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Register a new userSailing through the big crunch-big bang transition
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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.
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We point out a new phenomenon which seems to be generic in 4d effective theories of scalar fields coupled to Einstein gravity, when applied to cosmology. A lift of such theories to a Weyl-invariant extension allows one to define classical evolution through cosmological singularities unambiguously, and hence construct geodesically complete background spacetimes. An attractor mechanism ensures that, at the level of the effective theory, generic solutions undergo a big crunch/big bang transition by contracting to zero size, passing through a brief antigravity phase, shrinking to zero size again, and re-emerging into an expanding normal gravity phase. The result may be useful for the construction of complete bouncing cosmologies like the cyclic model.
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.
We study the chameleon field dark matter, dubbed textit{scalaron}, in $F(R)$ gravity in the Big Bang Nucleosynthesis (BBN) epoch. With an $R^{2}$-correction term required to solve the singularity problem for $F(R)$ gravity, we first find that the scalaron dynamics is governed by the $R^{2}$ term and the chameleon mechanism in the early universe, which makes the scalaron physics model-independent regarding the low-energy scale modification. In viable $F(R)$ dark energy models including the $R^{2}$ correction, our analysis suggests the scalaron universally evolves in a way with a bouncing oscillation irrespective of the low-energy modification for the late-time cosmic acceleration. Consequently, we find a universal bound on the scalaron mass in the BBN epoch, to be reflected on the constraint for the coupling strength of the $R^2$ term, which turns out to be more stringent than the one coming from the fifth force experiments. It is then shown that the scalaron naturally develops a small enough fluctuation in the BBN epoch, hence can avoid the current BBN constraint placed by the latest Planck 2018 data, and can also have a large enough sensitivity to be hunted by the BBN, with more accurate measurements for light element abundances as well as the baryon number density fraction.
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 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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