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Register a new userReconstructing a general inflationary action
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If inflation is to be considered in an unbiased way, as possibly originating from one of a wide range of underlying theories, then observations need not be simply applied to reconstructing the inflaton potential, V(phi), or a specific kinetic term, as in DBI inflation, but rather to reconstruct the inflationary action in its entirety. We discuss the constraints that can be placed on a general single field action from measurements of the primordial scalar and tensor fluctuation power spectra and non-Gaussianities. We also present the flow equation formalism for reconstructing a general inflationary Lagrangian, L(X,phi), with X={1/2}partial_muphipartial^muphi, in a general gauge, that reduces to canonical and DBI inflation in the specific gauge partial L/partial X = c_s^{-1}.
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The BICEP2 collaboration has recently released data showing that the scalar-to-tensor ratio $r$ is much larger than expected. The immediate consequence, in the context of $f(R)$ gravity, is that the Starobinsky model of inflation is ruled out since it predicts a value of $r$ much smaller than what is observed. Of course, the BICEP2 data need verification, especially from Planck with which there is some tension, therefore any conclusion seems premature. However, it is interesting to ask what would be the functional form of $f(R)$ in the case when the value of $r$ is different from the one predicted by the Starobinsky model. In this paper, we show how to determine the form of $f(R)$, once the slow-roll parameters are known with some accuracy. The striking result is that, for given values of the scalar spectral index $n_{S}$ and $r$, the effective Lagrangian has the form $f(R)=R^{zeta}$, where $zeta=2-varepsilon$ and $|varepsilon|ll 1$. Therefore, it appears that the inflationary phase of the Universe is best described by a $R^{2}$ theory, with a small deviation that, as we show, can be obtained by quantum corrections.
We carry out a numerical calculation of the bispectrum in generalised trajectories of canonical, single--field inflation. The trajectories are generated in the Hamilton-Jacobi (HJ) formalism based on Hubble Slow Roll (HSR) parameters. The calculation allows generally shape and scale dependent bispectra, or dimensionless $f_{NL}$, in the out-of-slow-roll regime. The distributions of $f_{NL}$ for various shapes and HSR proposals are shown as an example of how this procedure can be used within the context of Monte Carlo exploration of inflationary trajectories. We also show how allowing out-of-slow-roll behaviour can lead to a bispectrum that is relatively large for equilateral shapes.
We demonstrate that the gravity wave background amplitude implies a robust upper bound on the ratio: lambda / H^{-1} < e^60, where lambda is the proper wavelength of fluctuations of interest and H^{-1} is the horizon at the end of inflation. The bound holds as long as the energy density of the universe does not drop faster than radiation subsequent to inflation. This limit implies that the amount of expansion between the time the scales of interest leave the horizon and the end of inflation, denoted by e^N, is also bounded from above, by about e^60 times a factor that involves an integral over the first slow-roll parameter. In other words, the bound on N is model dependent -- we show that for vast classes of slow-roll models, N < 67. The quantities, lambda / H^{-1} or N, play an important role in determining the nature of inflationary scalar and tensor fluctuations. We suggest ways to incorporate the above bounds when confronting inflation models with observations. As an example, this bound solidifies the tension between observations of cosmic microwave background (CMB) anisotropies and chaotic inflation with a phi^4 potential by closing the escape hatch of large N (< 62).
What is the physical origin of dark energy? Could this energy be originated by other fields than the inflaton? In this work we explore the possibility that the expansion of the universe can be driven by a condensate of spinors. These spinors are free of interactions on 5D relativistic vacuum in an extended de Sitter spacetime. The extra coordinate is considered as noncompact. After making a static foliation on the extra coordinate, we obtain an effective 4D (inflationary) de Sitter expansion which describes an inflationary universe. In view of our results we conclude that the condensate of spinors here studied could be an interesting candidate to explain the presence of dark energy in the early universe.
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use $N_f$--quadratic inflation as an illustrative example, finding that the number of $e$-folds $N_*$ between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.
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