1,063 research outputs found
Cosmological parameter estimation and the spectral index from inflation
Accurate estimation of cosmological parameters from microwave background
anisotropies requires high-accuracy understanding of the cosmological model.
Normally, a power-law spectrum of density perturbations is assumed, in which
case the spectral index can be measured to around using
microwave anisotropy satellites such as MAP and Planck. However, inflationary
models generically predict that the spectral index of the density
perturbation spectrum will be scale-dependent. We carry out a detailed
investigation of the measurability of this scale dependence by Planck,
including the influence of polarization on the parameter estimation. We also
estimate the increase in the uncertainty in all other parameters if the scale
dependence has to be included. This increase applies even if the scale
dependence is too small to be measured unless it is assumed absent, but is
shown to be a small effect. We study the implications for inflation models,
beginning with a brief examination of the generic slow-roll inflation
situation, and then move to a detailed examination of a recently-devised hybrid
inflation model for which the scale dependence of may be observable.Comment: 6 pages LaTeX file with one figure incorporated (uses mn.sty and
epsf). Important modifications to result
Higher order corrections to primordial spectra from cosmological inflation
We calculate power spectra of cosmological perturbations at high accuracy for
two classes of inflation models. We classify the models according to the
behaviour of the Hubble distance during inflation. Our approximation works if
the Hubble distance can be approximated either to be a constant or to grow
linearly with cosmic time. Many popular inflationary models can be described in
this way, e.g., chaotic inflation with a monomial potential, power-law
inflation and inflation at a maximum. Our scheme of approximation does not rely
on a slow-roll expansion. Thus we can make accurate predictions for some of the
models with large slow-roll parameters.Comment: 13 pages, 1 figure; section on consistency relations of inflation
added; accepted by Physics Letters
Distribution of particles which produces a "smart" material
If is the scattering amplitude, corresponding to a
potential , where is a bounded domain, and
is the incident plane wave, then we call the radiation
pattern the function , where the unit vector
, the incident direction, is fixed, and , the wavenumber, is
fixed. It is shown that any function , where is the
unit sphere in , can be approximated with any desired accuracy by a
radiation pattern: , where
is an arbitrary small fixed number. The potential ,
corresponding to , depends on and , and can be
calculated analytically. There is a one-to-one correspondence between the above
potential and the density of the number of small acoustically soft particles
, , distributed in an a priori given bounded
domain . The geometrical shape of a small particle is
arbitrary, the boundary of is Lipschitz uniformly with respect to
. The wave number and the direction of the incident upon
plane wave are fixed.It is shown that a suitable distribution of the above
particles in can produce the scattering amplitude ,
, at a fixed , arbitrarily close in the norm of
to an arbitrary given scattering amplitude
, corresponding to a real-valued potential .Comment: corrected typo
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