Towards a singularity-free inflationary universe?

Abstract

We consider the problem of constructing a non-singular inflationary universe in stringy gravity via branch changing, from a previously superexponentially expanding phase to an FRWlike phase. Our approach is based on the phase space analysis of the dynamics, and we obtain a no-go theorem which rules out the efficient scenario of branch changing catalyzed by dilaton potential and stringy fluid sources. We furthermore consider the effects of stringloop corrections to the gravitational action in the form recently suggested by Damour and Polyakov. These corrections also fail to produce the desired branch change. However, focusing on the possibility that these corrections may decouple the dilaton, we deduce that they may lead to an inflationary expansion in the presence of a cosmological constant, which asymptotically approaches Einstein-deSitter solution.Submitted to Nuclear Physics B theory are imminent. In most cases, the route taken was minimalistic in philosophy, consisting of inventing and incorporating changes to account for some of the phenomenologically dictated mechanisms. This approach has been only partially satisfactory, failing to produce a model capable of dealing comprehensively with the shortcomings of Einstein's theory, which proved deserving of respect even in its demise.On the other hand, the ongoing quest for the unified theory of interactions in Nature has finally produced a promising contender, which has withstood theoretical scrutiny up to date. The advent of string theory [3], based on a fundamentally different assumption about the nature of matter, has been supported mainly by the description of gravity in a manner equivalent to other forces, and perhaps even more importantly, by the absence of some of the 1 obstacles encountered in the failed attempts to quantize General Relativity. Thrusting from the initial success, many studies have sprung up investigating gravitational aspects of string theory, and in particular the early universe cosmology [4]- [20]. The justification for this interest can be naturally found in the fact that string theory, while claiming to unify gravity with the other forces of nature, must give us the means to investigate the regions where the standard model has failed to give satisfactory answers. The aforementioned cosmological problems, especially the problem of the initial singularity, fall precisely in this category. In addition, results of these investigations should provide us with ways to test the compatibility of string theory with the Nature.While the early investigations of string cosmology have indicated the presence of some of the coveted mechanisms to tackle the encountered problems, they have also burdened us with a host of new difficulties. In a typical cosmological setting, most of the advantages and the difficulties can be attributed to the presence of a new field, the scalar dilaton, which comes in response to the requirement of conformal invariance of string world-sheet theories. The dilaton has been recognized as a natural candidate for the inflato...

String cosmology

“…It should be noted that these are the defining properties of the (+) and (-) branches. As pointed out in [26], the identification of the (+) branch with the domain of negative times and the (-) branch with that of positive times is just a coincidence. In general, this identification does not necessarily hold, especially when a dilaton potential is present.…”

“…This assumes the solution of the graceful exit problem which all the tree-level inflationary solutions have to face. In fact, in [26] it is shown that a smooth transition from the (+) to the (-) branch in the low-energy effective theory (that is, to lowest order in the inverse string tension α ′ ), is not possible.…”

Long-Wavelength Approximation for String Cosmology with Barotropic Perfect Fluid

“…However, due to rather general no-go theorems [14] a smooth connection of these two branches turned out to be impossible, at least without some kind of higher order corrections. In the case of a perfect barotropic fluid, mutually dual solutions (23)- (25) and (31) with barotropic index Γ (cf [17,18]).…”

“…We find a quasi-isotropic solution for the field equations in the zero approximation (neglecting all spatial gradients) which include both post-big bang and pre-big bang [9,10,11,12] cosmological models. It has been demonstrated [13,14] that a smooth transition from a pre-big bang branch to a post-big bang branch (the graceful exit problem, see also [15,16,17]) is impossible in this approximation, even if we incorporate some dilaton potential, or cosmological constant. We analyze the nature of discontinuities which are contained in cosmological models based on a quasi-isotropic solution with a barotropic perfect fluid as a matter source (cf [18]).…”

Erratum: Cosmological solutions in M and string theory [Phys. Rev. D57, 7340 (1998)]

“…There have been numerous efforts attempting to explore the effects of string theory in cosmology [2] - [21]. One could characterize the main aims of many of these studies as either an attempt to utilize the additional degrees of freedom in the massless sector to induce inflation [2,3,6,7,8,10,11] or developing arguments on the type of modifications to Einstein gravity which are necessary to avoid a cosmological singularity [9,13,14,16,18,19,20].…”