ORIGIN OF INFLATION Anupam Mazumdar lancaster university We mostly Concentrate on CMB 99% of INFLATION papers are HALF complete!! Wednesday, 23 October 13
Confusions/Conclusions BBN LHC • Inflaton can not be an arbitrary field • Quantifying the Reheat Temperature • Sub-Planckian VEV inflationary models can generate large tensor-to-scalar ratio Wednesday, 23 October 13
Confusion-1 CMB Perturbations Einstein’s Gravity + Equation of State, No modification of GR is required at Low Energies inflation dilutes all matter !! You must explain the relevant DOF. & NOT Just the equation of State 99% of INFLATION papers are happy with an equation of state argument for reheating, whether they are SM or some other radiation -- who cares? ( its part of assumption !! ) Wednesday, 23 October 13
The Inflaton Vacuum cannot be arbitrary: it must know our existence! BBN LHC NO Hidden Radiation - ONLY Standard Model DOF A.M & Rocher, Phys. Rept. (2011), Particle Physics Models of Inflation & Curvaton Wednesday, 23 October 13
Standard Model Higgs The last 50-60 e-foldings of inflation must happen in a visible sector The action ? validity of EFT ? Embedding higgs inflation in sugra does not help introduces more unknown parameters mssm higgses with D-flat direction can overcome these issues Wednesday, 23 October 13
R + R 2 It is utterly INCOMPLETE ! Starobinsky d 4 x √− g [ RF 1 ( � ) R + RF 2 ( � ) ∇ µ ∇ ν R µ ν + R µ ν F 3 ( � ) R µ ν + R ν � µ F 4 ( � ) ∇ ν ∇ λ R µ λ S q = + R λσ F 5 ( � ) ∇ µ ∇ σ ∇ ν ∇ λ R µ ν + RF 6 ( � ) ∇ µ ∇ ν ∇ λ ∇ σ R µ νλσ + R µ λ F 7 ( � ) ∇ ν ∇ σ R µ νλσ λ F 8 ( � ) ∇ µ ∇ σ ∇ ν ∇ ρ R µ νλσ + R µ 1 ν 1 F 9 ( � ) ∇ µ 1 ∇ ν 1 ∇ µ ∇ ν ∇ λ ∇ σ R µ νλσ + R ρ + R µ νλσ F 10 ( � ) R µ νλσ + R ρ µ νλ F 11 ( � ) ∇ ρ ∇ σ R µ νλσ + R µ ρ 1 νσ 1 F 12 ( � ) ∇ ρ 1 ∇ σ 1 ∇ ρ ∇ σ R µ ρνσ F 13 ( � ) ∇ ρ 1 ∇ σ 1 ∇ ν 1 ∇ ν ∇ ρ ∇ σ R µ νλσ + R µ 1 ν 1 ρ 1 σ 1 F 14 ( � ) ∇ ρ 1 ∇ σ 1 ∇ ν 1 ∇ µ 1 ∇ µ ∇ ν ∇ ρ ∇ σ R µ νλσ ] + R ν 1 ρ 1 σ 1 ( µ Gravity Invokes Higher Order Corrections ∞ Z R + R F 1 ( ⇤ ) R + R µ ν F 2 ( ⇤ ) R µ ν + R µ ναβ F 3 ( ⇤ ) R µ ναβ ⇤ d 4 x √− g ⇥ S = ∞ ∆ L = √− g ( α R 2 + β R 2 µ ν + γ R 2 αβ µ ν ) X a n ⇤ n F i ( ⇤ ) = n Classical Gravity becomes 2 F 1 ( ⇤ ) + F 2 ( ⇤ ) + 2 F 3 ( ⇤ ) = 0 WEAK in the UV (Asymptotic Freedom) Biswas, Gerwick, Koivisto & AM, Phys. Rev. Lett. (2012) Wednesday, 23 October 13
BESIDES... GRAVITY/SUPERGRAVITY YOU NEED TO INVOKE THE BSM this is what Nature Cares for !! Wednesday, 23 October 13
Singlet Inflaton has no preference: Billion Hidden Sectors vs. 1 SM φ φ Standard ˜ g 2 φ 2 H 2 , ( Hq L ) q R , FF Model M ∗ M ∗ N Hidden N Hidden N Hidden Hidden φ X X X h i ¯ ˜ φ 2 g 2 i χ 2 i , φ ψ i ψ i , G i G i Sector M ∗ i i i φ N Hidden , h i , g i ??? ◆ ρ X ✓ T R Ω X h 2 ≈ 10 17 10 9 GeV ρ inf Over abundant dark matter from Direct Inflaton decay!! SM Wednesday, 23 October 13
When does the notion of temperature makes sense after Inflation ? Standard Reheat temperature since 1980s This assumes thermalization is achieved instantly at the time of radiation domination How Good the assumption of instant thermalization is? Wednesday, 23 October 13
Quantifying Reheat Temperature Standard estimation of reheat temperature is wrong Matter Domination Radiation Domination Instant thermalization Delayed thermalization AM+Zaldivar, 1310.5143 Wednesday, 23 October 13
Last 50-60 e-folds MUST happen within a Visible Sector M p TeV MSSM/SM Inflation can happen in Many Many VACUA, BUT the Lightest states are naturally displaced from their minimum The lightest states are presumably MSSM/SM Wednesday, 23 October 13
why MSSM ? Predictive power Visible sector inflation ( e.g. MSSM inflaton ) (P)Reheating Visible sector d.o.f. e.g. MSSM Precise determination of T R Direct decay Thermal / non-thermal leptogenesis, Thermal relics EW baryogenesis, ... Affleck-Dine baryogenesis Visible sector Q-ball decay dark matter ( e.g. LSP ) Known Couplings SUSY breaking scale is the main uncertainty Wednesday, 23 October 13
SUSY Flat directions V Shift symmetry L as a Gauge Invariant LH u operator minimises the Potential H u SUSY is broken LH u V L Shift symmetry is broken H u Enqvist, Mazumdar, Phys. Rept. (2004) Wednesday, 23 October 13
Gauge invariant Inflatons SU (3) × SU (2) l × U (1) Y 1 1 1 u 1 d 2 d 3 d γ d β u α 3 = 3 φ 1 = 3 φ 3 φ 2 = √ √ √ 1 � φ ⇥ � 0 ⇥ 1 1 L b L 1 L 2 e 3 e 3 = 3 φ L a 1 = 2 = φ √ √ √ 0 3 3 ✓ 0 ◆ 1 ✓ φ ◆ 1 H u H d H d = H u = φ √ √ 0 2 2 SU (3) × SU (2) l × U (1) Y × U (1) B − L ✓ 0 ◆ 1 1 ✓ φ ◆ 1 H u = 3 φ N = NH u L L = φ √ 3 √ 0 √ 3 Allahverdi, Enqvist, Bellido, AM, (PRL, 2006), (JCAP, 2007), Allahverdi, Kusenko, AM, JCAP (2007), Allahverdi, Dutta, AM (PRL 2007), Chatterjee, AM, JCAP (2011) Wednesday, 23 October 13
MSSM Inflaton Potential 2 Φ n � � ∂ W X W ∼ λ � � V = Soft SUSY terms + M n − 3 � � ∂ Φ p n> 3 � � Inflection Point You can compute the potential from first principle without assuming ad-hoc interactions Higher order corrections can be included within Effective field theory Potentials are constructed by small perturbations Allahverdi, Enqvist, Garcia-Bellido, around the Enhanced Gauge Symmetry Point AM, PRL (2006), JCAP (2006) Wednesday, 23 October 13
Constructing a Potential at the lowest order V ( | φ | ) = 1 2 m 2 | φ | 2 − Ah 3 φ 3 + h 2 | φ | 4 ( n = 3) φ 6 + λ 2 | φ | 10 V ( | φ | ) = 1 2 m 2 | φ | 2 − A λ ( n = 6) 6 M 3 M 6 p p Inflation takes place always Below Planck VeV Allahverdi, Enqvist, Garcia-Bellido, AM, PRL (2006), JCAP (2006), Bueno-Sanchez, Dimopoulos, Lyth, JCAP (2006), Allahverdi, Kusenko AM, JCAP (2006), Allahverdi, Dutta, AM, PRL (2007) Wednesday, 23 October 13
LHC & PLANCK JOINT Constraints on Inflatons Renormalization Group W = λ ( LLe )( LLe ) or λ ( udd )( udd ) Equations can relate LHC M 3 M 3 scale to Inflationary scale p p LLe LHC Rules Planck Out P ζ = 2 . 196 +0 . 051 − 0 . 060 × 10 − 9 n s = 0 . 960 ± 0 . 073 udd Boehm, DaSilva, AM & Pukartas, PRD (2012), Wang, Pukartas & AM, JCAP (2013) Wednesday, 23 October 13
Can MSSM inflation produce large tensor to scalar ratio? Wednesday, 23 October 13
N=1 SUGRA & MSSM Inflation MSSM Heavy H ≥ m φ 10 − 1 GeV ≤ H inf ≤ 9 . 2 × 10 13 GeV 10 − 1 GeV ≤ H inf ≤ 9 . 2 × 10 13 GeV H ≥ m φ H ≤ m φ 70 efolds 50 efolds H ≥ m φ Choudhury, AM, Pal, JCAP (2013) Wednesday, 23 October 13
Correlation between CMB + Dark mater Dark Matter stop tachyonic CMB / PLANCK Constraints Dark Matter (around 400 GeV) 125 GeV Higgs Large Higgsino component stau LSP Higgs Mass +Dark matter constraint + CMB for udd Inflaton Boehm, DaSilva, AM & Pukartas, PRD (2012), Wang, Pukartas & AM JCAP (2013) (hep-ph/1303.535) Wednesday, 23 October 13
ONE MORE BSM ... NMSSM NMSSM: can invoke successful electroweak baryogenesis via 1st order phase transition Planck P ζ = 2 . 196 +0 . 051 − 0 . 060 × 10 − 9 n s = 0 . 960 ± 0 . 073 Higgs Mass constraint Dark matter constraint 1st order phase transition Inflationary constraint for udd inflaton Balasz+AM+ Pukartas + White 1309.5091 Wednesday, 23 October 13
LAST 50-60 E-FOLDS MUST HAPPEN WITHIN A VISIBLE SECTOR Dark P ζ ∝ k n s − 1 r = P T Hidden UV Matter P ζ Radiation completion P ζ Abundance Pure Gravity Required No prediction +SM No No String Required Theory prediction prediction Required but Extra Higgs NO Quantum Inflation Physics Gravity Visible Required but Sector, NO within Matter i.e.MSSM sector Stringy inflation is still helpful but not during last 50-60 e-folds... R + R 2 Gravity is utterly incomplete : requires higher derivative terms Wednesday, 23 October 13
Confusion-3 Large Tensor to Scalar Ratio can be obtained by Sub-Planckian VEV Inflation Inflection Point Inflation Ben-Dayan, R. Brustein, JCAP (2009), Hotchkiss, AM, Seshadri, JCAP (2012) Choudhury, AM, Pal, JCAP (2013), Choudhury, AM, 1306.4496 Wednesday, 23 October 13
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