Dark Energy, the Electroweak Vacua, and Collider Phenomenology Eric Greenwood, Evan Halstead, Robert Poltis, and Dejan Stojkovic arXiv: [hep-ph] Buffalo-Case-Cornell-Syracuse Workshop On Cosmology and Astro-particle Physics December 8-9, 2008

Motivation 95% of the energy content of universe is still a mystery to us The majority of the universe is in the form of dark energy Most proposals to address this problem involve the introduction of a new scalar field We expect new physics to kick in around the TeV scale

Introduction The current accelerated expansion of the universe may be driven by an already “known” field-the Standard Model Higgs field. We do not address the cosmological constant problem, but instead propose a mechanism that might explain the accelerated expansion of the universe. We will modify the Standard Model Higgs potential by adding dimension 6 and 8 (non-renormalizable) operators.

Description of Model  Retain the standard 2 nd order electroweak phase transition  Allow the formation of two new symmetric vacua after the 2 nd order electroweak phase transition is completed  The newer vacua eventually become the true vacua (global minima) of the potential  Tunneling probability from the false (old) vacua to the true (new) vacua must be sufficiently suppressed

Our potential is written as This potential may be rewritten as  We allow non-renormalizable operators to be included, as the Standard Model is generally accepted as an effective low-energy theory.  The ε o term introduces a controlled fine tuning of V(  ), similar to Stojkovic, Starkman, and Matsuo (PRD, 2008).

To account for finite temperature effects, we add a thermal mass to the potential. We choose to have all temperature effects be contained in our fine tuning parameter ε, so that At a critical temperature,, the temperature-dependant parameter ε(T crit ) = 0.  the vacua at ±  1 and ±  2 are degenerate.

T>>T crit T=T crit T=0 Temperature Evolution of V(  )

Tunneling Rate If the temperature of the universe today is below the critical temperature, then we live in a false (local, but not global) vacuum. Because a lower energy state exists, every point in the universe will eventually tunnel to the lower energy state. You are here The semi-classical transition probability per unit space-time volume is given by  What is the lifetime of such a meta-stable state?

Tunneling Rate  our universe has a four volume ~ t Hubble 4  Therefore, we require Γ t Hubble 4  1  Using t Hubble ~10 10 years, we find that the above requirement is satisfied if ε o ≤ TeV -4.  Notice that because today we reside in the  =  1 vacuum, we set V(  1 ) = (10 -3 eV) 4. This is the only fine tuned value in our model.

Tunneling Rate The transition rate is small in the current (cold) universe. But how does the transition rate behave in the high temperature limit? The temperature dependence of the Euclidean action affects the transition probability as Therefore in the high temperature limit, the transition rate to the  1 vacuum state is large.

Tunneling Rate This high temperature expression is valid until just below the critical temperature, which places a stronger constraint on the fine tuning-parameter. ε o ~ TeV -4

Because the Higgs couples to other Standard Model particles, it is possible to test this model in colliders. Vachaspati (PRD, 2004) showed that given a set of eigenvalues, it is possible to use the inverse scattering method to reconstruct the original potential. Experimental Signatures

Field Excitations But if we excite the field that extrapolates between the vacua, it is possible to learn about the overall shape of the potential. Exciting the field locally only probes the local structure of the potential. Physically, these kink solutions correspond to closed domain walls…bubbles of true vacuum!

Reconstruction Of the Field Using the Inverse Scattering Method Theory written in standard form Schrödinger equation determines the excitation spectrum where  o (x) is the kink solution Zero mode is related to the shape of the potential (Bogomol’nyi equation)

Reconstruction Of the Field Using the Inverse Scattering Method With the proper eigenvalues (ω n ’s), it is possible to reconstruct an order 8 potential and obtain the constant terms of our model (ε o, λ ’ s, etc …). Assume we know the spectrum of energy eigenvalues {ω n 2 }:

Bubble Nucleation At the LHC At the LHC, bubbles of true vacuum may be created. Each Bubble has two competing terms:  a volume term which tends to make the bubble expand  surface tension term which tends to make the bubble collapse.  A critical bubble (volume term balances the surface tension term) requires many individual excitations coherently supposed. N quanta > 10 9 ( 1 /ε o ) 3

Bubble Nucleation At the LHC The creation of a critical bubble is enormously suppressed. We may still produce smaller excitations, or sub-critical bubbles. These sub-critical bubbles will collapse under their own surface tension. These bubbles will most likely be produced in a highly excited state (not in a spherically symmetric ground state). The decay of these bubbles will give us the energy eigenvalues of the potential. N quanta > 10 9 ( 1 /ε o ) 3

If the difference between the two vacua is small (  V  0, or equivalently, ε o  0), the bubble nucleation rate will be very small. VV Because bubbles nucleate slowly, the expansion of the universe tends to dilute regions of true vacuum, and the majority of space remains in the false vacuum. Future of the Universe I:  V  0 End Result: A few regions of true vacuum in an inflating sea of false vacuum.

Future of the Universe II:  V Is “Large” If the difference between the two vacua is not fine tuned, the phase transition may be completed faster than the expansion can dilute regions of true vacuum. Bubbles of true vacuum percolate throughout the entire universe. End Result: The entire universe ends up in the true vacuum state. Standard Model particles have a different mass than they have today.  Outside the bubbles the Higgs field has a vev of  1, while on the inside the Higgs field has a vev of  2.

Future of the Universe III: Phase Transition To Happen Soon  If the difference between the two vacua takes on (perhaps) the most generic value of ε o ~ 0.01 TeV -4, then the phase transition will happen soon. End Result: We end up in a black hole in a collapsing universe.  Because the characteristic energy scale is of the order 100 GeV, and by our requirement that V(  1 ) ~ eV 4 implies that the true vacuum at  =  2 is deeply AdS.  Any initial perturbations grow rapidly in the shrinking space-time.

Conclusions  A nice feature of this model is that we do not need to introduce a new field decoupled from the rest of the universe.  Unlike many other theories, we can probe the global structure of the potential, opposed to only the local structure of the potential.  We expect new physics to kick in close to the TeV scale. Our model does not solve the cosmological constant problem, but addresses the dark energy problem.  note an interesting numerology: (TeV/M PL )TeV≈10 -3 eV hints towards a possible gravitational origin of this small number.

Photo credits Wally Pacholka Chandra.harvard.edu Apod-NASA New Scientist Thank You

Extra Slides