Testing creation cold dark matter cosmology with the radiation temperature–redshift relation

Abstract

The standard $\varLambda \hbox {CDM}$ model can be mimicked at the background and perturbative levels (linear and non-linear) by a class of gravitationally induced particle production cosmology dubbed CCDM cosmology. However, the radiation component in the CCDM model follows a slightly different temperature–redshift T(z)-law which depends on an extra parameter, $\nu _r$, describing the subdominant photon production rate. Here we perform a statistical analysis based on a compilation of 36 recent measurements of T(z) at low and intermediate redshifts. The likelihood of the production rate in CCDM cosmologies is constrained by $\nu _r = 0.024^{+0.026}_{-0.024}$ ($1\sigma$ confidence level), thereby showing that $\varLambda$CDM ($\nu _r=0$) is still compatible with the adopted data sample. Although being hardly differentiated in the dynamic sector (cosmic history and matter fluctuations), the so-called thermal sector (temperature law, abundances of thermal relics and CMB power spectrum) offers a clear possibility for crucial tests confronting $\varLambda$CDM and CCDM cosmologies.

Appendix A: Kinetic Theory and Temperature Law

In this appendix, we use the extended Boltzmann equation for gravitationally particle production, proposed in previous works [58, 71], to get the temperature evolution of the relic radiation.

In a multi-fluid approach, each component has its own equation with its corresponding production rate. The extended Boltzmann equation describing this gravitational, non-collisional (each component evolves freely from the others), process is

$$\begin{aligned} \frac{\partial f_i}{\partial t}-H\left( 1-\frac{\varGamma _i}{3H} \right) p\frac{\partial f_i}{\partial p}=0, \end{aligned}$$

(A1)

where $f_i$ and $\varGamma _i$ are, respectively, the distribution function and the production rate for the i-th component.

For a relativistic quantum gas, the distribution function is [72]

$$\begin{aligned} f=\frac{1}{e^{-\varTheta +\beta E}+\epsilon }, \end{aligned}$$

(A2)

where $\varTheta$ is the relativistic chemical potential, $\beta = 1/T$, where T is the temperature, and $\epsilon =\pm 1$ counts for different quantum statistics.

In the case of a relativistic bosonic gas with creation rate $\varGamma _r$ (CMB radiation), by inserting () into () we obtain (see also [58]):

$$\begin{aligned} \frac{{\dot{\varTheta }}}{{\dot{\beta }}}=E\left[ 1- H \frac{\beta }{{\dot{\beta }}}\left( 1-\frac{\varGamma _r}{3H} \right) \right] , \end{aligned}$$

(A3)

which has the solution ${\dot{\varTheta }}=0$ and

$$\begin{aligned} \frac{\dot{T}_r}{T_r}=-\frac{\dot{a}}{a}+\frac{\varGamma _r}{3}, \end{aligned}$$

(A4)

where a is the scale factor and $\varGamma _r$ stands for the radiation production rate. The above expression is the same as Eq. 15 which was deduced based on the thermodynamic approach. In the limit $\frac{\varGamma _r}{3H}\ll 1$, Eqs.  and are reduced to the usual ones (see equations (3.70) and (3.71) in) [73].