Generating hierarchy and inflation in supergravity Tirthabir Biswas IGC, Penn-State University With A. Notari, hep-ph/ With A. Notari, S. Alexander & N. Okada in prep.

The Hierarchy Problem The Hierarchy Problem Fundamental scales are widely seperated Why is gravity so much weaker than Electro-weak? Related (?) hierarchies: Little hierarchy problem: Little hierarchy problem: Hierarchy in quark masses: few MeV to Tev Hierarchy in quark masses: few MeV to Tev Attempts at solving the Hierarchy problem: SUSY: if broken at ~ Tev can protect the hierarchy SUSY: if broken at ~ Tev can protect the hierarchy Extra dimensions: Single fundamental mass scale (M ew ) Extra dimensions: Single fundamental mass scale (M ew ) M pl is derived, depends on extra-dimensions. M pl is derived, depends on extra-dimensions. Ratio can be made small by having them warped [RS] or large [ADD] Ratio can be made small by having them warped [RS] or large [ADD]

Old Inflation (Guth) Slow-roll Inflation very successful, but Concrete realization in ST or PP have been difficult Concrete realization in ST or PP have been difficult Typical scenarios involve fine tuning issues Typical scenarios involve fine tuning issues Inflation from false vacuum energy Why can’t it work? If tunneling rate, the Hubble rate If tunneling rate, the Hubble rate not enough inflation not enough inflation If, never-ending inflation If, never-ending inflation

“Graceful” Old Inflation f(Φ) has a minimum, e.g. f(Φ) has a minimum, e.g. Non-minimal coupling implies Φ & Non-minimal coupling implies Φ & effective M pl evolves during inflation from false vacuum effective M pl evolves during inflation from false vacuum Even if initially Even if initially Hubble rate decreases as Planck scale increases Hubble rate decreases as Planck scale increases Inflation ends when Inflation ends when At this point bubbles nucleate and collide and reheats the universe At this point bubbles nucleate and collide and reheats the universe Einstein frame: hill top inflation with Einstein frame: hill top inflation with & reproduces observed tilt & amplitude reproduces observed tilt & amplitude

Generating Hierarchy When exponential inflation ends, & f(Φ) ~ O(1) When exponential inflation ends, & f(Φ) ~ O(1) Universe expands as power law still driven by false energy Universe expands as power law still driven by false energy as long as f(Φ) > Φ 2 as long as f(Φ) > Φ 2 f(Φ) starts to grow f(Φ) starts to grow Finally the universe tunnels from the false vacuum having generated Finally the universe tunnels from the false vacuum having generated

Future Research Signatures Fundamental scale ~ Tev, new physics at LHC Fundamental scale ~ Tev, new physics at LHC Reheat temperature ~ Tev, gravity waves detectable at Reheat temperature ~ Tev, gravity waves detectable at LISA. Accurate calculation required. LISA. Accurate calculation required.Missing Concrete PP or ST (supergravity) set-up Concrete PP or ST (supergravity) set-up Requires a small hierarchy Requires a small hierarchy A small “unprotected” parameter β A small “unprotected” parameter β Quasi-periodic potential to stabilize Φ after tunneling to avoid 5 th force constraints Quasi-periodic potential to stabilize Φ after tunneling to avoid 5 th force constraints Why SM doesn’t couple to Φ? Why SM doesn’t couple to Φ?

Supergravity Embedding Advantages Non-minimal coupling: Naturally given by Kahler potential Non-minimal coupling: Naturally given by Kahler potential But, it also determines kinetic piece. What works? But, it also determines kinetic piece. What works? & Hierarchy: power law phase inflating Hierarchy: power law phase inflating False vacuum: In SQCD such non-susy vacuum exists [Intrilligator et. al] False vacuum: In SQCD such non-susy vacuum exists [Intrilligator et. al] Moreover, & one can have [Dine et. al] Moreover, & one can have [Dine et. al] One can have long lived metastable vacua One can have long lived metastable vacua Periodic potential: A coupling of Φ to the SQCD sector generates an F F † term which generates a periodic potential for Φ via chiral condensation of fermions. Periodic potential: A coupling of Φ to the SQCD sector generates an F F † term which generates a periodic potential for Φ via chiral condensation of fermions.