Higgs inflation Syksy Rsnen University of Helsinki Department
- Slides: 23
Higgs inflation Syksy Räsänen University of Helsinki Department of Physics and The Helsinki Institute of Physics Kobe University, 22. 11. 2016 www. helsinki. fi/yliopisto 1
Nothing above the Standard Model • It has been widely expected that there is physics beyond the Standard Model at the electroweak (EW) scale. • No such physics has been seen at LHC (nor at Tevatron, LEP 2, LEP). • Direct detection experiments have shown that dark matter does not consist of particles with EW scale mass and weak strength interactions. Kobe University, 22. 11. 2016 2
No new scale • One motivation for new physics at the EW scale is the hierarchy problem. • Why is the electroweak scale (specifically, the Higgs mass) so much smaller than a grand unified theory scale? • New physics at the EW scale is supposed to protect the Higgs mass from loop corrections. • There is no evidence (such as proton decay) for a grand unified theory. • A simple possibility is that there is no new scale above the EW scale (until gravity is important). Kobe University, 22. 11. 2016 3
What we need • There is evidence for four kinds of new physics (accelerated expansion aside): • Neutrino masses • Baryogenesis • Dark matter • Inflation • In the �� MSM, three right-handed neutrinos are added, with masses ~10 ke. V, 1 Ge. V, to solve the first three problems. (Asaka, Blanchet, Shaposhnikov: hep-ph/0505013, 1106. 5019) • Higgs inflation is separate idea, but follows the philosophy of adding nothing beyond the EW scale except gravity. Kobe University, 22. 11. 2016 4
The Standard Model and Einstein gravity • Here �� is the SM Higgs field. • We choose units such that M=1. • The SM tree level Higgs potential is (v=246 Ge. V): Kobe University, 22. 11. 2016 5
Observations and inflation • Inflation must last long (N=50), field must roll slowly and perturbation amplitude must be right. • Slow-roll parameters: • Observationally, they are constrained as: • ns is the spectral index, r is the tensor-to-scalar ratio • The amplitude is Kobe University, 22. 11. 2016 . 6
No inflation with minimal coupling to gravity • For potential, observations require • The value measured at the LHC is . . • Because of loop corrections, the coupling runs, . • Typically, �� becomes negative for large field values, so tiny positive value is not a problem. (We assume �� >0. ) • However, getting enough e-folds and the right amplitude is not possible. • Conclusion: SM Higgs minimally coupled to gravity does not give working inflation. (Isidori et al: 0712. 0242, Hamada et al: 1308. 6651, Fairbairn et al: 1403. 7483) Kobe University, 22. 11. 2016 7
The Standard Model in curved spacetime • Non-minimal coupling is the only dimension 4 operator missing from the combined Einstein-Hilbert + SM action. • Non-zero �� is generated by renormalisation, even if put classically to zero: it is a required part of theory. • The non-minimal coupling enables Higgs inflation. (Bezrukov and Shaposhnikov: 0710. 3755) Kobe University, 22. 11. 2016 8
Conformal transformation to the minimally coupled frame • It’s easiest to study the dynamics in the minimally coupled frame. • Inflationary predictions are frame-independent. • The conformal transformation is . • To get a canonical kinetic term, we define new field �� : • Polynomial potential is transformed into an exponential potential. Kobe University, 22. 11. 2016 9
Predictions of Higgs inflation on the plateau • The action is with . • In the exponentially flat plateau, we get • For N=50 (Figueroa et al: 1504. 04600), we get Kobe University, 22. 11. 2016 10
Excellent fit Planck team: 1502. 02114 Kobe University, 22. 11. 2016 11
When the action is not enough • Complication: the classical action is not enough to specify theory. • There are two sources of ambiguity. • Quantum: how to calculate loop corrections? • Gravity: what are the gravitational degrees of freedom? Kobe University, 22. 11. 2016 12
Renormalising the non-renormalisable • Let us first consider the quantum issue. • Renormalisability is crucial for the flat potential: • Because of gravity, theory is not renormalisable. • Loop corrections boil down to prescriptions. Kobe University, 22. 11. 2016 13
The trouble with renormalisation • Do change of frame and quantisation commute? • Inflationary perturbations are equivalent for a fixed potential, the issue is loop corrections. • What is the path integral measure and how does it change in the conformal transformation? (Hamada et al: 1610. 05885) • Power counting suggests that perturbative unitarity is lost at MPl/�� , not MPl. (Burgess et al: 0902. 4465) • It is possible to use the SM renormalisation group equations at and switch to the chiral EW model (Higgs frozen) at. • We can parametrise the jump in between. Kobe University, 22. 11. 2016 14
LHC cosmology • Due to loop corrections, inflationary predictions depend on Higgs and top mass. • Consistency condition between cosmology and colliders. • One loop corrections spoil agreement between LHC and CMB. • Taking into account two loops (and ignoring nonrenormalisability) brings agreement back. • Non-trivial fact. • Until renormalisation is understood, results are provisional. • Loop corrections also open up new inflation regimes. Kobe University, 22. 11. 2016 15
Loop-corrected potential • Different inflationary possibilities: • • Plateau: apparently not spoiled by loops. Inflection point: can give. False vacuum: new physics needed for graceful exit. Hilltop: under investigation. (Enckell, Enqvist, SR, Tomberg) Kobe University, 22. 11. 2016 16
The many faces of Einstein gravity • Let’s now turn to the gravitational ambiguity. • Usually the gravitational degrees of freedom are taken to be the metric and its first and second derivative. • Variation of the Einstein-Hilbert action does not give the Einstein equation, unless the York-Gibbons-Hawking boundary term is added. • In the Palatini formalism, the metric and the connection are independent degrees of freedom. • • No boundary term is needed. First order formalism, allows canonical quantisation. • In the Einstein-Hilbert case, metric and Palatini are equivalent. • Not so with a non-minimally coupled scalar field! Kobe University, 22. 11. 2016 17
Palatini vs. metric • In the conformal transformation the Ricci tensor does not change. , • Hence the field transformation is different: • (Metric case: ) (Bauer and Demir: 0803. 2664) • The potential is • (Metric case: Kobe University, 22. 11. 2016 . ) 18
Predictions of Higgs inflation on the plateau à la Palatini • For plateau inflation, we get • (Metric case: ) • For N=50, we get • (Metric case: ) • One factor of �� less, so bigger �� needed. Also, r is smaller. Kobe University, 22. 11. 2016 19
Higgs inflation at the inflection point • Inflection point Higgs inflation was introduced in Allison: 1306. 6931. • It was emphasised after the BICEP 2 results as a way to get (Hamada et al: 1403. 5043, Bezrukov and Shaposhnikov: 1403. 6078). • Existence and properties of the inflection point are sensitive to quantum corrections. • Inflationary predictions depend on the choice of gravitational degrees of freedom. Kobe University, 22. 11. 2016 20
Inflection point inflation: metric vs. Palatini (preliminary) metric Palatini (SR and Wahlman) (Colour shows running of the spectral index �� < 0. 03. ) • Metric formulation predicts that r is observable by next generation experiments (COr. E, Litebird, PIXIE), Palatini not. Kobe University, 22. 11. 2016 21
Higgs at the crossroads of quantum and gravity • Higgs inflation uses only the known particle physics and gravity degrees of freedom. • Tree level results agree with observations. • Metric case prediction for r will be tested by next generation CMB experiments. • The issue of quantum corrections is not settled. • Consistency conditions between cosmology and colliders. • Have to specify the gravitational degrees of freedom. • • Formulations that are equivalent for Einstein gravity differ when there is a non-minimally coupled scalar field: Palatini, teleparallel, . . . Higgs inflation could be used to observationally determine the right gravitational degrees of freedom. Kobe University, 22. 11. 2016 22
Dark matter direct detection limits LUX collaboration and LZ collaboration: 1611. 05525 Kobe University, 22. 11. 2016 23
- Fysiikkaa runoilijoille
- Futa inflation meaning
- Helsinki university physics
- Sisu helsinki university
- Episykli
- Englanti syksy 2018
- Syksy 2018 lukutaidon koe
- Syksy 2020 fysiikka
- Syksy tietovisa
- Psykologia ylioppilaskoe
- Fysiikka yo syksy 2002 ratkaisut
- Higgs singlet
- Higgs factory
- Cern geneva
- Higgs factory
- Higgs singlet
- Higgs singlet
- Two higgs doublet model
- Richard feynman
- Chelsea higgs wise
- Hungry higgs brætspil
- Higgs boson
- Higgs to tau tau
- Higgs