Is inflation compatible with string-induced galaxy formation

If the formation of galaxies is due to strings produced during a phase transition in the early universe, then the temperature of that phase transition is Tc > or approx. 3x10-3 mp ≅ 4x1016 GeV, where mp is the Planck mass. If there is also a preceding period of inflation with dH/dt/H2 ≤ 0, then it ceases at a value of the Hubble parameter which is constrained by He/mp < or approx. 6x10-5, which permits reheating of the universe to a temperature, Tr ≅ 2x10-3 ηmp, where η is the efficiency of reheating. Unless the 'inflaton' field φ is strongly coupled to matter, it turns out that η<<1, which implies that Tr<0, then the constraint upon He is weakened and it is possible to have both η<<1 and Tr > or approx. TC, thus permitting the subsequent production of strings. This idea can be realized in the higher-dimensional theory of Shafi and Wetterich, which includes higher-derivative terms R2 and a cosmological constant Λ. If R2 is proportional to the Euler-number density, as may be necessary for the theory to be free of ghosts, then no increase in Tr is possible. But a different, fine-tuned choice of parameters can cause an increase in Tr by a large factor. (orig.)