Chiu Man Ho, Thomas W. Kephart
We consider a 4+N dimensional Einstein gravity coupled to a non-linear sigma model. This theory admits a solution in which the N extra dimensions contract exponentially while the ordinary space expand exponentially. Physically, the non-linear sigma fields induce the dynamical compactification of the extra dimensions, which in turn drives inflation. No inflatons are required.
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Whichever could be the real theory of gravitation, the corresponding low-energy effective lagrangian will probably contain higher derivative terms. In this work we study the general conditions on those terms in order to produce enough inflation to solve some of the problems of the standard Friedmann-Robertson-Walker cosmology in absence of any inflaton field. We apply our results to some particular scenarios where higher derivative terms appear in the effective lagrangian for gravity like those coming from graviton (two)-loops or integrating out ordinary matter (like the one present in the Sta…
We point out that a model with scalar fields with a large nonminimal coupling to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear sigma model (NLSM). With the inclusion of not only the scalar fields but also the conformal mode of the metric, our definition of the target space of the NLSM is invariant under the frame transformation. We show that the $σ$-meson that linearizes this NLSM to be a linear sigma model (LSM) corresponds to the scalaron, the degree of freedom associated to the $R^2$ term in the Jordan frame. We demonstrate that quantum corrections inevitably ind…
We consider the renormalization group(RG) improved inflaton potential in unitarized Higgs inflation where the original Higgs inflation is unitarized by the addition of a real singlet scalar of sigma-model type. The sigma field coupling to the Higgs, which is introduced to reproduce a large non-minimal coupling of the Higgs below the sigma scalar threshold, also improves the Standard Model vacuum stability due to the RG running. Furthermore, the same sigma field coupling determines the reheating temperature or the number of efoldings. Considering the uncertainties in the number of efoldings in …
We consider the non-supersymmetric models of chaotic (driven by a quadratic potential) and hybrid inflation, taking into account the minimal possible radiative corrections to the inflationary potential. We show that two simple coupling functions f(sigma) (with a parameter ck involved) between the inflaton field, sigma, and the Ricci scalar curvature ensure, for sub-Planckian values of the inflaton field, observationally acceptable values for the spectral index, ns, and sufficient reheating after inflation. In the case of chaotic inflation we consider two models with large ck's resulting to ns=…
We consider a simple extension of the Standard Model Higgs inflation with one new real scalar field which preserves unitarity up to the Planck scale. The new scalar field (called sigma) completes in the ultraviolet the theory of Higgs inflation by linearizing the Higgs kinetic term in the Einstein frame, just as the non-linear sigma model is unitarized into its linear version. The unitarity cutoff of the effective theory, obtained by integrating out the sigma field, varies with the background value of the Higgs field. In our setup, both the Higgs field and the sigma field participate in the in…
We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the $R^2$ term and the tracker…
We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu-Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make the Kähler potential of the NLSM invariant in supergravity. This field must have a shift symm…
The angular power spectrum of the cosmic microwave background temperature anisotropy observed by WMAP has an anomalous dip at l~20 and bump at l~40. One explanation for this structure is the presence of features in the primordial curvature power spectrum, possibly caused by a step in the inflationary potential. The detection of these features is only marginally significant from temperature data alone. However, the inflationary feature hypothesis predicts a specific shape for the E-mode polarization power spectrum with a structure similar to that observed in temperature at l~20-40. Measurement …
In this paper we address the question how to discriminate whether the gauged isometry group G_Sigma of the Kahler manifold Sigma that produces a D-type inflaton potential in a Minimal Supergravity Model is elliptic, hyperbolic or parabolic. We show that the classification of isometries of symmetric cosets can be extended to non symmetric Sigma.s if these manifolds satisfy additional mathematical restrictions. The classification criteria established in the mathematical literature are coherent with simple criteria formulated in terms of the asymptotic behavior of the Kahler potential K(C) = 2 J(…
We explore constraints on various forms for the effective potential during inflation based upon a statistical comparison between inflation-generated fluctuations in the cosmic microwave background temperature and the COBE DMR results. Fits to the COBE 53A+B x 90A+B angular correlation function are obtained using simple analytic forms for the effective potential in chaotic inflation models. Not surprisingly, these fits are optimized for a nearly scale-free fluctuation power spectrum. However, from the chi^2 distribution for the fits we can set upper limits of n le 1.2 and n le 7 at the 1 sigma …
We identify models of supersymmetric hybrid inflation in which the tensor-to-scalar ratio, a canonical measure of gravity waves produced during inflation, can be as large as 0.03 or so, which will be tested by the Planck satellite experiment. The scalar spectral index lies within the WMAP one sigma bounds, while $|d n_s / d\ln k| \lesssim 0.01$.
The small-scale CMB temperature we observe on the sky is modulated by perturbations that were super-horizon at recombination, giving differential focussing and lensing that generate a non-zero bispectrum even for single-field inflation where local physics is identical. Understanding this signal is important for primordial non-Gaussianity studies and also parameter constraints from the CMB lensing bispectrum signal. Because of cancellations individual effects can appear larger or smaller than they are in total, so a full analysis may be required to avoid biases. I relate angular scales on the s…
ACT-Inspired Kaehler-Based Inflationary Attractors
本研究构建了与ACT观测结果相符的新型Kaehler暴胀吸引子，结合混沌势得到与数据一致且参数依赖性弱的可观测量，还给出超引力实现，具备亚普朗克暴胀、大张量标量比等优势。
From N- to (p,N)- Inflationary Attractors in view of ACT
本文探讨了两种分数Kaehler势在暴胀路径上简化为N/(1-ϕ^{q_M})^p形式的机制，通过非线性σ模型与混沌暴胀势结合，确定了(p,N)-暴胀吸引子，其观测特征与ACT DR6数据兼容。
We present a general polynomial chaotic inflation model in supergravity, for which the predicted spectral index and tensor-to-scalar ratio can lie within the 1 sigma region allowed by the Planck results. Most importantly, the predicted tensor-to-scalar ratio is large enough to be probed in the on-going and future B-mode experiments. We study the inflaton dynamics and the subsequent reheating process in a couple of specific examples. The non-thermal gravitino production from the inflaton decay can be suppressed in a case with a discrete Z_2 symmetry. We find that the reheating temperature can b…
We present here the effective theory of inflation `a la Ginsburg-Landau in which the inflaton potential is a polynomial. The slow-roll expansion becomes a systematic 1/N expansion where N ~ 60. The spectral index and the ratio of tensor/scalar fluctuations are n_s - 1 = O(1/N), r = O(1/N) while the running turns to be d n_s/d \ln k = O(1/N^2) and can be neglected. The energy scale of inflation M ~ 0.7 10^{16} GeV is completely determined by the amplitude of the scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo Markov Chains (MCMC) analysis of the available CMB+LSS d…
Cosmic Inflation at the Crossroads
通过在近三百个单场慢滚暴胀模型中进行贝叶斯模型比较，基于三阶慢滚原初功率谱分析最新宇宙微波背景与重子声波振荡数据，发现超过40%的模型被强烈反对，约20%受支持，并证实了再加热运动学对模型预测精度的关键影响。
Single field inflationary models with a non-minimal kinetic term (also called k-inflationary models) can be characterised by the so-called sound flow functions, which complete the usual Hubble flow hierarchy. These parameters appear in the primordial power spectra of cosmological perturbations at leading order and, therefore, affect the resulting Cosmic Microwave Background (CMB) anisotropies. Using the fifth year Wilkinson Microwave Anisotropy Probe (WMAP5) data, we derive the marginalised posterior probability distributions for both the sound and Hubble flow parameters. In contrast to the st…
We follow the evolution of the curvaton on superhorizon scales and check that the spectral tilt of the curvaton perturbations is unchanged as the curvaton becomes non-relativistic. Both inflation and pre-big bang cosmology can be treated since the curvaton mechanism within the two scenarios works the same way. We also discuss the amplitude of the density perturbations, which leads to some interesting constrains on the pre-big bang scenario. It is shown that within a SL(3,R) non-linear sigma model one of the three axions has the right coupling to the dilaton and moduli to yield a flat spectrum …
Using a large N sigma model approximation we explicitly calculate the power spectrum of gravitational waves arising from a global phase transition in the early universe and we confirm that it is scale invariant, implying an observation of such a spectrum may not be a unique feature of inflation. Moreover, the predicted amplitude can be over 3 orders of magnitude larger than the naive dimensional estimate, implying that even a transition that occurs after inflation may dominate in Cosmic Microwave Background polarization or other gravity wave signals.
We consider the inflation model of a singlet scalar field (sigma field) with both quadratic and linear non-minimal couplings where unitarity is ensured up to the Planck scale. We assume that a $Z_2$ symmetry for the sigma field is respected by the scalar potential in Jordan frame but it is broken explicitly by the linear non-minimal coupling due to quantum gravity. We discuss the impacts of the linear non-minimal coupling on various dynamics from inflation to low energy, such as a sizable tensor-to-scalar ratio, a novel reheating process with quartic potential dominance, and suppressed physica…
We explore the role of non-Gaussian fluctuations in primordial black hole (PBH) formation and show that the standard Gaussian assumption, used in all PBH formation papers to date, is not justified. Since large spikes in power are usually associated with flat regions of the inflaton potential, quantum fluctuations become more important in the field dynamics, leading to mode-mode coupling and non-Gaussian statistics. Moreover, PBH production requires several sigma (rare) fluctuations in order to prevent premature matter dominance of the universe, so we are necessarily concerned with distribution…
We study the cosmological evolution of a type-0 string theory by employing non-criticality, which may be induced by fluctuations of the D3 brane worlds. We check the consistency of the approach to O(alpha ') in the corresponding sigma-model. The ten-dimensional theory is reduced to an effective four-dimensional model, with only time dependent fields. We show that the four-dimensional universe has an inflationary phase and graceful exit from it, while the other extra dimensions are stabilized to a constant value, with the fifth dimension much larger than the others. We pay particular attention …
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