Galaxy merging and number vs. apparent magnitude relation for the universe with a time-decaying cosmological term

¹ Department of Physics, Tokyo University of Science, Shinjuku-ku, Tokyo, 162-8601, Japan e-mail: zen_komiya@ybb.ne.jp; kawabata@rs.kagu.tus.ac.jp
² Grid Technology Research Center, National Institute of Advanced Industrial Science and Technology Ibaraki 305-8568, Japan

Received: 25 October 2005
Accepted: 13 December 2005

Abstract

Aims. An attempt is made to constrain the values of the cosmological parameters together with the galaxy merging factor η on the basis of a comparison between the observed galaxy number counts vs. their apparent magnitudes relation ( relation) with those theoretically constructed for the universe with a time-decaying cosmological term Λ. Methods. We assume that the galaxy number density evolution can be represented sufficiently well by a function of the redshift z of the form . Three variations of the cosmological term with time τ are considered, (1) , (2)  with a being the scale factor, and (3)  with H the Hubble parameter. The optimum ranges for the decaying parameters (l, m, and n), the density parameters  and , as well as T_mg (the timescale for the merger of a pair of galaxies) and the redshift z_mg for the first onset of galaxy merger are sought based on statistical analysis using likelihood functions given by  evaluations. Results. In the case of the type I models, for instance, we find that , T_mg = 0.3 Gyr, , and , from which a cosmic age of  Gyr results. These model parameters lead to . As a consistency check, we have also carried out computations of the cosmic microwave background radiation (CMBR) spectrum, and have made comparisons with WMAP measurements. We found that it is necessary to somewhat modify the parameter values obtained above on account of the high sensitivity of η to the value of T_mg. The final model that was found to account for both the observed  relation and the WMAP measurements of the CMBR spectrum is as follows: ,  Gyr, , , . The age of this model universe is 14.6 Gyr, which is still sufficiently high to cope with the “new” cosmic age problem.