From Inflation to TeV physics: Higgs Reheating in RG Improved Cosmology Yi-Fu Cai June 18, 2013 in Hefei CYF, Chang, Chen, Easson & Qiu, 1304.6938
Two Standard Models Cosmology CMB: Cobe (1989), WMAP (2001), Planck (2009) SuperNovae (1998) LSS: SDSS (2000) LCDM Particle Physics: Glashow s EW theory in 1960 Salam and Weinberg in 1967 For years until LHC SM of Particle Physics
Two Standard Models A new resonance at 125 GeV, compatible with the Higgs boson with 5 sigma Cosmology CMB: Cobe (1989), WMAP (2001), Planck (2009) SuperNovae (1998) LSS: SDSS (2000) LCDM Particle Physics: Glashow s EW theory in 1960 Salam and Weinberg in 1967 For years until LHC SM of Particle Physics
Two Standard Models To address the horizon, flatness, monopole problems and to explain the formation of LSS, inflation is suggested to occur in early universe which is driven by a inflaton scalar; To explain the origin of the masses of elementary particles, it is believed there exists a Higgs boson in SM; Before LHC, no elementary scalar particle was observed in Nature. è Is there any connection between early universe inflaton and the Higgs boson?
Outline The scenario of RG improved inflation Asymptotical safe gravity and f(r) correspondence Realization of the Starobinsky Model From Inflationary scale to particle physics scale Higgs inflation Higgs reheating Higgs modulated reheating in RG improved inflation The model Perturbation: linear and nonlinear Constraint by Planck
RG improved inflation Basic idea: View the RG improved Einstein-Hilbert action as an effective f(r) model and study its implication to early universe. Asymptotically Safe Gravity (Weinberg 1977,1979) with Einstein truncation where p is the RG cutoff scale beyond which the UV modes are argued to be integrated out. In IR regime, G and Λ flow to constants and thus Einstein gravity recovers; In UV limit, G and Λ flow to a UV fixed point according to beta functions.
Asymptotically Safe Gravity To define the dimensionless gravitational and cosmological constants: The AS scenario suggests: Reuter, PRD 57, 971 (1998) Souma, Prog. Theor. Phys. 102, 181 (1999) Bonanno & Reuter, Phys. Rev. D 65, 043508 (2002) Litim, PRL 92, 201301 (2004) Codello & Percacci, PRL 97, 221301 (2006) CYF & Easson, JCAP 1009 (2010) 002
Asymptotically Safe Gravity We study the RG improved gravity in the regime that is sufficiently close to GR while still retaining linearized quantum corrections to the beta functions. Under this parameterization, one can obtain approximate forms of the couplings: The corresponding RG improved G and Λ are: With
Asymptotically Safe Gravity Varying the Lagrangian wrt the metric yields the generalized Einstein equation: The consistency of the Bianchi Identity requires: Then one can identify the running of the cutoff as: Eventually, AS gravity with Einstein truncation has an f(r) correspondence: CYF, Chang, Chen, Easson & Qiu, 1304.6938; See also, CYF & Easson, 1202.1285; Bonanno, 1203.1962; Hindmarsh & Saltas, 1203.3957 Interestingly, it provides a natural realization of R 2 inflation (Starobinsky 1980)
From Inflation to Particle Physics Any connection with particle physics? It has been argued that if there are no intermediate energy scales between the SM and AS scales, the mass of the Higgs boson is predicted to be m H = 126 GeV, with only several GeV uncertainty. Higgs Inflation Shaposhnikov & Wetterich, PLB 683,196 (2010) Higgs Reheating
in Standard Inflation Simone & Riotto, 1208.1344; Choi & Huang, 1209.2277; The Higgs is not a good candidate of inflaton as it is plagued by conceptual issues such as unitarity problem, and the stability of the potential near Planck scale. It may contribute to the primordial curvature perturbation and seed structure formation and CMB anisotropies through the processes such as modulated reheating of inflation; However, a severe fine tuning issue exists: Thus its contribution is subdominant.
in RG Improved Inflation CYF, Chang, Chen, Easson & Qiu, 1304.6938 Within the framework of RG improved inflationary cosmology motivated by AS gravity, we study the dynamics of a scalar field which can be interpreted as the Higgs field. The same as the R 2 inflation, the background trajectory of this model can provide sufficient inflationary e-folds and a graceful exit to a radiation dominated phase. The Higgs boson couples to gravity through a conformal factor that can relax the slow roll constraint. We study the possibility of generating primordial curvature perturbations through the Standard Model Higgs boson.
in RG improved inflation: Background Our starting point is The gravity sector is given by the f(r) correspondence The matter field Lagrangian includes the Higgs boson It is convenient to perform a Weyl rescaling The effective Lagrangian is reformulated as
in RG improved inflation: Background The total potential during inflation is given by For this model the slow roll parameters are
in RG improved inflation: Background The total potential during inflation is given by For this model the slow roll parameters are
in RG improved inflation: Background The total potential during inflation is given by For this model the slow roll parameters are
in RG improved inflation: Background The total potential during inflation is given by For this model the slow roll parameters are Therefore, within the RG improved inflation, the contribution through Higgs decay can become dominant.
in RG improved inflation: Background The background evolution of the Hubble parameter, scalar fields, and slow roll parameters of this model.
in RG improved inflation: Background The process of Higgs dependent decay: One generally can take the following Higgs dependent interactions: where χ and ψ are the scalar and spinor fields which constitute radiation in the early universe, the subscript represents the species of particles. Under this assumption the decay rate of the inflaton to the lowest order in coupling constants is At the moment of the phase transition from inflaton domination to radiation domination, we have H ~ Γ. As a consequence, the primordial curvature perturbation would be generated if this hyper-surface was modulated by the spatial dependent Higgs fluctuations.
in RG improved inflation: Perturbation At the moment of modulated reheating: H ~ Γ. Beginning of inflation After inflation, inflaton decays by a Higgs dependent Γ Γ = Γ(h) = Γ 0 + Γ 1 δh The CMB forms after reheating
in RG improved inflation: Perturbation In local ansatz, the curvature perturbation can be expanded order by order: The correlation functions are defined as They are related to variables of observable interests are
in RG improved inflation: Perturbation In modulated reheating, the decay of the inflaton occurs on a spatial hypersurface with a varying local decay rate, which is assumed to be a function of the Higgs boson. Thus, the local Hubble parameter on the slice of modulated decay satisfies the condition: H = Γ(h) On super-hubble scales, the curvature perturbation arisen from modulated decay is
in RG improved inflation: Perturbation In the conventional scenario of modulated reheating, there is Which is calculated at Hubble cross. However for our model, the Higgs boson and the inflaton are coupled through a conformal factor. Thus The power spectra seeded by Higgs and inflaton fluctuations are It is convenient to define a Higgs-to-curvature ratio By choosing a group of canonical value, there is q h = 1 when
in RG improved inflation: Perturbation The spectral indices of two spectra are The power spectrum of primordial tensor perturbation does not change, But the tensor-to-scalar ratio is changed to be This indicates that the amplitude of primordial gravitational wave is doubly suppressed in the Higgs-modulated reheating mechanism since both ε and 1-q h are small quantities.
in RG Improved Inflation: Non-Gaussianities For the nonlinear fluctuations seeded by the Higgs fluctuations, there exist two categories of seeds: by the nonlinear conversion from δh to ζ after inflation by the self interaction of the Higgs boson during inflation
in RG improved inflation: Non-Gaussianities The first type of non-gaussianities originates from the field fluctuations at super-hubble scales during the process of post-inflation modulated reheating. By matching the Higgs field fluctuation with the curvature perturbation order by order, then we get this part of universal nonlinearity parameters: Particularly, if Γ ~ h 2 and q h ~1, one obtains These nonlinearity parameters are sizable when compared with those in slow-roll inflation models, but still difficult to test observationally.
in RG improved inflation: Non-Gaussianities The second type of non-gaussianities originates from the non-quadratic potential of the lighter field, which in our model corresponds to the Higgs potential: V(h) ~ λh 4 /4. Performing the integral based on in-in formalism, one can derive the n- point correlation function of δh and then match to that of ζ. The nonlinearity parameters of local shape are These parameters of equilateral shape are
in RG improved inflation: Non-Gaussianities The nonlinearity parameters of second type are always negative which is very different from most of inflation models; The amplitudes of the second type of non-gaussianities are usually larger than those of the first type, this implies self interactions of the Higgs boson made the main contribution in generating nonlinear perturbations; These nonlinearity parameters are tightly bounded by Planck data, and therefore the model parameters are strongly constrained.
in RG improved inflation: Constraint Making use of the recently released Planck data, especially the power spectrum and the bounds on local nonlinearity parameters.
in RG improved inflation: Constraint This is a combined constraint on the inflationary Hubble rate and the amplitude of the Higgs boson during inflation. The color of the region reduces to a lighter tone as q h increases from zero to unity, which corresponds to a more severe fine-tuning problem towards the q h = 1 limit. This indicates that the case for the pure Higgs modulated reheating is not favored by data. The combined scenario of Higgs modulated reheating and inflationary perturbation, however, survives.
Summary Inflation may be driven by RG improved gravity and coincides with the Starobinsky model at Einstein truncation; Within this scenario, the cutoff scale flowing from Planck scale to TeV scale and naturally connect early universe physics and particle physics; Higgs boson can be the scalar field that seeds primordial curvature perturbation through modulated reheating; According to Planck data, one needs to combine the curvature perturbations generated by the Higgs modulated reheating with the fluctuations seeded by the inflaton itself.
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