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arXiv 0911.3536astro-ph.COgr-qc
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宇宙学红移的运动学分量

The kinematic component of the cosmological redshift

Michał Chodorowski

摘要:

人们普遍认为宇宙学红移不是多普勒频移。然而,Bunn和Hogg最近指出,要正确解决这个问题,必须将一个遥远星系的速度四维矢量传输到观测者的位置。通过沿着来自星系的光子的零测地线进行这样的传输,他们发现宇宙学红移纯粹是运动学的。在这里,我们认为,应该沿着连接银河系和观察者的世界线与恒定宇宙时间超曲面的交点的测地线传输速度四矢量。我们发现输运速度和到达光子的红移之间的关系不是由相对论多普勒公式给出的。相反,对于小的红移,它与众所周知的将红移分解为多普勒(运动学)分量和引力分量的非相对论分解相吻合。我们进行这样的分解任意大的红移,并推导出一个公式的运动学分量的宇宙学红移,适用于任何FLRW宇宙学。特别是,在一个Omega_m = 0.24和Omega_Lambda = 0.76的宇宙中,一个红移为6的类星体,在光子发射到我们今天的时候,其衰退速度v = 0.997c。这可以与v = 0.96c形成对比,如果红移完全是运动学的。因此,对于这种高红移源的衰退速度,早期宇宙减速的影响明显优于相对较近的加速的影响。最后但并非最不重要的是,我们表明,所谓的适当的衰退速度的星系,通常用于宇宙学,实际上是径向分量的星系的四个速度矢量。因此,它们确实可以达到超光速的值,但不应该被视为真实的速度。

英文摘要:

It is widely believed that the cosmological redshift is not a Doppler shift. However, Bunn & Hogg have recently pointed out that to settle properly this problem, one has to transport parallelly the velocity four-vector of a distant galaxy to the observer's position. Performing such a transport along the null geodesic of photons arriving from the galaxy, they found that the cosmological redshift is purely kinematic. Here we argue that one should rather transport the velocity four-vector along the geodesic connecting the points of intersection of the world-lines of the galaxy and the observer with the hypersurface of constant cosmic time. We find that the resulting relation between the transported velocity and the redshift of arriving photons is not given by a relativistic Doppler formula. Instead, for small redshifts it coincides with the well known non-relativistic decomposition of the redshift into a Doppler (kinematic) component and a gravitational one. We perform such a decomposition for arbitrary large redshifts and derive a formula for the kinematic component of the cosmological redshift, valid for any FLRW cosmology. In particular, in a universe with Omega_m = 0.24 and Omega_Lambda = 0.76, a quasar at a redshift 6, at the time of emission of photons reaching us today had the recession velocity v = 0.997c. This can be contrasted with v = 0.96c, had the redshift been entirely kinematic. Thus, for recession velocities of such high-redshift sources, the effect of deceleration of the early Universe clearly prevails over the effect of its relatively recent acceleration. Last but not least, we show that the so-called proper recession velocities of galaxies, commonly used in cosmology, are in fact radial components of the galaxies' four-velocity vectors. As such, they can indeed attain superluminal values, but should not be regarded as real velocities.

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