A Relationship between the Comoving Particle Number and the Effective Cosmological Constant

TL;DR

This paper establishes a relationship between the final relativistic particle number in a comoving volume and the effective cosmological constant, using a new concept called 'effective static friction' in inflationary cosmology.

Contribution

It introduces a novel relationship linking particle creation to the cosmological constant and derives evolution equations for particle number during inflation.

Findings

Derived a formula connecting particle number and cosmological constant.

Established an evolution equation for particle number in the universe.

Proposed a new inflaton field equation incorporating particle creation parameters.

Abstract

In order to discuss and obtain the remaining inflaton potential, we introduced an idea called "effective static friction" in our last paper to balance the "force", $\frac{dV}{d\phi}|_{\phi=\phi(t_{rest})}$, of inflaton. According to this idea, we now discover that, after the course of particle creation, there will be a relationship between the final relativistic particle number inside an arbitrary chosen comoving volume $N_r(t_{rest})$ and the effective cosmological constant $\Lambda$ in our Universe. This relationship can be expressed as $N_r(t_{rest})=(\frac{\ell^2m_\phi^2\Lambda}{4\pi G\sigma^2(t_{rest})})^{3/2}$ when we employ the classical chaotic model, $V(\phi)=1/2m_{\phi}^2\phi^2$, and consider that $\phi$ comes to rest at $t_{rest}$. Moreover, we obtain an evolution equation for the particle number ($N_r(t)$) inside the comoving volume. Meanwhile, a new inflaton field equation which contains parameters of $N_r(t)$ and "particle creation coefficients" can also be found. Importantly, the results illustrate the fact that $\Lambda$ and $N_r$ are the results of probability.