The Effect of Varying Sound Velocity on Primordial Curvature Perturbations

Progress of Theoretical Physics, May 2011

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.

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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)


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Masahiro Nakashima, Ryo Saito, Yu-ichi Takamizu, Jun'ichi Yokoyama. The Effect of Varying Sound Velocity on Primordial Curvature Perturbations, Progress of Theoretical Physics, 2011, pp. 1035-1052, 125/5, DOI: 10.1143/PTP.125.1035