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On the Stewart-Lyth Inverse Problem  [PDF]
Eloy Ayón-Beato,Alberto García,Ricardo Mansilla,César A. Terrero-Escalante
Physics , 2000,
Abstract: In this paper the Stewart-Lyth inverse problem is rewritten using the comoving scales as the basic parameter. It is shown that some information on the inflaton potential can be obtained from observations taking into account only the scalar power spectrum.
Stewart-Lyth Inverse Problem  [PDF]
Eloy Ayón-Beato,Alberto García,Ricardo Mansilla,César A. Terrero-Escalante
Mathematics , 2000, DOI: 10.1103/PhysRevD.62.103513
Abstract: In this paper the Stewart-Lyth inverse problem is introduced. It consists of solving two non-linear differential equations for the first slow-roll parameter and finding the inflaton potential. The equations are derived from the Stewart--Lyth equations for the scalar and tensorial perturbations produced during the inflationary period. The geometry of the phase planes transverse to the trajectories is analyzed, and conclusions about the possible behaviour for general solutions are drawn.
Evading Lyth bound in models of quintessential inflation  [PDF]
Md. Wali Hossain,R. Myrzakulov,M. Sami,Emmanuel N. Saridakis
Physics , 2014, DOI: 10.1016/j.physletb.2014.08.051
Abstract: Quintessential inflation refers to an attempt to unify inflation and late-time cosmic acceleration using a single scalar field. In this letter we consider two different classes of quintessential inflation, one of which is based upon a Lagrangian with non-canonical kinetic term $k^2(\phi)\partial^\mu \phi \partial_\mu \phi$ and a steep exponential potential while the second class uses the concept of steep brane world inflation. We show that in both cases the Lyth bound can be evaded, despite the large tensor-to-scalar ratio of perturbations. The post-inflationary dynamics is consistent with nucleosynthesis constraint in these cases.
The Lyth Bound of Inflation with a Tilt  [PDF]
Juan Garcia-Bellido,Diederik Roest,Marco Scalisi,Ivonne Zavala
Physics , 2014, DOI: 10.1103/PhysRevD.90.123539
Abstract: We provide strong evidence for universality of the inflationary field range: given an accurate measurement of $(n_s,r)$, one can infer $\Delta \phi$ in a model-independent way in the sub-Planckian regime for a range of universality classes of inflationary models. Both the tensor-to-scalar ratio as well as the spectral tilt are essential for the field range. Given the Planck constraints on $n_s$, the Lyth bound is strengthened by two orders of magnitude: whereas the original bound gives a sub-Planckian field range for $r \lesssim 2 \cdot 10^{-3}$, we find that $n=0.96$ brings this down to $r \lesssim 2 \cdot 10^{-5}$.
Gauge Fields and Inflation: Chiral Gravitational Waves, Fluctuations and the Lyth Bound  [PDF]
Peter Adshead,Emil Martinec,Mark Wyman
Physics , 2013, DOI: 10.1103/PhysRevD.88.021302
Abstract: Models of inflation involving non-Abelian gauge field backgrounds can produce gravitational waves at an observable level with a preferred handedness. This asymmetry comes about because the non-Abelian background generates parity-violation in the action for perturbations. In the specific model we study, Chromo-Natural Inflation, these gravitational waves can be produced at observable levels even when no field makes a super-Planckian field excursion, thus evading a common formulation of the Lyth bound. Unfortunately, when considered in concert with the scalar fluctuations, this chiral enhancement of the gravitational waves makes the model observationally inviable.
Sub-Planckian Two-Field Inflation Consistent with the Lyth Bound  [PDF]
John McDonald
Physics , 2014, DOI: 10.1088/1475-7516/2014/09/027
Abstract: The BICEP2 observation of a large tensor-to-scalar ratio, $r = 0.20^{+0.07}_{-0.05}$, implies that the inflaton $\phi$ in single-field inflation models must satisfy $\phi \sim 10M_{Pl}$ in order to produce sufficient inflation. This is a problem if interaction terms suppressed by the Planck scale impose a bound $\phi \; ^{<}_{\sim} \; M_{Pl}$. Here we consider whether it is possible to have successful sub-Planckian inflation in the case of two-field inflation. The trajectory in field space cannot be radial if the effective single-field inflaton is to satisfy the Lyth bound. By considering a complex field $\Phi$, we show that a near circular but aperiodic modulation of a $|\Phi|^{4}$ potential can reproduce the results of $\phi^2$ chaotic inflation for $n_{s}$ and $r$ while satisfying $|\Phi|\; ^{<}_{\sim} \; 0.01 M_{Pl}$ throughout. More generally, for models based on a $|\Phi|^{4}$ potential, the simplest sub-Planckian models are equivalent to $\phi^{2}$ and $\phi^{4/3}$ chaotic inflation.
Evading the Lyth Bound in Hybrid Natural Inflation  [PDF]
Arthur Hebecker,Sebastian C. Kraus,Alexander Westphal
Physics , 2013, DOI: 10.1103/PhysRevD.88.123506
Abstract: Generically, the gravitational-wave or tensor-mode contribution to the primordial curvature spectrum of inflation is tiny if the field-range of the inflaton is much smaller than the Planck scale. We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models. More specifically, we consider models where an axion-like shift symmetry keeps the inflaton potential flat (up to non-perturbative cosine-shaped modulations), but inflation nevertheless ends in a waterfall-regime, as is typical for hybrid inflation. In such hybrid natural inflation scenarios (examples are provided by Wilson line inflation and fluxbrane inflation), the slow-roll parameter $\epsilon$ can be sizable during an early period (relevant for the CMB spectrum). Subsequently, $\epsilon$ quickly becomes very small before the tachyonic instability eventually terminates the slow roll regime. In this scenario, one naturally generates a considerable tensor-mode contribution in the curvature spectrum, collecting nevertheless the required amount of e-foldings during the final period of inflation. While non-observation of tensors by Planck is certainly not a problem, a discovery in the medium to long term future is realistic.
Inflation and Alternatives with Blue Tensor Spectra  [PDF]
Yi Wang,Wei Xue
Physics , 2014, DOI: 10.1088/1475-7516/2014/10/075
Abstract: We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experiments do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.
On the Lyth bound and single field slow-roll inflation  [PDF]
Gabriel German
Physics , 2014,
Abstract: We take a pragmatic, model independent approach to single field slow-roll inflation by imposing conditions to the slow-roll parameter $\epsilon$ and its derivative $\epsilon^{\prime }.$ To accommodate the recent (large) values of $r$ reported by the BICEP2 collaboration we advocate for a decreasing $\epsilon$ during most part of inflation. However because at $\phi_{\mathrm{H}}$, at which the perturbations are produced, some $50$ $-$ $60$ e-folds before the end of inflation, $\epsilon$ is increasing we thus require that $\epsilon$ develops a maximum for $\phi > \phi_{\mathrm{H}}$ and then decrease to small values where most e-folds are produced. The end of inflation might occur trough a hybrid field and a small $\Delta\phi$ is obtained with a sufficiently thin $\epsilon$ which, however, should not conflict with the curvature of the potential measured by the second slow-roll parameter $\eta$. The conclusion is that under these circumstances $\Delta\phi$ and the spectral index $n_{\mathrm{s}}$ are restricted to narrow windows of values.
Stability analysis of chromo-natural inflation and possible evasion of Lyth's bound  [PDF]
Emanuela Dimastrogiovanni,Marco Peloso
Physics , 2012, DOI: 10.1103/PhysRevD.87.103501
Abstract: We perform the complete stability study of the model of chromo-natural inflation (Adshead and Wyman '12), where, due to its coupling to a SU(2) vector, a pseudo-scalar inflaton chi slowly rolls on a steep potential. As a typical example, one can consider an axion with a sub-Planckian decay constant f. The phenomenology of the model was recently studied (Dimastrogiovanni, Fasiello, and Tolley '12) in the m_g >> H limit, where m_g is the mass of the fluctuations of the vector field, and H the Hubble rate. We show that the inflationary solution is stable for m_g > 2 H, while it otherwise experiences a strong instability due to scalar perturbations in the sub-horizon regime. The tensor perturbations are instead standard, and the vector ones remain perturbatively small. Depending on the parameters, this model can give a gravity wave signal that can be detected in ongoing or forthcoming CMB experiments. This detection can occur even if, during inflation, the inflaton spans an interval of size Delta chi = O (f) which is some orders of magnitude below the Planck scale, evading a well known bound that holds for a free inflaton (Lyth '97).
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