Mode coupling on a geometrodynamical quantization of an inflationary universe
TL;DR: In this article, a geometrodynamical quantization of an inflationary universe is considered in order to estimate quantum-gravity effects for the primordial perturbations, and the back-reaction produced by all the modes of the system is included in their computations.
Abstract: A geometrodynamical quantization of an inflationary universe is considered in order to estimate quantum-gravity effects for the primordial perturbations. Contrary to previous studies in the literature, the back-reaction produced by all the modes of the system is included in our computations. Even if at a classical level the assumption that every mode evolves independently provides a good estimate for the dynamics, our results explicitly show that this is not the case when considering quantum-gravity effects. More precisely, both the self-interaction, as well as the back-reaction from other modes, provide a correction of the same order of magnitude to the usual power spectrum as computed in the approximation of quantum field theory on classical backgrounds. In particular, these quantum-gravity effects introduce certain characteristic scale-dependence on the expression of the power spectrum.
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TL;DR: In this paper, the perturbations arising from gravitationally induced stimulated creation were computed for a general statistical density operator that describes an initial mixed state that includes probabilities for nonzero numbers of scalar perturbation to be present at early times during inflation and showed that the initial presence of quanta can significantly enhance non-Gaussianities in the so-called squeezed limit.
Abstract: Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally induced spontaneous creation of perturbations from an initial vacuum state. In this paper, we compute the perturbations arising from gravitationally induced stimulated creation when perturbations are already present in the initial state. The effect of these initial perturbations is not diluted by inflation and survives to its end, and beyond. We consider a generic statistical density operator $\ensuremath{\rho}$ describing an initial mixed state that includes probabilities for nonzero numbers of scalar perturbations to be present at early times during inflation. We analyze the primordial bispectrum for general configurations of the three different momentum vectors in its arguments. We find that the initial presence of quanta can significantly enhance non-Gaussianities in the so-called squeezed limit. Our results show that an observation of non-Gaussianities in the squeezed limit can occur for single-field inflation when the state in the very early inflationary Universe is not the vacuum, but instead contains early-time perturbations. Valuable information about the initial state can then be obtained from observations of those non-Gaussianities.
196 citations
TL;DR: In this paper, the authors examined the effect of ignorance in the initial condition for inflationary perturbations, due to unknown new physics at a high scale M. They showed that for M ∼ 20H, such initial states always (substantially) suppress the tensor to scalar ratio.
Abstract: The inflationary cosmology paradigm is very successful in explaining the CMB anisotropy to the percent level. Besides the dependence on the inflationary model, the power spectra, spectral tilt and non-Gaussianity of the CMB temperature fluctuations also depend on the initial state of inflation. Here, we examine to what extent these observables are affected by our ignorance in the initial condition for inflationary perturbations, due to unknown new physics at a high scale M. For initial states that satisfy constraints from backreaction, we find that the amplitude of the power spectra could still be significantly altered, while the modification in bispectrum remains small. For such initial states, M has an upper bound of a few tens of H, with H being the Hubble parameter during inflation. We show that for M ∼ 20H, such initial states always (substantially) suppress the tensor to scalar ratio. In particular we show that such a choice of initial conditions can satisfactorily reconcile the simple 1 m 2 φ 2 chaotic model with the Planck data (1)
148 citations
TL;DR: In this paper, the authors show that the Wigner function is not everywhere positive for any finite rk, hence its interpretation as a classical distribution function in phase space is impossible without some coarse graining procedure.
147 citations
TL;DR: In this article, the authors numerically calculate the local-type signal in the cosmic microwave background (CMB) that would be measured for such models (including the full transfer function and 2D projection).
Abstract: Single-field slow-roll inflation with a nonvacuum initial state has an enhanced bispectrum in the local limit. We numerically calculate the local-type ${f}_{\mathrm{NL}}$ signal in the cosmic microwave background (CMB) that would be measured for such models (including the full transfer function and 2D projection). The nature of the result depends on several parameters, including the occupation number ${N}_{k}$, the phase angle ${\ensuremath{\theta}}_{k}$ between the Bogoliubov parameters, and the slow-roll parameter $ϵ$. In the most conservative case, where one takes ${\ensuremath{\theta}}_{k}\ensuremath{\approx}{\ensuremath{\eta}}_{0}k$ (justified by physical reasons discussed within) and $ϵ\ensuremath{\lesssim}0.01$, we find that $0l{f}_{\mathrm{NL}}l1.52(ϵ/0.01)$, which is likely too small to be detected in the CMB. However, if one is willing to allow a constant value for the phase angle ${\ensuremath{\theta}}_{k}$ and ${N}_{k}=\mathcal{O}(1)$, ${f}_{\mathrm{NL}}$ can be much larger and/or negative (depending on the choice of ${\ensuremath{\theta}}_{k}$), e.g. ${f}_{\mathrm{NL}}\ensuremath{\approx}28(ϵ/0.01)$ or $\ensuremath{-}6.4(ϵ/0.01)$; depending on $ϵ$, these scenarios could be detected by Planck or a future satellite. While we show that these results are not actually a violation of the single-field consistency relation, they do produce a value for ${f}_{\mathrm{NL}}$ that is considerably larger than that usually predicted from single-field inflation.
147 citations
TL;DR: The primordial power spectrum of density fluctuations is derived in the framework of quantum cosmology using a Born-Oppenheimer approximation to the Wheeler-DeWitt equation for an inflationary universe with a scalar field and quantum gravitational corrections are obtained.
Abstract: We derive the primordial power spectrum of density fluctuations in the framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer approximation to the Wheeler-DeWitt equation for an inflationary universe with a scalar field. In this way, we first recover the scale-invariant power spectrum that is found as an approximation in the simplest inflationary models. We then obtain quantum gravitational corrections to this spectrum and discuss whether they lead to measurable signatures in the cosmic microwave background anisotropy spectrum. The nonobservation so far of such corrections translates into an upper bound on the energy scale of inflation.
138 citations