[Paper Review] Cooling in the Universe

S. Rahvar|ArXiv.org|Mar 10, 2006

Earth Systems and Cosmic Evolution2 references3 citations

TL;DR

This paper provides a general relativistic explanation for cosmic cooling by modeling the thermal peculiar velocity of particles in an expanding universe. It shows that particle momentum decreases as $1/a$, leading to energy loss and cooling proportional to $1/a$ for relativistic particles and $1/a^2$ for non-relativistic particles, resolving a pedagogical gap in classical thermodynamic interpretations of cosmic expansion.

ABSTRACT

One of the questions in the cosmology courses is the cooling mechanism of cosmic fluid during it expansion according to classical concepts of the thermodynamics. In this short pedagogical paper, we quote the questions and give a natural approach dealing with this problem by measuring the dispersion velocity of the particles in the cosmic fluid by a comoving observer. We show that the thermal motion of the particles in the cosmic fluid deviates from the Hubble flow and follows the geodesics governed by the gravity of the homogeneous universe. The dynamics of the "thermal peculiar velocity" of the particles leads in an expanding universe, momentum of the particles relax by the inverse of the expansion factor and the result is losing the energy of particles, hence cooling the universe.

Motivation & Objective

• To resolve the pedagogical confusion around cosmic cooling in standard cosmology textbooks.
• To provide a natural general relativistic framework for understanding how particle momentum and energy decrease during cosmic expansion.
• To clarify why the universe cools despite being adiabatic, by focusing on the dynamics of thermal peculiar velocities.
• To derive the scaling of temperature with the scale factor $a$ for both relativistic and non-relativistic fluids.

Proposed method

• Model the cosmic fluid using the Friedmann-Robertson-Walker (FRW) metric with $ds^2 = dt^2 - a^2 dx^2$.
• Apply the geodesic equation in comoving time to describe particle motion in the expanding universe.
• Derive the equation of motion for the comoving spatial coordinate, showing $dx/d\tau \propto a^{-2}$.
• Use the chain rule and the definition of peculiar velocity $v_{\text{pec}} = a \, dx/dt$ to relate $v_{\text{pec}}$ to the scale factor.
• Incorporate relativistic momentum via $p = m_0 v_{\text{pec}} / \sqrt{1 - v_{\text{pec}}^2}$ to obtain $p \propto 1/a$.
• Relate particle energy to momentum and use statistical mechanics to connect energy to temperature, yielding $T \propto 1/a$ for relativistic fluids and $T \propto 1/a^2$ for non-relativistic fluids.

Experimental results

Research questions

• RQ1 Why does the universe cool during expansion if it is thermodynamically adiabatic?
• RQ2 How does the momentum of cosmic particles evolve in an expanding spacetime according to general relativity?
• RQ3 What is the correct relativistic derivation of temperature scaling with the scale factor $a$?
• RQ4 Why do classical thermodynamic analogies fail to explain cosmic cooling?

Key findings

• The momentum of particles in the cosmic fluid decreases as $1/a$ due to the expansion of the universe, as derived from the geodesic equation in FRW spacetime.
• The relativistic energy of particles scales as $E \propto 1/a$, leading to a temperature scaling of $T \propto 1/a$ for relativistic fluids such as photons.
• For non-relativistic particles, energy scales as $E \propto 1/a^2$, resulting in a faster temperature decrease of $T \propto 1/a^2$.
• The cooling arises not from heat transfer or work against a boundary, but from the relativistic dynamics of thermal peculiar velocities in an expanding spacetime.
• The approach resolves the pedagogical issue of why classical thermodynamic explanations are insufficient for cosmic cooling.