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We derive the slow-roll conditions for a non-minimally coupled scalar field (extended quintessence) during the radiation/matter dominated era extending our previous results for thawing quintessence. We find that the ratio $ddotphi/3Hdotphi$ becomes constant but negative, in sharp contrast to the ratio for the minimally coupled scalar field. We also find that the functional form of the equation of state of the scalar field asymptotically approaches that of the minimally coupled thawing quintessence.
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We investigate the cosmological observational test of the extended quintessence model, i.e. a scalar-tensor gravity model with a scalar field potential serving as dark energy, by using the Planck 2018 cosmic microwave background (CMB) data, together with the baryon acoustic oscillations (BAO) and redshift-space distortion (RSD) data. As an example, we consider the model with a Brans-Dicke kinetic term $frac{omega(phi)}{phi} phi_{;mu} phi^{;mu} $ and a quadratic scalar potential $V (phi) = A + B (phi - phi_0) + frac{C}{2} (phi - phi_0)^2$, which reduces to general relativity (GR) in the limit $omega(phi) to infty$, and the cosmological constant in the limit $B=C=0$. In such a model the scalar field typically rolls down the potential and oscillates around the minimum of $V (phi)$. We find that the model parameter estimate for the CMB+BAO+RSD data set is given by $lg alpha = -3.6 _{-0.54}^{+0.66}~ (68%)$, corresponding to $ 3.8 times 10^5 < omega_0 < 9.5 times 10^7~ (68%)$, and $lg C = 4.9 pm 1.4~ (68%) $. However, the GR $Lambda$CDM model can fit the data almost as good as this extended quintessence model, and is favored by the Akaike information criterion (AIC). The variation of the gravitational constant since the epoch of Recombination is constrained to be $0.97 < G_{rm rec}/G_0 < 1.03~ (1 sigma)$. In light of recent report that the CMB data favors a closed universe, we consider the case with non-flat geometry in our fit, and find that the mean value of $Omega_k$ shifts a little bit from $-0.049$ to $-0.036$, and the parameters in our model are not degenerate with $Omega_k$.
Multiple inflation is a model based on N=1 supergravity wherein there are sudden changes in the mass of the inflaton because it couples to flat direction scalar fields which undergo symmetry breaking phase transitions as the universe cools. The resulting brief violations of slow-roll evolution generate a non-gaussian signal which we find to be oscillatory and yielding f_NL ~ 5-20. This is potentially detectable by e.g. Planck but would require new bispectrum estimators to do so. We also derive a model-independent result relating the period of oscillations of a phase transition during inflation to the period of oscillations in the primordial curvature perturbation generated by the inflaton.
We numerically calculate the evolution of second order cosmological perturbations for an inflationary scalar field without resorting to the slow-roll approximation or assuming large scales. In contrast to previous approaches we therefore use the full non-slow-roll source term for the second order Klein-Gordon equation which is valid on all scales. The numerical results are consistent with the ones obtained previously where slow-roll is a good approximation. We investigate the effect of localised features in the scalar field potential which break slow-roll for some portion of the evolution. The numerical package solving the second order Klein-Gordon equation has been released under an open source license and is available for download.
We present a complete formulation of the scalar bispectrum in the unified effective field theory (EFT) of inflation, which includes the Horndeski and beyond-Horndeski Gleyzes-Langlois-Piazza-Vernizzi classes, in terms of a set of simple one-dimensional integrals. These generalized slow-roll expressions remain valid even when slow-roll is transiently violated and encompass all configurations of the bispectrum. We show analytically that our expressions explicitly preserve the squeezed-limit consistency relation beyond slow-roll. As an example application of our results, we compute the scalar bispectrum in a model in which potential-driven G-inflation at early times transitions to chaotic inflation at late times, showing that our expressions accurately track the bispectrum when slow-roll is violated and conventional slow-roll approximations fail.
We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter $epsilon(phi)$ and its derivatives $epsilon^{prime }(phi)$ and $epsilon^{primeprime }(phi)$, thereby extracting general conditions on the tensor-to-scalar ratio $r$ and the running $n_{sk}$ at $phi_{H}$ where the perturbations are produced, some $50$ $-$ $60$ $e$-folds before the end of inflation. We find quite generally that for models where $epsilon(phi)$ develops a maximum, a relatively large $r$ is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter $xi_2(phi)$. To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic $epsilon(phi)$ decreasing during most part of inflation. Since at $phi_{H}$ the slow-roll parameter $epsilon(phi)$ is increasing, we thus require that $epsilon(phi)$ develops a maximum for $phi > phi_{H}$ after which $epsilon(phi)$ decrease to small values where most $e$-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion $Deltaphi_eequiv |phi_H-phi_e |$ is obtained with a sufficiently thin profile for $epsilon(phi)$ which, however, should not conflict with the second slow-roll parameter $eta(phi)$. As a consequence of this analysis we find bounds for $Delta phi_e$, $r_H$ and for the scalar spectral index $n_{sH}$. Finally we provide examples where these considerations are explicitly realised.
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