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We show that a combination of the simplest $alpha$-attractors and KKLTI models related to Dp-brane inflation covers most of the area in the ($n_{s}$, $r$) space favored by Planck 2018. For $alpha$-attractor models, there are discrete targets $3alpha=1,2,...,7$, predicting 7 different values of $r = 12alpha/N^{2}$ in the range $10^{-2} gtrsim r gtrsim 10^{-3}$. In the small $r$ limit, $alpha$-attractors and Dp-brane inflation models describe vertical $beta$-stripes in the ($n_{s}$, $r$) space, with $n_{s}=1-beta/N$, $beta=2, {5over 3},{8over 5}, {3over 2},{4over 3}$. A phenomenological description of these models and their generalizations can be achieved in the context of pole inflation. Most of the $1sigma$ area in the ($n_{s}$, $r$) space favored by Planck 2018 can be covered models with $beta = 2$ and $beta = 5/3$. Future precision data on $n_s$ may help to discriminate between these models even if the precision of the measurement of $r$ is insufficient for the discovery of gravitational waves produced during inflation.
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Hilltop inflation models are often described by potentials $V = V_{0}(1-{phi^{n}over m^{n}}+...)$. The omitted terms indicated by ellipsis do not affect inflation for $m lesssim 1$, but the most popular models with $n =2$ and $4$ for $m lesssim 1$ are ruled out observationally. Meanwhile in the large $m$ limit the results of the calculations of the tensor to scalar ratio $r$ in the models with $V = V_{0}(1-{phi^{n}over m^{n}})$, for all $n$, converge to $r= 4/N lesssim 0.07$, as in chaotic inflation with $V sim phi$, suggesting a reasonably good fit to the Planck data. We show, however, that this is an artifact related to the inconsistency of the model $V = V_{0}(1-{phi^{n}over m^{n}})$ at $phi > m$. Consistent generalizations of this model in the large $m$ limit typically lead to a much greater value $r= 8/N$, which negatively affects the observational status of hilltop inflation. Similar results are valid for D-brane inflation with $V = V_{0}(1-{m^{n}over phi^{n}})$, but consistent generalizations of D-brane inflation models may successfully complement $alpha$-attractors in describing most of the area in the ($n_{s}$, $r$) space favored by Planck 2018.
We study to what extent the spectral index $n_s$ and the tensor-to-scalar ratio $r$ determine the field excursion $Deltaphi$ during inflation. We analyse the possible degeneracy of $Delta phi$ by comparing three broad classes of inflationary models, with different dependence on the number of e-foldings $N$, to benchmark models of chaotic inflation with monomial potentials. The classes discussed cover a large set of inflationary single field models. We find that the field range is not uniquely determined for any value of $(n_s, r)$; one can have the same predictions as chaotic inflation and a very different $Delta phi$. Intriguingly, we find that the field range cannot exceed an upper bound that appears in different classes of models. Finally, $Delta phi$ can even become sub-Planckian, but this requires to go beyond the single-field slow-roll paradigm.
We briefly summarize the impact of the recent Planck measurements for string inflationary models, and outline what might be expected to be learned in the near future from the expected improvement in sensitivity to the primordial tensor-to-scalar ratio. We comment on whether these models provide sufficient added value to compensate for their complexity, and ask how they fare in the face of the new constraints on non-gaussianity and dark radiation. We argue that as a group the predictions made before Planck agree well with what has been seen, and draw conclusions from this about what is likely to mean as sensitivity to primordial gravitational waves improves.
In this work, we study the key role of generic Effective Field Theory (EFT) framework to quantify the correlation functions in a quasi de Sitter background for an arbitrary initial choice of the quantum vacuum state. We perform the computation in unitary gauge, in which we apply the St$ddot{text{u}}$ckelberg trick in lowest dimensional EFT operators which are broken under time diffeomorphism. In particular, using this non-linear realization of broken time diffeomorphism and truncating the action by considering the contribution from two derivative terms in the metric, we compute the two-point and three-point correlations from scalar perturbations and two-point correlation from tensor perturbations to quantify the quantum fluctuations observed in the Cosmic Microwave Background (CMB) map. We also use equilateral limit and squeezed limit configurations for the scalar three-point correlations in Fourier space. To give future predictions from EFT setup and to check the consistency of our derived results for correlations, we use the results obtained from all classes of the canonical single-field and general single-field $P(X,phi)$ model. This analysis helps us to fix the coefficients of the relevant operators in EFT in terms of the slow-roll parameters and effective sound speed. Finally, using CMB observations from Planck we constrain all these coefficients of EFT operators for the single-field slow-roll inflationary paradigm.
Several unexpected features have been observed in the microwave sky at large angular scales, both by WMAP an by Planck. Among those features is a lack of both variance and correlation on the largest angular scales, alignment of the lowest multipole moments with one another and with the motion and geometry of the Solar System, a hemispherical power asymmetry or dipolar power modulation, a preference for odd parity modes and an unexpectedly large cold spot in the Southern hemisphere. The individual p-values of the significance of these features are in the per mille to per cent level, when compared to the expectations of the best-fit inflationary $Lambda$CDM model. Some pairs of those features are demonstrably uncorrelated, increasing their combined statistical significance and indicating a significant detection of CMB features at angular scales larger than a few degrees on top of the standard model. Despite numerous detailed investigations, we still lack a clear understanding of these large-scale features, which seem to imply a violation of statistical isotropy and scale invariance of inflationary perturbations. In this contribution we present a critical analysis of our current understanding and discuss several ideas of how to make further progress.
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