Astroparticle Physics

264 12 InflationΩ gravity waves = ϱ gravity wavesϱ c= h2 ω 212H 2 . (12.42)gravity-wave detectionnew experimentalpossibilities?This would result in distortions of gravity-wave antennaeon the order of h = 10 −27 for kHz gravity waves. Eventhough present gravitational-wave antennae do not reach thiskind of sensitivity, a detection of the predicted gravitationalwavebackground at the level expected in inflationary modelswould result in a credibility comparable to that whichwas achieved for the Big Bang by the observation of the2.7 K blackbody radiation.Even though the detection of gravity waves has not beenestablished experimentally, it might still be possible in thefuture to find means of testing these predictions of inflationarymodels with new techniques or new ideas. At the time ofthe discovery of the blackbody radiation in 1965 by Penziasand Wilson it seemed unrealistic to assume that one mightbe able to measure the spectrum at the level at which it isknown now. With future satellites, like with the EuropeanPlanck mission, even further improvements are envisaged.12.11 Problems1. A value of the cosmological constant Λ can be estimatedfrom the Friedmann equation extended by the cosmologicalterm. It is often said that this value disagrees byabout 120 orders of magnitude with the result from theexpected vacuum energy in a unified supergravity theory.How can this factor be illustrated?2. Work out the time dependence of the size of the universefor a flat universe with a cosmological constant Λ.3. Work out the time evolution of the universe if Λ werea dynamical constant (Λ = Λ 0 (1 + αt)) for a Λ-dominated flat universe.4. Estimate the size of the universe at the end of the inflationperiod (≈ 10 −36 s). Consider that for a matterdominateduniverse its size scales as t 2 3 , while for aradiation-dominated universe one has R ∼ t 1 2 .