The Effect of Varying Sound Velocity on Primordial Curvature Perturbations
Masahiro Nakashima
1
2
Ryo Saito
1
2
Yu-ichi Takamizu
1
Jun'ichi Yokoyama
0
1
0
Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo
, Kashiwa 277-8582,
Japan
1
Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo
,
Tokyo 113-0033, Japan
2
Department of Physics, Graduate School of Science, The University of Tokyo
,
Tokyo 113-0033, Japan
We study the effects of sudden change in the sound velocity on primordial curvature perturbation spectrum in inflationary cosmology, assuming that the background evolution satisfies the slow-roll condition throughout. It is found that the power spectrum acquires oscillating features which are determined by the ratio of the sound speed before and after the transition and the wavenumeber which crosses the sound horizon at the transition, and their analytic expression is given. In some values of those parameters, the oscillating primordial power spectrum can better fit the observed Cosmic Microwave Background temperature anisotropy power spectrum than the simple power-law power spectrum, although introduction of such a new degree of freedom is not justified in the context of Akaike's Information Criterion.
-
Standard inflationary cosmology1)3) predicts nearly scale-invariant power
spectrum of the primordial perturbation.4)7) Such a power-law like perturbation
spectrum 2
kns1, where is the comoving curvature perturbation and ns is the
scalar spectral index with ns 1, has been preferred also from a number of
obserbations.8) If we look into the detailed structure of the Cosmic Microwave Background
(CMB) temperature anisotropy, some hints of small deviations from the simplest
form of the curvature perturbation power spectrum show up. Among those,
anomalously low values of the quadrupole moment or several sharp glitches in the large
scale WMAP data corresponing to 20 40 are famous and most intensively
studied.9) Furthermore, several groups have reported strong evidence of the
deviation from a simple power-law type power spectrum by reconstructing the primordial
power spectrum from the WMAP data.10)19) In particular, Ichiki et al.20), 21) claim
that they found an oscillatory modulation localized around the comoving
wavenumber k 0.009[Mpc1] ( 120) in the power spectrum at 99.995% confidence level.
Theoretical calculation for the power spectrum has been also sophisticated
recently and some inflation models based on a realistic high-energy physics can generate
peculiar features on the curvature perturbation. Those include the so-called
TransPlanckian effect,22)24) particle production due to the coupling between the inflaton
and another scalar filed,25)27) temporal violation of the slow-rolling of the inflaton
field,28)35) and some other models.36), 37) To go further into the accurate
cosmology, it is crucial to study further the details of the primordial perturbations. This
leads us to the detailed structure of the inflaton Lagrangian or the true high-energy
physics that has been realized in our Universe.
In this paper, we concentrate on the role of the sound velocity, which is defined
as the propagating speed of the linear perturbation in the next section. In some
highenergy physics theories, there appear non-canonical kinetic terms in the Lagrangian
and in that case the sound velocity deviates from unity.38), 39) Furthermore, if those
kinetic terms of the inflaton field couple to some time-dependent variables which can
be seen, for example, in DBI inflation scenario,40) the values of the sound velocity
can change during inflation.41)43) Then we have to consider the possibility of some
non-trivial dynamics of the perturbation. As a result, new degrees of freedom such
as the sound velocity may be observed in the CMB temperature fluctuation and be
tested in the future high-precision CMB observations such as PLANCK or CMBpol.
This paper is organized as follows. In the next section, we comment on the
background evolution in our scenario and introduce the sound velocity. In 3, the basic
variables and its evolution equation for the curvature perturbation are described.
Then we consider the particular types of the variation of the sound velocity. The
first type is a step-like function, which is discussed in 4, and the second type is a
top-hat type function, which we will study in 5. The last section is devoted to a
summury and discussion.
2. Background assumption and sound velocity
In the standard single inflaton field with a canonical kinetic term, the sound
velocity cs defined by the propagation speed of linear perturbation has the value
equal to the speed of light, namely, cs = 1. This is easily checked by considering the
action of the canonical inflaton field,
S =
R + X + V () , X = 12 g,
the situation changes completely. In this action, expanding around FRW metric up
where R denote the Einstein-Hilbert action and we set the reduced Planck scale
to unity (8G = 1). Expanding the action aro (...truncated)