Inflation and Higgs Fuminobu Takahashi (Tohoku & IPMU) 14th - PowerPoint PPT Presentation

Inflation and Higgs Fuminobu Takahashi (Tohoku & IPMU) 14th February 2015 HPNP2015@Toyama

Planck data out Color: CMB temperature Texture: direction of polarization

Quadratic chaotic inflation is disfavored. Planck, 1502.01589 (n s , r)

Quadratic chaotic inflation is disfavored. Planck, 1502.01589 (n s , r)

(Planck TT, lowP, BAO) N e ff N e ff = 3 . 15 ± 0 . 23

scenarios such as Higgs portal dark radiation. The bound now starts to constrain interesting K. Jeong, FT, 1305.6521 0.6 0.5 SU � 3 � ' 0.4 � N eff 0 . 01 SU � 2 � ' � SU � 2 � ' 0 . 1 0.3 Br( h → invisible) = 0 . 2 U � 1 � ' with fermions � N f � 5 � L e ff = 1 µ ν F 0 µ ν | H | 2 F 0 0.2 SU � 2 � ' Λ 2 φ 0.1 U � 1 � ' 0.0 3 4 5 6 7 Log 10 � � Φ � GeV �

scenarios such as Higgs portal dark radiation. The bound now starts to constrain interesting K. Jeong, FT, 1305.6521 0.6 0.5 SU � 3 � ' 0.4 � N eff 0 . 01 SU � 2 � ' � SU � 2 � ' 0 . 1 0.3 Br( h → invisible) = 0 . 2 U � 1 � ' with fermions � N f � 5 � L e ff = 1 µ ν F 0 µ ν | H | 2 F 0 0.2 SU � 2 � ' Λ 2 φ 0.1 U � 1 � ' 0.0 3 4 5 6 7 Log 10 � � Φ � GeV �

Accelerated cosmic expansion solves various theoretical problems of the std. big bang cosmology. Inflation � ��� One way to realize the inflationary expansion is the slow- roll inflation. Linde `82, Albrecht and Steinhardt `82 Guth `81, Sato `80, Starobinsky `80, Kazanas `80, Brout, Englert, Gunzig, `79 δφ = H V 2 π

Fluctuations of volume Distortion of space in a volume-conserving way

Scalar mode Inflaton’s quantum fluctuations induce fluctuations in time and volume. Super-horizon modes do not evolve. : gravitational potential : curvature perturbations ds 2 = − (1 + Φ ) dt 2 + a ( t ) 2 (1 + 2 Ψ ) d x 2 Φ Ψ

Tensor mode Tensor mode perturbations are fluctuations of graviton itself. ds 2 = − dt 2 + a ( t ) 2 ( δ ij + h ij ) dx i dx j h ij : traceless, divergent-free tensor = graviton . h ij ∼ H inf M P

Observation vs Theory Scalar mode Tensor mode V : the inflaton potential

The inflaton excursion exceeds the Planck scale for r > O(10 -3 ). Lyth 1997 •Inflaton field excursion •Inflation energy scale Lyth bound: V inf ' (2 ⇥ 10 16 GeV) 4 ⇣ r ⌘ 0 . 1 After inflation During inflation φ

Planck 2015 results XX Predicted values of (n s , r) Quadratic chaotic infl

SM Higgs inflation The SM Higgs potential needs to be modified at large field values for successful inflation h

SM Higgs inflation The SM Higgs potential needs to be modified at large field values for successful inflation (1)Non-canonical kinetic term (2)Non-minimal coupling to gravity h

Higgs inflation with running kinetic term The quadratic chaotic inflation is possible, but it is now The transition is at h = O(10 13 )GeV. FT 1006.2801, disfavored by Planck. Needs some extension e.g. polynomial chaotic inflation. normalized field. If a kinetic term grows at large field values, the potential gets flatter in terms of the canonically Nakayama and FT, 1008.2956,1008.4467, Hertzberg, 1110.5650 h 4 p h c ∼ 1 / ξ ˆ h 2 e.g.) L = 1 ( ∂ h ) 2 − λ h 2 − v 2 � 2 1 + ξ h 2 � � � 2 4 for h ⌧ 1 / p ξ λ ˆ h 4  for h ⌧ 1 / p ξ  h  V (ˆ  h ) ⇠ ˆ h ⇠ for h � 1 / p ξ p ξ h 2 for h � 1 / p ξ ξ ˆ λ h 2  

Higgs inflation with running kinetic term disfavored by Planck. Needs some extension e.g. polynomial chaotic inflation. The transition is at h = O(10 13 )GeV. FT 1006.2801, Nakayama, FT, Yanagida, 1303.7315 The quadratic chaotic inflation is possible, but it is now potential gets flatter in terms of the canonically Nakayama and FT, 1008.2956,1008.4467, Hertzberg, 1110.5650 normalized field. If a kinetic term grows at large field values, the h 4 p h c ∼ 1 / ξ ˆ h 2 e.g.) L = 1 ( ∂ h ) 2 − λ h 2 − v 2 � 2 1 + ξ h 2 � � � 2 4 for h ⌧ 1 / p ξ λ ˆ h 4  for h ⌧ 1 / p ξ  h  V (ˆ  h ) ⇠ ˆ h ⇠ for h � 1 / p ξ p ξ h 2 for h � 1 / p ξ ξ ˆ λ h 2  

Higgs inflation w/ non-minimal coupling The potential for a canonically normalized scalar in the Einstein frame is where Salopek, Bond, Bardeen, `89, Bezrukov and Shaposhnikov `07 p h � M P / ξ 1 � 2 e − p h ( φ ) � v 2 � 2 ' λ M 4 ✓ ◆ V ( φ ) = 1 λ φ 2 P � MP 3 Ω 4 4 ξ 2 4

Potential becomes Higgs inflation w/ non-minimal coupling Salopek, Bond, Bardeen, `89, Bezrukov and Shaposhnikov `07 1 � 2 e − p h ( φ ) � v 2 � 2 ' λ M 4 ✓ ◆ V ( φ ) = 1 λ φ 2 P � 3 MP Ω 4 4 ξ 2 4 h ∼ M P √ ξ ∼ 10 16 GeV p flatter at h & M P / ξ

Case of non-minimal coupling: Unitarity is OK during inflation, SM Higgs inflation •Consistent with the Planck data •Reheating takes place naturally •Minimal particle content EW vacuum. but it matters at high E in the Strengths: Caveats: •Higher dim. operators assumed to be negligible. •Large coupling required by the COBE normalization. ⇢ 0 . 13 running kinetic term n s ' 0 . 967 , r ' 3 ⇥ 10 − 3 nonminimal coupling ✓ λ ◆ 1 / 2 ✓ N ◆ ξ ' 1 . 7 ⇥ 10 4 0 . 13 60 •Quartic coupling runs, and it is sensitive to m t

The SM near-criticality The SM vacua is at the border between stability and meta-stability. Why?? Andreassen, Frost, Schwartz, 1408.0292

At the border, there is another minimum at around the Planck scale, which has the same energy as the EW vacuum. The SM near-criticality cf. “Multiple point principle” - There should be several degenerate vacua in energy. Hamada, Oda, Kawai, Park, 1408.4864 Bennett, Nielsen `94 Froggatt, Nielsen `96 See 1212.5716 for arguments based on non-locality and various apps.

Topological Higgs Inflation •Domain walls connecting the EW and Planck scale vacua. Domain wall Hamada, Oda, FT 1408.5556 V V v Planck v EW h h ≈ v P lanck h ≈ 0 x

Topological Higgs Inflation •Domain walls connecting the EW and Planck scale vacua. Domain wall Hamada, Oda, FT 1408.5556 V V w & H − 1 v Planck v EW h h ≈ v P lanck h ≈ 0 x

Topological Higgs Inflation wall thick: Inflation occurs inside domain walls if they are sufficiently helps to satisfy this bound. to gravity The non-minimal coupling Higgs inflation. The SM criticality may be related to the topological Domain •Domain walls connecting the EW and Planck scale vacua. Hamada, Oda, FT 1408.5556 V V w & H − 1 v Planck v EW h h ≈ v P lanck h ≈ 0 x v P lanck & a few M P N.B. Another inflation needed to generate δ ∼ 10 − 5

Uplifting by new physics •Negative effective potential may be lifted by new physics effects above a certain scale. New physics V e ff h 6 Λ 2 NP h

Domain walls in the Higgs potential •Domain walls can be formed if the two vacua are (quasi)-degenerate. 8 173.28 7 173.29 6 173.30 V H /10 28 GeV 4 5 4 3 2 1 0 0 0.5 1 1.5 2 2.5 ϕ /10 8 GeV

•Unstable domain walls annihilate, generating GWs. Domain walls in the Higgs potential Position of the false vacuum T R = 3 × 10 8 GeV 10 -2 y early decay t i s n e d ( V f / V max ) 1/4 y g r e n n o i e t a n i m 10 -3 o s d W D a aLIGO i B ET 10 12 10 13 ϕ f /GeV Kitajima, FT, 1502.03725

•Unstable domain walls annihilate, generating GWs. Position of the false vacuum Domain walls in the Higgs potential T R = 10 4 GeV 10 -3 y early decay t i s n e d ( V f / V max ) 1/4 y g 10 -4 DW domination r e n e s a i LISA B DECIGO 10 -5 10 8 10 9 10 10 10 11 10 12 ϕ f /GeV Kitajima, FT, 1502.03725

Higgs new inflation GUT Higgs new inflation was extensively studied in the early 80s. � ��� Hawking `82, Starobinsky `82, Guth and Pi `82 It was, however, soon abandoned because CW corrections lead to too large density perturbations. V

1. SUSY 2. Cancellations between gauge and Yukawa couplings. 3. Very small gauge and Yukawa couplings 4. Extra damping mechanism 5. Gauge singlet inflaton Known solutions Hawking `82, Ellis, Nanopoulos, Olive, Tamvakis `82 Hawking `82, Starobinsky `82, Guth and Pi `82 Kolb, Turner Starobinsky `82, Baremboim, Chun, Lee, 1309.1695 Nakayama, FT 1108.0070,1203.0323 Shafi, Vilenkin `84, Pi `84 The last solution became popular since then. Now let us revisit the first solution using SUSY.

SUSY B-L Higgs new inflation Senoguz and Shafi, `04, cf. Asaka et al `99 is fixed by COBE normalization. The B-L breaking scale (inflaton VEV) In SUSY, two Higgs are required for anomaly cancellation. Planck units adopted � ��� Φ ( − 2) , Inflaton: φ 2 = ¯ � � � Φ ¯ Φ Φ (+2) , � ⇣ � 2 ⌘ Φ ¯ v 2 � � W = χ Φ V ( φ ) ' v 4 � kv 4 φ 2 � v 2 φ 4 + φ 8 · · · M P = 1 δφ = H V 2 π v B − L = h φ i ⇠ 10 15 GeV h φ i ⇠ 10 15 GeV