Mafalda Dias, David Seery
We present a simple and efficient method to compute the superhorizon evolution of the spectral index in multi-field inflationary models, using transport equation techniques. We illustrate the evolution of n_s with time for various interesting potentials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We investigate the impact of the post-inflationary thermal histories on the cosmic graviton spectrum caused by the inflationary variation of their refractive index. Depending on the frequency band, the spectral energy distribution can be mildly red, blue or even violet. Wide portions of the parameter space lead to potentially relevant signals both in the audio range (probed by the advanced generation of terrestrial interferometers) and in the mHz band (where space-borne detectors could be operational within the incoming score year). The description of the refractive index in conformally relate…
The scalar-tensor Dirac-Born-Infeld (DBI) inflation scenario provides a simple mechanism to reduce the large values of the boost factor associated with single field models with DBI action, whilst still being able to drive 60 efolds of inflation. Using a slow-roll approach, we obtain an analytical expression for the spectral index of the perturbations and, moreover, determine numerically the regions of the parameter space of the model capable of giving rise to a power spectrum with amplitude and spectral index within the observed bounds. We find that regions that exhibit significant DBI effects…
We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, tauNL and gNL, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, and obtain its third-order part for the first time. We clarify how the 'backwards' formal…
In conventional model independent approaches, the power spectrum of primordial perturbations is characterized by such free parameters as spectral index, its running, the running of running, and the tensor-to-scalar ratio. In this work we, show that, at least for simple inflationary potentials, one can find the primordial scalar and tensor power spectra exactly by resumming over all the running terms. In this model-dependent method, we expand the power spectra about the pivot scale to find the series terms as functions of the e-folding number for some single field models of inflation. Interesti…
We investigate a fluid description of inflationary cosmology. It is shown that the three observables of the inflationary universe: the spectral index of the curvature perturbations, the tensor-to-scalar ratio of the density perturbations, and the running of the spectral index, can be compatible with the Planck analysis. In addition, we reconstruct the equation of state (EoS) for a fluid from the spectral index of the curvature perturbations consistent with the Planck results. We explicitly demonstrate that the universe can gracefully exit from inflation in the reconstructed fluid models. Furth…
I construct a class of single small field models of inflation that can predict an observable gravitational wave signal in the cosmic microwave background anisotropoies, contrary to popular wisdom. The spectral index, its running, the tensor to scalar ratio and the number of e-folds can cover all the parameter space currently allowed by cosmological observations. A unique feature of models in this class is their ability to predict a negative spectral index running in accordance with recent cosmic microwave background observations. I comment on the new class of models from an effective field the…
In this paper we investigate the implications of having a varying second slow-roll index on the canonical scalar field inflationary dynamics. We shall be interested in cases that the second slow-roll can take small values and correspondingly large values, for limiting cases of the function that quantifies the variation of the second slow-roll index. As we demonstrate, this can naturally introduce a smooth transition between slow-roll and constant-roll eras. We discuss the theoretical implications of the mechanism we introduce and we use various illustrative examples in order to better understa…
We investigate the descriptions for the observables of inflationary models, in particular, the spectral index of curvature perturbations, the tensor-to-scalar ratio, and the running of the spectral index, in the framework of perfect fluid models and $F(R)$ gravity theories through the reconstruction methods. Furthermore, the perfect fluid and $F(R)$ gravity descriptions of inflation are compared with the recent cosmological observations such as the Planck satellite and BICEP2 experiment. It is demonstrated with explicit examples that perfect fluid may lead to the inflationary universe consiste…
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
本文研究了在暴胀理论中谱指数运行为正的可能性，通过分析ACT数据和其他物理证据，探讨了在最小耦合标量场引力和修正引力中如何获得正运行的谱指数，并指出Einstein-Gauss-Bonnet理论在兼容GW170817事件的情况下，可以轻松实现正运行的谱指数。
We consider the running of the spectral index as a probe of both inflation itself, and of the overall evolution of the very early universe. Surveying a collection of simple single field inflationary models, we confirm that the magnitude of the running is relatively consistent, unlike the tensor amplitude, which varies by orders of magnitude. Given this target, we confirm that the running is potentially detectable by future large scale structure or 21 cm observations, but that only the most futuristic measurements can distinguish between these models on the basis of their running. For any speci…
PyTransport constitutes a straightforward code written in C++ together with Python scripts which automatically edit, compile and run the C++ code as a Python module. It has been written for Unix-like systems (OS X and Linux). Primarily the module employs the transport approach to inflationary cosmology to calculate the tree-level power-spectrum and bispectrum of user specified models of multi-field inflation, accounting for all sub and super-horizon effects. The transport method we utilise means only coupled differential equations need to be solved, and the implementation presented here combin…
I consider the generic model independent predictions of the theory of quantum cosmological perturbations. To describe the stage of cosmic inflation, where these perturbations are amplified, the hydrodynamical approch is used. The inflationary stage is completely characterized by the deviation of the equation of state from cosmological constant which is a smooth function of the number of e-folds until the end of inflation. It is shown that in this case the spectral index should deviate from the flat one at least by 3 percent irrespective of any particular scenario. Given the value of the spectr…
We extend previous classifications of inflationary models by means of their behaviour at large-N, where N is the number of e-foldings. In addition to the perturbative 1/N case, whose slow-roll parameters fall off as powers of 1/N, we introduce the constant, non-perturbative and logarithmic classes. This covers the large majority of inflationary models. Furthermore, we calculate the running of the spectral tilt for all these classes. Remarkably, we find that the tilt's runnings essentially cluster around the permil level. We comment on the implications for future experiments.
The dynamical evolution of the refractive index of the tensor modes of the geometry produces a specific class of power spectra characterized by a blue (i.e. slightly increasing) slope which is directly determined by the competition of the slow-roll parameter and of the rate of variation of the refractive index. Throughout the conventional stages of the inflationary and post-inflationary evolution, the microwave background anisotropies measurements, the pulsar timing limits and the big-bang nucleosythesis constraints set stringent bounds on the refractive index and on its rate of variation. Wit…
We show that the spectral energy distribution of relic gravitons mildly increases for frequencies smaller than the $μ$Hz and then flattens out whenever the refractive index of the tensor modes is dynamical during a quasi-de Sitter stage of expansion. For a conventional thermal history the high-frequency plateau ranges between the mHz and the audio band but it is supplemented by a spike in the GHz region if a stiff post-inflationary phase precedes the standard radiation-dominated epoch. Even though the slope is blue at intermediate frequencies, it may become violet in the MHz window. For a vari…
We explore whether multifield inflationary models make unambiguous predictions for fundamental cosmological observables. Focusing on $N$-quadratic inflation, we numerically evaluate the full perturbation equations for models with 2, 3, and $\mathcal{O}(100)$ fields, using several distinct methods for specifying the initial values of the background fields. All scenarios are highly predictive, with the probability distribution functions of the cosmological observables becoming more sharply peaked as $N$ increases. For $N=100$ fields, 95% of our Monte Carlo samples fall in the ranges $n_s \in (0.…
Reheating and Inflationary dynamics driven by an inverse tangent potential
本文研究了由反切线势驱动的暴胀与再加热动力学，通过分析普朗克和ACT数据，验证了该势作为替代标准暴胀势的可行性。
In light of the recent Planck 2015 results for the measurement of the CMB anisotropy, we study simple inflationary models in the context of the Gauss-Bonnet brane-world cosmology. The brane-world cosmological effect modifies the power spectra of scalar and tensor perturbations generated by inflation and causes a dramatic change for the inflationary predictions of the spectral index ($n_s$) and the tensor-to-scalar ratio ($r$) from those obtained in the standard cosmology. In particular, the power spectrum of tensor perturbation is suppressed due to the Gauss-Bonnet brane-world cosmological eff…
The Parameter Dependence of $\mathbf{n_{s}}$ and $\mathbf{r}$ of the Scalar Power Spectrum during Single-Field Slow-Roll Inflation: A Comparative Study of Inflationary Potentials
本研究聚焦单场慢滚暴胀的标量功率谱参数，推导谱指数与张标比，对比四类暴胀模型的起源与数学形式，并通过Planck数据检验模型结果、分析偏差。
Heavy Field Effects on Inflationary Models in Light of ACT Data
本文探讨了重场在膨胀模型中通过增加$ n_s $和$ α_s $与ACT数据的兼容性，扩展了传统膨胀模型并提出了具体模型实现。
Inflationary interpretation of the stochastic gravitational wave background signal detected by pulsar timing array experiments
本研究检验脉冲星计时阵探测的随机引力波背景信号的暴胀起源可能性，发现其需极蓝张量谱与极低再加热温度，现有暴胀模型难以满足，火劫模型振幅不足，同时给出相关联合后验分布的二元高斯近似表达式。
Approximate reconstruction of inflationary potential with ACT observations
针对ACT最新标量谱指数测量与传统暴胀模型的张力，通过特定参数化方法重建出KKLT暴胀势，该势在慢滚近似下可作为与观测一致的广泛暴胀场景的有效近似。
One of the most important achievements of inflationary cosmology is to predict a departure from scale invariance of the power spectrum for scalar curvature cosmological fluctuations. This tilt is understood as a consequence of a quasi de Sitter classical equation of state describing the inflationary dark energy dominated era. Here, following previous work, we find a departure of scale invariance for the quantum Fisher information associated to de Sitter vacuum for scalar quantum spectator modes. This gives rise to a purely quantum cosmological tilt with a well defined dependence on energy scal…
We provide an update on five relatively well motivated inflationary models in which the inflaton is a Standard Model singlet scalar field. These include i) the textbook quadratic and quartic potential models but with additional couplings of the inflaton to fermions and bosons, which enable reheating and also modify the naive predictions for the scalar spectral index $n_s$ and $r$, ii) models with Higgs and Coleman-Weinberg potentials, and finally iii) a quartic potential model with non-minimal coupling of the inflaton to gravity. For $n_s$ values close to 0.96, as determined by the WMAP9 and P…
We consider first order perturbation theory for a non-minimally coupled inflaton field without assuming an adiabatic equation of state. In general perturbations in non-minimally coupled theory may be non-adiabatic. However under the slow-roll assumptions the perturbation theory may look like adiabatic one. We show in the frame-work of perturbation theory, that our results of spectral index and bound on no-minimal coupling parameter agree with the results obtained using the adiabatic equation of state by the earlier authors.
Reheating phase of inflationary Universe can be modeled by parameters $T_{\text{reh}}$, $\bar{w}_{\text{reh}}$ and $N_{\text{reh}}$, which can be constrained by the scalar spectral amplitude $A_{s}$ and the scalar spectral index $n_{s}$. On the other hand the low multipole anomalies in the CMB can be modeled by suitable features in the inflaton potential. We show that the parameters of these features in the inflaton potential provide additional constraints on the reheating parameters. For several single field models we find that the reheating parameters are substantially more constrained by th…
In this letter we shall demonstrate that the viable $F(R)$ gravities can be classified mainly into two classes of inflationary attractors, either the $R^2$ attractors or the $α$-attractors. To show this, we shall derive the most general relation between the tensor-to-scalar ratio $r$ and the spectral index of primordial curvature perturbations $n_s$, namely the $r-n_s$ relation, by assuming that the slow-roll condition constrains the values of the slow-roll indices. As we show, the relation between the tensor-to-scalar ratio and the spectral index of the primordial curvature perturbations has …
In this work we solved the equation of scalar and tensor perturbations for the generalized Starobinsky inflationary model using the improved uniform approximation method and the phase-integral method up to third-order in deviation. We compare our results with the numerical integration. We have obtained that both semiclassical methods reproduce the scalar power spectra $P_{S,T}$, the scalar spectral index $n_S$, and the tensor-to-scalar ratio $r$. Also we present our results in the $(n_S,r)$ plane.
A rigorous constraint analysis on cosmic inflation entails several probes which collectively survey an extensive range of energy scales. We complement the cosmic microwave background data with an updated compilation of the cosmic abundance limits of primordial black holes, with which we infer stringent constraints on the runnings of the scalar spectral index. These constraints are notably improved by further including imminent measurements of the cosmic microwave background spectral distortions, clearly illustrating the effectiveness of joint large-scale and small-scale cosmological surveys.
Motivated by the recent CMB $B$-mode observation announced by the BICEP2 collaboration, we study simple inflationary models in the Randall-Sundrum brane-world cosmology. Brane-world cosmological effects alter the inflationary predictions of the spectral index ($n_s$) and the tensor-to-scalar ratio ($r$) from those obtained in the standard cosmology. In particular, the tensor-to-scalar ratio is enhanced in the presence of the 5th dimension, and simple inflationary models which predict small $r$ values in the standard cosmology can yield $r$ values being compatible with the BICEP2 result, $r=0.2…
An inflationary model in the framework of noncommutative space-time may generate a nontrivial running of the scalar spectral index, but usually induces a large tensor-to-scalar ratio simultaneously. With the latest observational data from the Planck mission, we reexamine the inflationary scenarios in a noncommutative space-time. We find that either the running of the spectral index is tiny compared with the recent observational result, or the tensor-to-scalar ratio is too large to allow a sufficient number of $e$-folds. As examples, we show that the chaotic and power-law inflation models with …
If the refractive index of the relic gravitons increases during a conventional stage of inflationary evolution the spectral energy density is blue at intermediate frequencies above the fHz and then flattens out after a knee that is typically smaller than the mHz. We investigate here the conditions leading to a sufficiently large spectral energy density in the nHz range where some peculiar signatures observed with the pulsar timing arrays have been recently attributed to cosmic gravitons. If these potential evidences are combined with the most recent bounds provided by wide-band interferometers…
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "delta N" Tay…
In the lights of current BICEP2 observations accompanied with the PLANCK satellite results, it has been observed that the simple single field chaotic inflationary models provide a good agreement with their spectral index n_s and large tensor-to-scalar ratio r (0.15 <r <0.26). To explore the other simple models, we consider the fractional-chaotic inflationary potentials of the form V_0 phi^(a/b) where a and b are relatively prime. We show that such kind of inflaton potentials can be realized elegantly in the supergravity framework with generalized shift symmetry and a nature bound a/b < 4 for c…
In the light of the Planck 2015 results, we update simple inflationary models based on the quadratic, quartic, Higgs and Coleman-Weinberg potentials in the context of the Randall-Sundrum brane-world cosmology. Brane-world cosmological effect alters the inflationary predictions of the spectral index ($n_s$) and the tensor-to-scalar ratio ($r$) from those obtained in the standard cosmology. In particular, the tensor-to-scalar ratio is enhanced in the presence of the 5th dimension. In order to maintain the consistency with the Planck 2015 results for the inflationary predictions in the standard c…
We investigate the dependency of Higgs inflation on the non-renormalisable matching between the low energy Standard Model limit and the inflationary regime at high energies. We show that for the top mass range $m_t \gtrsim 171.8$ GeV the scenario robustly predicts the spectral index $n_s \simeq 0.97$ and the tensor-to-scalar ratio $r\simeq 0.003$. The matching is however non-trivial, even the best-fit values $m_h=125.09$ GeV and $m_t=173.21$ GeV require a jump $δλ\sim 0.01$ in the Higgs coupling below the inflationary scale. For $m_t\lesssim 171.8$ GeV, the matching may generate a feature in t…
We explore a fluid description of the inflationary universe. In particular, we investigate a fluid model in which the equation of state (EoS) for a fluid includes bulk viscosity. We find that the three observables of inflationary cosmology: the spectral index of the curvature perturbations, the tensor-to-scalar ratio of the density perturbations, and the running of the spectral index, can be consistent with the recent Planck results. We also reconstruct the explicit EoS for a fluid from the spectral index of the curvature perturbations compatible with the Planck analysis. In the reconstructed …
The temperature at the end of reheating and the length of this cosmological phase can be bound to the inflationary observables if one considers the cosmological evolution from the time of Hubble crossing until today. There are many examples in the literature where it is made for single-field inflationary models and a constant equation of state during reheating. We adopt two simple varying equation of state parameters during reheating, combine the allowed range of the reheating parameters with the observational limits of the scalar perturbations spectral index and compare the constraints of som…
For the inflaton field we determine a new exact solution by using the Lie symmetry analysis. Specifically, we construct a second-order differential master equation for arbitrary scalar field potential by assuming that the spectral index for the density perturbations $n_{s}$ and the scalar to tensor ratio $r$ are related as $n_{s}-1=h\left( r\right) $. Function $h\left( r\right) $ is classified according to the admitted Lie symmetries for the master equation. The possible admitted Lie symmetries form the $A_{2}$, $A_{3,2}$, $A_{3,3}$ and $sl\left( 3,R\right) $ Lie algebras. The new inflationary…
A new approach is given for the implementation of boundary conditions used in solving the Mukhanov-Sasaki equation in the context of inflation. The familiar quantization procedure is reviewed, along with a discussion of where one might expect deviations from the standard approach to arise. The proposed method introduces a (model dependent) fitting function for the z"/z and a"/a terms in the Mukhanov-Sasaki equation for scalar and tensor modes, as well as imposes the boundary conditions at a finite conformal time. As an example, we employ a fitting function, and compute the spectral index, alon…
CMB Constraints on Pre-Inflationary Axion Dark Matter Isocurvature
利用Planck、ACT和SPT的最新CMB数据，更新了对暴胀前轴子模型中具有不同谱指数的冷暗物质等曲率扰动的约束，发现联合数据集对谱指数的约束略有改善，但对固定谱指数的等曲率振幅约束未加强。
Running of the spectral index: Reconciling the CMB with the Lyman-$α$ Forest
结合CMB和Lyman-α森林数据，约束谱指数运行α_s和β_s，发现非零运行偏好，并展示局部特征暴胀势可解释尺度依赖。
We investigate the role of bulk viscous pressure on the warm inflationary modified Chaplygin gas in brane-world framework in the presence of standard scalar field. We assume the intermediate inflationary scenario in strong dissipative regime and constructed the inflaton, potential, entropy density, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor-to-scalar ratio. We develop various trajectories such as $n_s - N$, $n_s - r$ and $n_s - α_s$ (where $n_s$ is the spectral index, $α_s$ is the running of spectral index, $N$ is the number of e-folds and $r$ is te…
Gravitational reheating formulas and bounds in oscillating backgrounds II: Constraints on the spectral index and gravitational dark matter production
本文建立了引力重加热温度与标量扰动谱指数的关系以约束暴胀模型，并证明了在暗物质粒子与重加热粒子质量相关时，引力重加热可作为产生暗物质的可行机制。
Returning Back to Mukhanov Parametrization of Inflationary Equation of State
结合Planck 2018数据与Hamilton-Jacobi形式重新审视暴胀状态方程的Mukhanov参数化，发现现有观测值可有效约束模型参数，并指出未来CMB任务对引力波的探测结果将决定该参数化的存亡。
We address the problem of determining inflationary characteristics in a model independent way. We start from a recently proposed equation which allows to accurately calculate the value of the inflaton at horizon crossing $ϕ_k$. We then use an equivalent form of this equation to write a formula that relates the number of e-folds from horizon crossing to the pivot scale $N_{ke}+N_{ep}$ with the tensor-to-scalar index $r$, hence a general bound for $N_{ke}+N_{ep}$ follows. $N_{ke}$ is the number of e-folds from the scale factor $a_k$ during inflation to the end of inflation at $a_e$ and $N_{ep}$ …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。