In models like axion monodromy, temporal features during inflation which are not associated with its ending can produce scalar, and to a lesser extent, tensor power spectra where deviations from scale-free power law spectra can be as large as the deviations from scale invariance itself. Here the standard slow-roll approach breaks down since its parameters evolve on an efolding scale $ΔN$ much smaller than the efolds to the end of inflation. Using the generalized slow-roll approach, we show that the expansion of observables in a hierarchy of potential or Hubble evolution parameters comes from a Taylor expansion of the features around an evaluation point that can be optimized. Optimization of the leading-order expression provides a sufficiently accurate approximation for current data as long as the power spectrum can be described over the well-observed few efolds by the local tilt and running. Standard second-order approaches, often used in the literature, ironically are worse than leading-order approaches due to inconsistent evaluation of observables. We develop a new optimized next-order approach which predicts observables to $10^{-3}$ even for $ΔN\sim 1$ where all parameters in the infinite hierarchy are of comparable magnitude. For models with $ΔN \ll 1$, the generalized slow-roll approach provides integral expressions that are accurate to second order in the deviation from scale invariance. Their evaluation in the monodromy model provides highly accurate explicit relations between the running oscillation amplitude, frequency and phase in the curvature spectrum and parameters of the potential.
Most of the inflationary models that are in agreement with the Planck data rely on the presence of non-renormalizable operators. If the connection to low energy particle physics is made, the renormalization group (RG) introduces a sensitivity to ultraviolet (UV) physics that can be crucial in determining the inflationary predictions. We analyse this effect for the Standard Model (SM) augmented with non-minimal derivative couplings to gravity. Our set-up reduces to the SM for small values of the Higgs field, and allows for inflation in the opposite large field regime. The one-loop beta function…
Inflationary cosmology proposes that the early Universe undergoes accelerated expansion, driven, in simple scenarios, by a single scalar field, or inflaton. The form of the inflaton potential determines the initial spectra of density perturbations and gravitational waves. We show that constraints on the duration of inflation together with the BICEP3/Keck bounds on the gravitational wave background imply that higher derivatives of the potential are nontrivial with a confidence of 99%. Such terms contribute to the scale-dependence, or running, of the density perturbation spectrum. We clarify the…
As a contribution to a viable candidate for a standard model of cosmology, we here show that pre-inflationary quantum fluctuations can provide a scenario for the long-sought initial conditions for the inflaton field. Our proposal is based on the assumption that at very high energies (higher than the energy scale of inflation) the vacuum-expectation value (VeV) of the field is trapped in a false vacuum and then, due to renormalization-group (RG) running, the potential starts to flatten out toward low energy, eventually tending to a convex one which allows the field to roll down to the true vacu…
In this work we shall provide a model-independent general calculation of the running of the spectral index for vacuum $F(R)$ gravities. We shall exploit the functional form of the spectral index and of the tensor-to-scalar ratio in order to present a general $n_s-r$ relation for vacuum $F(R)$ gravity theories. As we show, viable $F(R)$ gravity theories can be classified to two classes of models regarding their prediction for the running spectral index. The $R^2$-attractor models predict a running of the spectral index in the range $-10^{-3}<a_s<-10^{-4}$, which classifies them in the same univ…
ACT Data and Positive Running of the Spectral Index for Scalar Theory and Modified Gravity
ICREA（加泰罗尼亚高级研究院）；Institute of Space Sciences (IEEC-CSIC)（空间科学研究所）；Department of Physics, Aristotle University of Thessaloniki（萨洛尼卡亚里士多德大学物理系）；Center for Theoretical Physics, Khazar University（阿塞拜疆可汗大学理论物理中心）
Cosmological inflation predicts that the scalar spectral index "runs" with scale. Constraints on the values of the spectral runnings, $α_s\equiv \textrm{d} n_s/\textrm{d}\ln k$ and $β_s\equiv \textrm{d}α_s/\textrm{d}\ln k$, therefore provide a fundamental test of the physics of inflation. Here we study the feasibility of measuring the runnings when information from upcoming large-volume galaxy surveys is used to supplement the information provided by a CMB-S4 experiment, particularly focusing on the effect of including high-$k$, nonlinear scales. Since these measurements will be sensitive to m…
We compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means the theory $R+R^{2}+C^{2}$ with the fakeon prescription/projection for $C^{2}$). The spectra are functions of the inflationary running coupling $α(1/k)$ and satisfy the cosmic renormalization-group flow equations, which determine the tilts and the running coefficients. The tensor fluctuations receive contributions from the spin-2 fakeon $χ_{μν}$ at every order of the expansion in powers of $α\sim 1/115$. The dependen…
Running into tension: primordial black holes from ultra-slow-roll inflation, spectral running, and the Hubble tension
University of Trento（特伦托大学）；Trento Institute for Fundamental Physics and Applications (TIFPA)-INFN（特伦托基础物理与应用研究所（TIFPA）-意大利国家核物理研究所）；New York University Abu Dhabi（纽约大学阿布扎比分校）
Current measurements of the temperature and polarization anisotropy power spectra of the Cosmic Microwave Background (CMB) seem to indicate that the naive expectation for the slow-roll hierarchy within the most simple inflationary paradigm may not be respected in nature. We show that a primordial power spectra with localized features could in principle give rise to the observed slow-roll anarchy when fitted to a featureless power spectrum. Future CMB missions have the key to disentangle among the two possible paradigms and firmly establish the slow-roll mechanism as the responsible one for the…
We study the running of power spectra in inflationary cosmology as a renormalization-group flow from the de Sitter fixed point. The beta function is provided by the equations of the background metric. The spectra of the scalar and tensor fluctuations obey RG evolution equations with vanishing anomalous dimensions in the superhorizon limit. By organizing the perturbative expansion in terms of leading and subleading logs, we calculate the spectral indices, their runnings, the runnings of the runnings, etc., to the next-to-leading log order in quantum gravity with fakeons (i.e., the theory $R+R^{…
We show that a CP-violating interaction induced by a derivative coupling between the running vacuum and a non-conserving baryon current may dynamically break CPT and trigger baryogenesis through an effective chemical potential. By assuming a non-singular class of running vacuum cosmologies which provides a complete cosmic history (from an early inflationary de Sitter stage to the present day quasi-de Sitter acceleration), it is found that an acceptable baryon asymmetry is generated for many different choices of the model parameters. It is interesting that the same ingredient (running vacuum en…
In previous works we have derived a Running Vacuum Model (RVM) for a string Universe, which provides an effective description of the evolution of 4-dimensional string-inspired cosmologies from inflation till the present epoch. In the context of this "stringy RVM" version, it is assumed that the early Universe is characterised by purely gravitational degrees of freedom, from the massless gravitational string multiplet, including the antisymmetric tensor field. The latter plays an important role, since its dual gives rise to a `stiff' gravitational-axion "matter", which in turn couples to the gr…
The next generation of cosmological observations will be sensitive to small deviations from a pure power law in the primordial power spectrum of the curvature perturbations. In the context of slow-roll inflation, these deviations are expected and correspond to the so-called running of the spectral index. Their measurement would bring as much information as the discovery of deviations from scale invariance. However, robust parameter inference requires to marginalize over any possible higher order uncertainties, which have been, up to now, not fully determined. We tackle this issue by deriving t…
We study the $R^p$ inflationary model of [Muller:1989rp] for $p>2$ using the result of Ref. [Motohashi:2014tra]. After reproducing the observable quantities: the power spectral index $n_s$, its corresponding running $α=\frac{dn_s}{d\ln(k)}$ and the tensor to scalar ration $r$ in terms of e-folding number $N$ and $p$, we show that $R^p$ inflation model is still alive as $p$ is from $2$ to $2.02$. In this range, our calculation confirms that $n_s$ and $r$ agree with observations and $α$ is of order $10^{-4}$ which needs more precise observational constraints. We find that, as the value of $p$ in…
If the inflaton couples to other degrees of freedom that populate the post-inflationary stage, such coupling modifies the dynamics of the inflaton \emph{during} inflation. We consider light fermions Yukawa coupled to the inflaton as "unobserved" degrees of freedom integrated out of the total density matrix. Tracing out these degrees of freedom yields a \emph{mixed} density matrix whose time evolution is described by an effective field theory. We show that the coupling leads to profuse fermion pair production for super-Hubble inflaton fluctuations which lead to the \emph{growth of entanglement …
In this work we re-investigate pros and cons of mutated hilltop inflation. Applying Hamilton-Jacobi formalism we solve inflationary dynamics and find that inflation goes on along the ${\cal W}_{-1}$ branch of the Lambert function. Depending on the model parameter mutated hilltop model renders two types of inflationary solutions: one corresponds to small inflaton excursion during observable inflation and the other describes large field inflation. The inflationary observables from curvature perturbation are in tune with the current data for a wide range of the model parameter. The small field br…
Inflationary models with power-law potentials are starting to be severely constrained by the recent measurements of Cosmic Microwave Background anisotropies provided by the Planck Satellite and by the BICEP2 telescope. In particular, models with power-law potentials $V(φ)\propto φ^n$ with $n \ge 2$ are strongly disfavored by present data since they predict a sizable contribution of gravitational waves with a tensor/scalar ratio of $r\sim0.15$ that is at odds with current limits. A non-minimal coupling to gravity has been proposed as a physical mechanism to lower the predictions for $r$. In thi…
In light of the most recent cosmological observations, we provide new updated constraints on the slow-roll inflation in different extended scenarios beyond the $Λ\rm{CDM}$ cosmological model. Along with the usual six parameters, we simultaneously vary different combinations of additional parameters, including the running of the scalar spectral index $α_s$, its running of running $β_s$, the tensor amplitude $r$ and the spatial curvature $Ω_k$. From the Planck 2018 data, we find no evidence for a scalar running or a running of running, while analyzing the Atacama Cosmology Telescope data combine…
The primordial power spectrum informs the possible inflationary histories of our universe. Given a power spectrum, the ensuing cosmic microwave background is calculated and compared to the observed one. Thus, one focus of modern cosmology is building well-motivated inflationary models that predict the primordial power spectrum observables. The common practice uses analytic terms for the scalar spectral index $n_s$ and the index running $α$, forgoing the effort required to evaluate the model numerically. However, the validity of these terms has never been rigorously probed and relies on perturb…
