (2013) 041 91

SC,AM,SP, JCAP 07 (2013) 041 92

SC,AM,SP, JCAP 07 (2013) 041 93

Reconstruction of inflationary potential 95

Reconstruction of inflationary potential ALGORITHM 96

Reconstruction of inflationary potential Inflationary observables at CMB scale ALGORITHM 97

Reconstruction of inflationary potential Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM 98

Reconstruction of inflationary potential Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM Construct potential and its derivatives at CMB scale 99

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

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

Reconstruction of inflationary potential Inflationary observables at CMB scale Assume Slow-Roll ALGORITHM Construct potential and its derivatives at CMB scale SC,AM,arXiv:1403.5549,1404.3398, SC,arXiv:1406.7618 Reconstructed potential Using matrix inversion technique further construct the co-efficient of Taylor 102 expansion

Reconstruction of inflationary potential SC,AM,arXiv:1403.5549,1404.3398, SC,arXiv:1406.7618 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

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

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

Let us take Planck+WP+High L +BICEP2: 106

Let us take Planck+WP+High L +BICEP2: 107

Let us take Planck+WP+High L +BICEP2: New consistency relations SC,AM,arXiv:1403.5549 108

Let us take Planck+WP+High L +BICEP2: SC,AM,arXiv:1403.5549 New consistency relations 109

TT 110

TE 111

EE EE 112

BB 113

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:1403.5549 3. 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

115

Field excursion is super-planckian or Sub-Planckian??? 116

Field excursion is super-planckian or Sub-Planckian??? Effective field theory prescription Valid??? 117

EFT with Large r????? 118

Tensor-to scalar ratio: 119

Tensor-to scalar ratio: SC,AM,NPB 882 (2014) 386 SC,AM,arXiv:1403.5549,1404.3398, SC,arXiv:1406.7618 120

Tensor-to scalar ratio: SC,AM,NPB 882 (2014) 386 SC,AM,arXiv:1403.5549,1404.3398, SC,arXiv:1406.7618 121

In RS Model: 122

In RS Model: SC,arXiv:1406.7618 123

In RS Model: SC,arXiv:1406.7618 124

Bottom lines High scale models of inflations are favoured after BICEP2. 125

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

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

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

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

Open issues and future prospects Need to check which class of potentials are more favoured by the proposed reconstruction technique. 135

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

Thanks for your time time. 138