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Register a new userModified scalar and tensor spectra in spinor driven inflation
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One of the firm predictions of the single-scalar field inflationary cosmology is the consistency relation between the scalar and tensor perturbations. It has been argued that such a relation, if observationally verified, would offer strong support for the idea of inflation. In this letter, we critically analyze the validity of the consistency relation in the context of spinflation. Spinflaton -- a scalar condensate of the Elko field -- has a single scalar degree of freedom and leads to the identical acceleration equation as the single canonical scalar field. We obtain the perturbation equations for the Einstein-Elko system and show that (i) The scalar perturbations are purely adiabatic and speed of the perturbations is identically one. (ii) In the slow-roll limit, the scalar and tensor perturbations are nearly scale-invariant and (iii) Obtain the consistency relations for the scalar and tensor spectra.
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We constrain cosmological models where the primordial perturbations have both an adiabatic and a (possibly correlated) cold dark matter (CDM) or baryon isocurvature component. We use both a phenomenological approach, where the primordial power spectra are parametrized with amplitudes and spectral indices, and a slow-roll two-field inflation approach where slow-roll parameters are used as primary parameters. In the phenomenological case, with CMB data, the upper limit to the CDM isocurvature fraction is alpha<6.4% at k=0.002Mpc^{-1} and 15.4% at k=0.01Mpc^{-1}. The median 95% range for the non-adiabatic contribution to the CMB temperature variance is -0.030<alpha_T<0.049. Including the supernova (or large-scale structure, LSS) data, these limits become: alpha<7.0%, 13.7%, and -0.048<alpha_T< 0.042 (or alpha<10.2%, 16.0%, and -0.071<alpha_T<0.024). The CMB constraint on the tensor-to-scalar ratio, r<0.26 at k=0.01Mpc^{-1}, is not affected by the nonadiabatic modes. In the slow-roll two-field inflation approach, the spectral indices are constrained close to 1. This leads to tighter limits on the isocurvature fraction, with the CMB data alpha<2.6% at k=0.01Mpc^{-1}, but the constraint on alpha_T is not much affected, -0.058<alpha_T<0.045. Including SN (or LSS) data, these limits become: alpha< 3.2% and -0.056<alpha_T<0.030 (or alpha<3.4% and -0.063<alpha_T<-0.008). When all spectral indices are close to each other the isocurvature fraction is somewhat degenerate with the tensor-to-scalar ratio. In addition to the generally correlated models, we study also special cases where the perturbation modes are uncorrelated or fully (anti)correlated. We calculate Bayesian evidences (model probabilities) in 21 different cases for our nonadiabatic models and for the corresponding adiabatic models, and find that in all cases the data support the pure adiabatic model.
The form of the inflationary potential is severely restricted if one requires that it be natural in the technical sense, i.e. terms of unrelated origin are not required to be correlated. We determine the constraints on observables that are implied in such natural inflationary models, in particular on $r$, the ratio of tensor to scalar perturbations. We find that the naturalness constraint does not require $r$ to be lare enough to be detectable by the forthcoming searches for B-mode polarisation in CMB maps. We show also that the value of $r$ is a sensitive discriminator between inflationary models.
We study chaotic inflation in the context of modified gravitational theories. Our analysis covers models based on (i) a field coupling $omega(phi)$ with the kinetic energy $X$ and a nonmimimal coupling $zeta phi^{2} R/2$ with a Ricci scalar $R$, (ii) Brans-Dicke (BD) theories, (iii) Gauss-Bonnet (GB) gravity, and (iv) gravity with a Galileon correction. Dilatonic coupling with the kinetic energy and/or negative nonminimal coupling are shown to lead to compatibility with observations of the Cosmic Microwave Background (CMB) temperature anisotropies for the self-coupling inflaton potential $V(phi)=lambda phi^{4}/4$. BD theory with a quadratic inflaton potential, which covers Starobinskys $f(R)$ model $f(R)=R+R^{2}/(6M^{2})$ with the BD parameter $omega_{BD}=0$, gives rise to a smaller tensor-to-scalar ratio for decreasing $omega_{BD}$. In the presence of a GB term coupled to the field $phi$, we express the scalar/tensor spectral indices $n_{s}$ and $n_{t}$ as well as the tensor-to-scalar ratio $r$ in terms of two slow-roll parameters and place bounds on the strength of the GB coupling from the joint data analysis of WMAP 7yr combined with other observations. We also study the Galileon-like self-interaction $Phi(phi) X squarephi$ with exponential coupling $Phi(phi) propto e^{muphi}$. Using a CMB likelihood analysis we put bounds on the strength of the Galileon coupling and show that the self coupling potential can in fact be made compatible with observations in the presence of the exponential coupling with $mu>0$.
Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified as the expectation value of a quantum field, evolving in a quantum effective potential. The shape of this potential is determined by the underlying tree-level potential, dressed by quantum corrections from the scalar field itself and the metric perturbations. Following [1], we compute the effective scalar field equations and the corrected Friedmann equations to quadratic order in both scalar field, scalar metric and tensor perturbations. We identify the quantum corrections from different sources at leading order in slow-roll, and estimate their magnitude in benchmark models of inflation. We comment on the implications of non-minimal coupling to gravity in this context.
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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