Higgs inflation Syksy Rsnen University of Helsinki Department

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Higgs inflation Syksy Räsänen University of Helsinki Department of Physics and The Helsinki Institute

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

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

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

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.

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

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

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

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

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 . •

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

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

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

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

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

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.

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.

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.

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,

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

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

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

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,

Dark matter direct detection limits LUX collaboration and LZ collaboration: 1611. 05525 Kobe University, 22. 11. 2016 23