Classical evolution and quantum generation in generalized gravity theories including string corrections and tachyons: Unified analyses

Abstract

We present cosmological perturbation theory based on generalized gravity theories including string theory correction terms and a tachyonic complication. The classical evolution as well as the quantum generation processes in these variety of gravity theories are presented in unified forms. These apply both to the scalar-and tensor-type perturbations. Analyses are made based on the curvature variable in two different gauge conditions often used in the literature in Einstein's gravity; these are the curvature variables in the comoving (or uniform-field) gauge and the zero-shear gauge. Applications to generalized slow-roll inflations and its consequent power spectra are derived in unified forms which include wide range of inflationary scenarios based on Einstein's gravity and others.

De Sitter ground state of scalar-tensor gravity and its primordial perturbation

“…The quantum mechanism of primordial fluctuations in the generalized gravity including string corrections and tachyon has been discussed in detail in [18]. Now we extend this study to STG.…”

“…The potential (18) has no lower bound, and thus stability problem may appear, which will be studied in our next work. Here we only note that its dynamics is not very similar to an ordinary scalar since the Ricci scalar R is involved in its dynamics.…”

“…ǫ 1 and ǫ 2 are directly inherited from general relativity, while ǫ 3 and ǫ 4 are new parameters for attached freedoms to STG. Under a slow-roll approximation, |ǫ i | << 1, we get the power spectrum of the adiabatic vacuum perturbation P S on large scale [18],…”

“…In the above equations, we have made some calculations compared with the original definitions of ǫ i , (i = 1, 2, 3, 4) in [18]. ǫ 1 and ǫ 2 are directly inherited from general relativity, while ǫ 3 and ǫ 4 are new parameters for attached freedoms to STG.…”

“…A gauge invariant approach on perturbations of STG cosmology is suggested in [17]. The cosmological perturbation theory has been made based on generalized gravity theories including string corrections and tachyon [18]. We extend this study to STG, and apply it to generalized slow-roll inflation and its consequent power spectra.…”