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In string theory, the traditional picture of a Universe that emerges from the inflation of a very small and highly curved space-time patch is a possibility, not a necessity: quite different initial conditions are possible, and not necessarily unlikely. In particular, the duality symmetries of string theory suggest scenarios in which the Universe starts inflating from an initial state characterized by very small curvature and interactions. Such a state, being gravitationally unstable, will evolve towards higher curvature and coupling, until string-size effects and loop corrections make the Universe bounce into a standard, decreasing-curvature regime. In such a context, the hot big bang of conventional cosmology is replaced by a hot big bounce in which the bouncing and heating mechanisms originate from the quantum production of particles in the high-curvature, large-coupling pre-bounce phase. Here we briefly summarize the main features of this inflationary scenario, proposed a quarter century ago. In its simplest version (where it represents an alternative and not a complement to standard slow-roll inflation) it can produce a viable spectrum of density perturbations, together with a tensor component characterized by a blue spectral index with a peak in the GHz frequency range. That means, phenomenologically, a very small contribution to a primordial B-mode in the CMB polarization, and the possibility of a large enough stochastic background of gravitational waves to be measurable by present or future gravitational wave detectors.
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We discuss general features of the $beta$-function equations for spatially flat, $(d+1)$-dimensional cosmological backgrounds at lowest order in the string-loop expansion, but to all orders in $alpha$. In the special case of constant curvature and a linear dilaton these equations reduce to $(d+1)$ algebraic equations in $(d+1)$ unknowns, whose solutions can act as late-time regularizing attractors for the singular lowest-order pre-big bang solutions. We illustrate the phenomenon in a first order example, thus providing an explicit realization of the previously conjectured transition from the dilaton to the string phase in the weak coupling regime of string cosmology. The complementary role of $alpha$ corrections and string loops for completing the transition to the standard cosmological scenario is also briefly discussed.
We present a short introduction to a non-standard cosmological scenario motivated by the duality symmetries of string theory, in which the big bang singularity is replaced with a big bounce at high but finite curvature. The bouncing epoch is prepared by a long (possibly infinitely extended) phase of cosmic evolution, starting from an initial state asymptotically approaching the string perturbative vacuum.
In a recent series of papers, we have shown that theories with scalar fields coupled to gravity (e.g., the standard model) can be lifted to a Weyl-invariant equivalent theory in which it is possible to unambiguously trace the classical cosmological evolution through the transition from big crunch to big bang. The key was identifying a sufficient number of finite, Weyl-invariant conserved quantities to uniquely match the fundamental cosmological degrees of freedom across the transition. In so doing we had to account for the well-known fact that many Weyl-invariant quantities diverge at the crunch and bang. Recently, some authors rediscovered a few of these divergences and concluded based on their existence alone that the theories cannot be geodesically complete. In this note, we show that this conclusion is invalid. Using conserved quantities we explicitly construct the complete set of geodesics and show that they pass continuously through the big crunch-big bang transition.
We solve for the cosmological perturbations in a five-dimensional background consisting of two separating or colliding boundary branes, as an expansion in the collision speed V divided by the speed of light c. Our solution permits a detailed check of the validity of four-dimensional effective theory in the vicinity of the event corresponding to the big crunch/big bang singularity. We show that the four-dimensional description fails at the first nontrivial order in (V/c)^2. At this order, there is nontrivial mixing of the two relevant four-dimensional perturbation modes (the growing and decaying modes) as the boundary branes move from the narrowly-separated limit described by Kaluza-Klein theory to the well-separated limit where gravity is confined to the positive-tension brane. We comment on the cosmological significance of the result and compute other quantities of interest in five-dimensional cosmological scenarios.
According to the most popular scenario, the early Universe should have experienced an accelerated expansion phase, called Cosmological Inflation, after which the standard Big Bang Cosmology would have taken place giving rise to the radiation-dominated epoch. However, the details of the inflationary scenario are far to be completely understood. Thus, in this paper we study if possible additional (exotic) cosmological phases could delay the beginning of the standard Big Bang history and alter some theoretical predictions related to the inflationary cosmological perturbations, like, for instance, the order of magnitude of the tensor-to-scalar ratio $r$.
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