Running Inflation in the Standard Model (0812.4946v3)

Abstract: An interacting scalar field with largish coupling to curvature can support a distinctive inflationary universe scenario. Previously this has been discussed for the Standard Model Higgs field, treated classically or in a leading log approximation. Here we investigate the quantum theory using renormalization group methods. In this model the running of both the effective Planck mass and the couplings is important. The cosmological predictions are consistent with existing WMAP5 data, with 0.967 < n_s < 0.98 (for N_e = 60) and negligible gravity waves. We find a relationship between the spectral index and the Higgs mass that is sharply varying for m_h ~ 120-135 GeV (depending on the top mass); in the future, that relationship could be tested against data from PLANCK and LHC. We also comment briefly on how similar dynamics might arise in more general settings, and discuss our assumptions from the effective field theory point of view.

• The paper demonstrates that a non-minimal coupling between the Higgs field and curvature supports inflation through a renormalization group improved effective action at two-loop level.
• It derives a predicted spectral index range of 0.967–0.98 for 60 e-foldings and correlates Higgs mass (around 120–135 GeV) with successful inflation.
• The study suggests that future measurements from PLANCK and the LHC can validate the Standard Model Higgs as a viable driver of early universe inflation.

Running Inflation in the Standard Model

The paper "Running Inflation in the Standard Model" by Andrea De Simone, Mark P. Hertzberg, and Frank Wilczek investigates the feasibility of using an interacting scalar field with significant coupling to curvature to support an inflationary universe scenario within the framework of the Standard Model. This paper examines the implications of treating the Higgs field quantum mechanically through renormalization group methods, expanding upon previous classical or leading log approaches.

Summary of Contribution

The authors focus on a non-minimal coupling model, where the Higgs field $H$ is coupled to the Ricci scalar $\mathcal{R}$ in the form $\xi H^\dagger H \mathcal{R}$. This framework is explored under the Standard Model, incorporating quantum corrections through a renormalization group improved effective action, calculated at two-loop level. The emphasis is on capturing the evolution of both the effective Planck mass and the couplings. One of the notable results is the derivation of a spectral index $n_s$ range $0.967 \lesssim n_s \lesssim 0.98$ for $N_e = 60$ e-foldings, aligning with WMAP5 observations and predicting negligible tensor perturbations. The analysis suggests a correlation between the spectral index and the Higgs mass, particularly sensitive for Higgs masses around 120-135 GeV, potentially testable with future observations from the PLANCK satellite and LHC.

Technical Details

The transition from classical to quantum treatment involves carefully considering the implications of renormalization group equations for the couplings $\lambda$ (the Higgs self-coupling), $y_t$ (top Yukawa coupling), and gauge couplings $g_i$. These are analyzed at a two-loop level, emphasizing the delicate interplay between the Higgs mass $m_h$ and the top quark mass $m_t$.

A major aspect of the analysis is the suppression of loop contributions by effective parameters during inflation, illustrated by a form of commutator function $s(\phi)$ that modifies quantum corrections in the effective potential. The effective action changes during inflation due to high $\phi$ values, leading to a decrease in $y_t$ and an increase in $\lambda$ driven by the gauge boson contributions, affecting the spectral index $n_s$.

Results and Implications

The analysis concludes with a predicted narrow range for the Higgs mass compatible with successful inflation scenarios, suggesting that observational constraints on $n_s$ could extrapolate bounds on $m_h$ yielding $m_h > 125.7\,\mbox{GeV}$ for successful cosmological inflation (depending on top quark mass and strong coupling values). The paper emphasizes that future experimental data from LHC, refining the measurement of the Higgs mass, could verify or challenge the applicability of the Standard Model Higgs as the driver of inflation.

If further observational and experimental data corroborate these results, they could provide strong evidence for the Standard Model as a valid framework for understanding early universe inflation. Furthermore, the paper calls into question the naturalness and subsequent hierarchy of non-minimal coupling models by highlighting the necessity of large $\xi$ to align theory with observational data.

Future Directions

This research suggests several lines for future exploration, such as considering the impact of yet unknown gravitational quantum corrections, extensions to the Standard Model that may alter renormalization running at high energies, and the incorporation of additional scalar fields or terms. In particular, attention to Planck data and further Higgs mass measurements will clarify the viability and falsifiability of running inflation.

Overall, the paper provides an intricate computation of how existing Standard Model fields might fulfill the roles necessary for early universe inflation, contributing significantly to theoretical cosmology and bridging high-energy physics with cosmological observations.