Over the past several years research in nonsingular cosmology, particularly LQC bounce models, has appeared at an increasing rate. Of particular interest are those papers suggesting ways that quantum cosmology bounce models might be tested. Since June 2008 enough papers have appeared that I thought it might be interesting to list them and try to get an overview. What kinds of ideas are being brought forward? Which, if any, seem applicable near-term? Which ideas suggest more remote, or even very unlikely, prospects? Since a review paper appeared in June 2008: http://0806.0339 I will not go back before that, assuming that the review covers earlier research adequately. And I will mention one one other June 2008 paper, the rest having appeared in July or later: http://arxiv.org/abs/0806.3082 Anomalous CMB polarization and gravitational chirality Carlo R. Contaldi, Joao Magueijo, Lee Smolin 5 pages (Submitted on 18 Jun 2008) "We consider the possibility that gravity breaks parity, with left and right handed gravitons coupling to matter with a different Newton's constant and show that this would affect their zero-point vacuum fluctuations during inflation. Should there be a cosmic background of gravity waves, the effect would translate into anomalous CMB polarization. Non-vanishing TB (and EB) polarization components emerge, revealing interesting experimental targets. Indeed if reasonable chirality is present a TB measurement would provide the easiest way to detect a gravitational wave background. We speculate on the theoretical implications of such an observation." http://arxiv.org/abs/0807.0160 Loop Quantum Cosmology corrections to inflationary models Michal Artymowski, Zygmunt Lalak, Lukasz Szulc 16 pages, 1 figure (Submitted on 1 Jul 2008) "In the recent years the quantization methods of Loop Quantum Gravity have been successfully applied to the homogeneous and isotropic Friedmann-Robertson-Walker space-times. The resulting theory, called Loop Quantum Cosmology (LQC), resolves the Big Bang singularity by replacing it with the Big Bounce. We argue that LQC generates also certain corrections to field theoretical inflationary scenarios. These corrections imply that in the LQC the effective sonic horizon becomes infinite at some point after the bounce and that the scale of the inflationary potential implied by the COBE normalisation increases. The evolution of scalar fields immediately after the Bounce becomes modified in an interesting way. We point out that one can use COBE normalisation to establish an upper bound on the quantum of length of LQG." http://arxiv.org/abs/0807.0712 Gravitational waves from the Big Bounce Jakub Mielczarek 19 pages, 9 figures (Submitted on 4 Jul 2008) "In this paper we investigate gravitational waves production during the Big Bounce phase inspired by the Loop Quantum Cosmology. We consider the influence of the holonomy corrections to the equation for tensor modes. We show that they act like additional effective graviton mass, suppressing gravitational waves creation. However, this effects can be treated perturbatively. We investigate the simplified model without these corrections and find its exact analytical solution. For this model we calculate a spectrum of the gravitational waves from the Big Bounce phase. The obtained spectrum decreases to zero for the low energy modes. Based on this observation we indicate that this effect can lead to the low CMB multipoles suppression and gives a potential way to test Loop Quantum Cosmology models. We also consider a scenario with a post-bounce inflationary phase. The obtained power spectrum gives qualitative explanation of the CMB spectra, including low multipoles suppression. This result is a challenge to construct a consistent bounce+inflation model in the Loop Quantum Cosmology." http://arxiv.org/abs/0807.1854 DSR as an explanation of cosmological structure Joao Magueijo (Submitted on 11 Jul 2008) "Deformed special relativity (DSR) is one of the possible realizations of a varying speed of light (VSL). It deforms the usual quadratic dispersion relations so that the speed of light becomes energy dependent, with preferred frames avoided by postulating a non-linear representation of the Lorentz group. The theory may be used to induce a varying speed of sound capable of generating (near) scale-invariant density fluctuations, as discussed in a recent Letter. We identify the non-linear representation of the Lorentz group that leads to scale-invariance, finding a universal result. We also examine the higher order field theory that could be set up to represent it." http://arxiv.org/abs/0808.0701 Effective theory for the cosmological generation of structure Martin Bojowald, Aureliano Skirzewski 8 pages, 1 figure (Submitted on 5 Aug 2008) "The current understanding of structure formation in the early universe is mainly built on a magnification of quantum fluctuations in an initial vacuum state during an early phase of accelerated universe expansion. One usually describes this process by solving equations for a quantum state of matter on a given expanding background space-time, followed by decoherence arguments for the emergence of classical inhomogeneities from the quantum fluctuations. Here, we formulate the coupling of quantum matter fields to a dynamical gravitational background in an effective framework which allows the inclusion of back-reaction effects. It is shown how quantum fluctuations couple to classical inhomogeneities and can thus manage to generate cosmic structure in an evolving background. Several specific effects follow from a qualitative analysis of the back-reaction, including a likely reduction of the overall amplitude of power in the cosmic microwave background, the occurrence of small non-Gaussianities, and a possible suppression of power for odd modes on large scales without parity violation." http://arxiv.org/abs/0808.2259 Time delay of light signals in an energy-dependent spacetime metric A. F. Grillo, E. Luzio, F. Mendez 5 pages. Physical Review D77, 104033 (2008) (Submitted on 16 Aug 2008) "In this note we review the problem of time delay of photons propagating in a spacetime with a metric that explicitly depends on the energy of the particles (Gravity-Rainbow approach). We show that corrections due to this approach -- which is closely related to DSR proposal -- produce for small redshifts (z<<1) smaller time delays than in the generic Lorentz Invariance Violating case." http://arxiv.org/abs/0810.0104 The gravitational wave background from super-inflation in Loop Quantum Cosmology E. J. Copeland, D. J. Mulryne, N. J. Nunes, M. Shaeri 8 pages, 3 figures (Submitted on 1 Oct 2008) "We investigate the behaviour of tensor fluctuations in Loop Quantum Cosmology, focusing on a class of scaling solutions which admit a near scale-invariant scalar field power spectrum. We obtain the spectral index of the gravitational field perturbations, and find a strong blue tilt in the power spectrum with [tex]n_t \approx 2[/tex]. The amplitude of tensor modes are, therefore, suppressed by many orders of magnitude on large scales compared to those predicted by the standard inflationary scenario where [tex]n_t \approx 0[/tex]." http://arxiv.org/abs/0810.2787 Proving Inflation: A Bootstrap Approach Latham Boyle (CITA), Paul J. Steinhardt (Princeton) 4 pages, 2 figures (Submitted on 16 Oct 2008) "We propose a way to test the essential idea underlying the inflationary paradigm: that the universe underwent a brief period of accelerated expansion followed by a long period of decelerated expansion." (This is included because the authors propose a test which could actually disfavor or even rule out the occurence of inflation, with major consequences for quantum cosmo. According to the authors, inflation scenarios are falsifiable.) http://arxiv.org/abs/0810.4330 Loop quantum cosmology and tensor perturbations in the early universe Gianluca Calcagni, Golam Mortuza Hossain 12 pages. Invited contribution to the special issue of Advanced Science Letters on "Quantum gravity, Cosmology and Black Holes" (Submitted on 23 Oct 2008) "We study the tensor modes of linear metric perturbations within an effective framework of loop quantum cosmology. After a review of inverse-volume and holonomy corrections in the background equations of motion, we solve the linearized tensor modes equations and extract their spectrum. Ignoring holonomy corrections, the tensor spectrum is blue tilted in the near-Planckian superinflationary regime and may be observationally disfavoured. However, in this case background dynamics is highly nonperturbative, hence the use of standard perturbative techniques may not be very reliable. On the other hand, in the quasi-classical regime the tensor index receives a small negative quantum correction, slightly enhancing the standard red tilt in slow-roll inflation. We discuss possible interpretations of this correction, which depends on the choice of semiclassical state."