Dissipative Liouville cosmology: A case study

Abstract

We consider solutions of the cosmological equations pertaining to a dissipative, dilatondriven off-equilibrium Liouville Cosmological model, which may describe the effective field theoretic limit of a non-critical string model of the Universe. The non-criticality may be the result of an early-era catastrophic cosmic event, such as a big-bang, brane-world collision etc. The evolution of the various cosmological parameters of the model are obtained, and the effects of the dilaton and off-shell Liouville terms, including briefly those on relic densities, which distinguish the model from conventional cosmologies, are emphasised. May 2006The current astrophysical data [1][2][3][4] are capable of placing stringent constraints on the nature of the dark energy, whose equation of state may be determined by means of an appropriate global fit. Most of the analyses so far are based on effective four-dimensional Robertson-Walker Universes, which satisfy on-shell dynamical equations of motion of the Einstein-Friedmann form. Even in modern approaches to brane cosmology, which are described by equations that deviate during early eras of the Universe from the standard Friedmann equation (which is linear in the energy density), the underlying dynamics is assumed to be of classical equilibrium (on-shell) nature, in the sense that it satisfies a set of equations of motion derived from the appropriate minimisation of an effective space-time Lagrangian.However, cosmology may not be an entirely classical equilibrium situation [5,6]. The initial Big Bang or other catastrophic cosmic event, such as the collision of two brane worlds in the modern context of brane theories [7], which led to the initial rapid expansion of the Universe, may have caused a significant departure from classical equilibrium dynamics in the early Universe, whose signatures may still be present at later epochs including the present era. In [6,8] there have been proposed specific models for the cosmological dark energy which are of this type, being associated with a rolling dilaton field that is a remnant of this non-equilibrium phase, described by a generic non-critical string theory [5,9,10]. The basic ingredient of this approach is the identification of target time with a local, dynamical (irreversible) renormalization group scale on the world sheet of the string [7,11], being representing by the so-called Liouville mode [5,10]. The consistency of the approach is guaranteed by the existence of solutions to the pertinent equations ("Liouville conditions") for the various background target-space fields over which the non-critical Liouville-dressed [9] σ-model propagates. The latter express the restoration of conformal invariance conditions after Liouville dressing. We call this scenario 'Q-cosmology' [6].It must be stressed that this Q-cosmology is physically very different from standard dilaton cosmologies in critical strings [12], where on-shell equations of motion for the background fields are satisfied. Our non-equilibrium, non-classical theory is not described...

Dilaton and off-shell (non-critical string) effects in Boltzmann equation for species abundances

“…In fact, upon the inclusion of matter backgrounds, including dark matter species, the associated equations, after compactification to four target-space dimensions, read in the Einstein frame [1]:…”

“…To leading order in an α' expansion, which we restrict ourselves in [1] and here, this equation in the Einstein frame reads:…”

“…A consistent solution of a(t), Φ(t), and the various densities, including back reaction of matter onto the space-time geometry, has been discussed in [1], where we refer the interested reader for further study. Also note that a preliminary comparison of such non-critical strings theories with astrophysical data, demonstrating consistency at present, is given in [20].…”

“…In a previous work [1] we have discussed a case study of dissipative Liouville-string cosmology, involving non critical string cosmological backgrounds, with the identification [2,3] of target time with the world-sheet zero mode of the Liouville field [4][5][6][7]. Such cosmologies were found to asymptote (in cosmic time) with the conformal backgrounds of [8][9][10], which are thus viewed as equilibrium (relaxation) configurations of the non-equilibrium cosmologies.…”

“…Essentially, the astrophysical data constraint severely in some cases the available phase-space distributions of favorite supersymmetric dark matter candidates such as neutralinos [16][17][18][19]. When off-equilibrium, non-critical string cosmologies are considered [1], which notably are consistent with the current astrophysical data from supernovae, as demonstrated recently [20], then there are significant modifications to the Boltzmann equation, stemming from extra sources (dilaton) and off-shell (non-critical, non equilibrium) terms, which affect the time evolution of the phase-space density of the species under consideration.…”